Overview.

Mathematical optimization.

In terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. This is done by defining a sequence of value functions "V", "V",..., "V" taking "y" as an argument representing the state of the system at times "i" from 1 to "n". The definition of "V"("y") is the value obtained in state "y" at the last time "n". The values "V" at earlier times "i" = "n" −1, "n" − 2,..., 2, 1 can be found by working backwards, using a recursive relationship called the Bellman equation. For "i" = 2,..., "n", "V" at any state "y" is calculated from "V" by maximizing a simple function (usually the sum) of the gain from a decision at time "i" − 1 and the function "V" at the new state of the system if this decision is made. Since "V" has already been calculated for the needed states, the above operation yields "V" for those states. Finally, "V" at the initial state of the system is the value of the optimal solution. The optimal values of the decision variables can be recovered, one by one, by tracking back the calculations already performed.

Control theory.

In control theory, a typical problem is to find an admissible control formula_1 which causes the system formula_2 to follow an admissible trajectory formula_3 on a continuous time interval formula_4 that minimizes a cost function The solution to this problem is an optimal control law or policy formula_6, which produces an optimal trajectory formula_3 and an optimized loss function formula_8. The latter obeys the fundamental equation of dynamic programming: a partial differential equation known as the Hamilton–Jacobi–Bellman equation, in which formula_10 and formula_11. One finds the minimizing formula_12 in terms of formula_13, formula_14, and the unknown function formula_15 and then substitutes the result into the Hamilton–Jacobi–Bellman equation to get the partial differential equation to be solved with boundary condition formula_16. In practice, this generally requires numerical techniques for some discrete approximation to the exact optimization relationship.  Alternatively, the continuous process can be approximated by a discrete system, which leads to a following recurrence relation analog to the Hamilton–Jacobi–Bellman equation: at the formula_18-th stage of formula_19 equally spaced discrete time intervals, and where formula_20 and formula_21 denote discrete approximations to formula_22 and formula_23. This functional equation is known as the Bellman equation, which can be solved for an exact solution of the discrete approximation of the optimization equation.

Example from economics: Ramsey's problem of optimal saving.

In economics, the objective is generally to maximize (rather than minimize) some dynamic social welfare function. In Ramsey's problem, this function relates amounts of consumption to levels of utility. Loosely speaking, the planner faces the trade-off between contemporaneous consumption and future consumption (via investment in capital stock that is used in production), known as intertemporal choice. Future consumption is discounted at a constant rate formula_24. A discrete approximation to the transition equation of capital is given by where formula_26 is consumption, formula_18 is capital, and formula_22 is a production function satisfying the Inada conditions. An initial capital stock formula_29 is assumed.  Let formula_30 be consumption in period, and assume consumption yields utility formula_31 as long as the consumer lives. Assume the consumer is impatient, so that he discounts future utility by a factor each period, where formula_32 be capital in period. Assume initial capital is a given amount formula_33, and suppose that this period's capital and consumption determine next period's capital as formula_34, where is a positive constant and formula_35 subject to formula_36 for all formula_37  Written this way, the problem looks complicated, because it involves solving for all the choice variables formula_38. (The capital formula_39 is not a choice variable—the consumer's initial capital is taken as given.)  The dynamic programming approach to solve this problem involves breaking it apart into a sequence of smaller decisions. To do so, we define a sequence of "value functions" formula_40, for formula_41 which represent the value of having any amount of capital at each time. There is (by assumption) no utility from having capital after death, formula_42.  The value of any quantity of capital at any previous time can be calculated by backward induction using the Bellman equation. In this problem, for each formula_37, the Bellman equation is  This problem is much simpler than the one we wrote down before, because it involves only two decision variables, formula_30 and formula_47. Intuitively, instead of choosing his whole lifetime plan at birth, the consumer can take things one step at a time. At time, his current capital formula_48 is given, and he only needs to choose current consumption formula_30 and saving formula_47.  To actually solve this problem, we work backwards. For simplicity, the current level of capital is denoted as. formula_51 is already known, so using the Bellman equation once we can calculate formula_52, and so on until we get to formula_53, which is the "value" of the initial decision problem for the whole lifetime. In other words, once we know formula_54, we can calculate formula_55, which is the maximum of formula_56, where formula_57 is the choice variable and formula_58.  Working backwards, it can be shown that the value function at time formula_59 is  where each formula_61 is a constant, and the optimal amount to consume at time formula_59 is  which can be simplified to  We see that it is optimal to consume a larger fraction of current wealth as one gets older, finally consuming all remaining wealth in period, the last period of life.

Computer programming.

There are two key attributes that a problem must have in order for dynamic programming to be applicable: optimal substructure and overlapping sub-problems. If a problem can be solved by combining optimal solutions to "non-overlapping" sub-problems, the strategy is called "divide and conquer" instead. This is why merge sort and quick sort are not classified as dynamic programming problems.  "Optimal substructure" means that the solution to a given optimization problem can be obtained by the combination of optimal solutions to its sub-problems. Such optimal substructures are usually described by means of recursion. For example, given a graph "G=(V,E)", the shortest path "p" from a vertex "u" to a vertex "v" exhibits optimal substructure: take any intermediate vertex "w" on this shortest path "p". If "p" is truly the shortest path, then it can be split into sub-paths "p" from "u" to "w" and "p" from "w" to "v" such that these, in turn, are indeed the shortest paths between the corresponding vertices (by the simple cut-and-paste argument described in "Introduction to Algorithms"). Hence, one can easily formulate the solution for finding shortest paths in a recursive manner, which is what the Bellman–Ford algorithm or the Floyd–Warshall algorithm does.  "Overlapping" sub-problems means that the space of sub-problems must be small, that is, any recursive algorithm solving the problem should solve the same sub-problems over and over, rather than generating new sub-problems. For example, consider the recursive formulation for generating the Fibonacci series: "F" = "F" + "F", with base case "F" = "F" = 1. Then "F" = "F" + "F", and "F" = "F" + "F". Now "F" is being solved in the recursive sub-trees of both "F" as well as "F". Even though the total number of sub-problems is actually small (only 43 of them), we end up solving the same problems over and over if we adopt a naive recursive solution such as this. Dynamic programming takes account of this fact and solves each sub-problem only once.  This can be achieved in either of two ways:  Some programming languages can automatically memoize the result of a function call with a particular set of arguments, in order to speed up call-by-name evaluation (this mechanism is referred to as "call-by-need"). Some languages make it possible portably (e.g. Scheme, Common Lisp, Perl or D). Some languages have automatic memoization built in, such as tabled Prolog and J, which supports memoization with the "M." adverb. In any case, this is only possible for a referentially transparent function. Memoization is also encountered as an easily accessible design pattern within term-rewrite based languages such as Wolfram Language.

Bioinformatics.

Dynamic programming is widely used in bioinformatics for the tasks such as sequence alignment, protein folding, RNA structure prediction and protein-DNA binding. The first dynamic programming algorithms for protein-DNA binding were developed in the 1970s independently by Charles DeLisi in USA and Georgii Gurskii and Alexander Zasedatelev in USSR. Recently these algorithms have become very popular in bioinformatics and computational biology, particularly in the studies of nucleosome positioning and transcription factor binding.

Examples: Computer algorithms.

Dijkstra's algorithm for the shortest path problem.

From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.  In fact, Dijkstra's explanation of the logic behind the algorithm, namely is a paraphrasing of Bellman's famous Principle of Optimality in the context of the shortest path problem.

Fibonacci sequence.

Using dynamic programming in the calculation of the "n"th member of the Fibonacci sequence improves its performance greatly. Here is a naïve implementation, based directly on the mathematical definition:  Notice that if we call, say, codice_1, we produce a call tree that calls the function on the same value many different times:  In particular, codice_7 was calculated three times from scratch. In larger examples, many more values of codice_8, or "subproblems", are recalculated, leading to an exponential time algorithm.  Now, suppose we have a simple map object, "m", which maps each value of codice_8 that has already been calculated to its result, and we modify our function to use it and update it. The resulting function requires only O("n") time instead of exponential time (but requires O("n") space):  This technique of saving values that have already been calculated is called "memoization"; this is the top-down approach, since we first break the problem into subproblems and then calculate and store values.  In the bottom-up approach, we calculate the smaller values of codice_8 first, then build larger values from them. This method also uses O("n") time since it contains a loop that repeats n − 1 times, but it only takes constant (O(1)) space, in contrast to the top-down approach which requires O("n") space to store the map.  In both examples, we only calculate codice_7 one time, and then use it to calculate both codice_12 and codice_13, instead of computing it every time either of them is evaluated.  The above method actually takes formula_65 time for large n because addition of two integers with formula_66 bits each takes formula_66 time. (The "n" fibonacci number has formula_66 bits.) Also, there is a closed form for the Fibonacci sequence, known as Binet's formula, from which the formula_19-th term can be computed in approximately formula_70 time, which is more efficient than the above dynamic programming technique. However, the simple recurrence directly gives the matrix form that leads to an approximately formula_71 algorithm by fast matrix exponentiation.

A type of balanced 0–1 matrix.

Consider the problem of assigning values, either zero or one, to the positions of an matrix, with even, so that each row and each column contains exactly zeros and ones. We ask how many different assignments there are for a given formula_19. For example, when, four possible solutions are  There are at least three possible approaches: brute force, backtracking, and dynamic programming.  Brute force consists of checking all assignments of zeros and ones and counting those that have balanced rows and columns ( zeros and ones). As there are formula_74 possible assignments, this strategy is not practical except maybe up to formula_75.  Backtracking for this problem consists of choosing some order of the matrix elements and recursively placing ones or zeros, while checking that in every row and column the number of elements that have not been assigned plus the number of ones or zeros are both at least. While more sophisticated than brute force, this approach will visit every solution once, making it impractical for larger than six, since the number of solutions is already 116,963,796,250 for = 8, as we shall see.  Dynamic programming makes it possible to count the number of solutions without visiting them all. Imagine backtracking values for the first row – what information would we require about the remaining rows, in order to be able to accurately count the solutions obtained for each first row value? We consider boards, where, whose formula_18 rows contain formula_77 zeros and formula_77 ones. The function "f" to which memoization is applied maps vectors of "n" pairs of integers to the number of admissible boards (solutions). There is one pair for each column, and its two components indicate respectively the number of zeros and ones that have yet to be placed in that column. We seek the value of formula_79 (formula_19 arguments or one vector of formula_19 elements). The process of subproblem creation involves iterating over every one of formula_82 possible assignments for the top row of the board, and going through every column, subtracting one from the appropriate element of the pair for that column, depending on whether the assignment for the top row contained a zero or a one at that position. If any one of the results is negative, then the assignment is invalid and does not contribute to the set of solutions (recursion stops). Otherwise, we have an assignment for the top row of the board and recursively compute the number of solutions to the remaining board, adding the numbers of solutions for every admissible assignment of the top row and returning the sum, which is being memoized. The base case is the trivial subproblem, which occurs for a board. The number of solutions for this board is either zero or one, depending on whether the vector is a permutation of formula_83 and formula_84 pairs or not.  For example, in the first two boards shown above the sequences of vectors would be The number of solutions is  Links to the MAPLE implementation of the dynamic programming approach may be found among the external links.

Checkerboard.

Consider a checkerboard with "n" × "n" squares and a cost function codice_14 which returns a cost associated with square codice_15 (codice_16 being the row, codice_17 being the column). For instance (on a 5 × 5 checkerboard), Thus codice_18  Let us say there was a checker that could start at any square on the first rank (i.e., row) and you wanted to know the shortest path (the sum of the minimum costs at each visited rank) to get to the last rank; assuming the checker could move only diagonally left forward, diagonally right forward, or straight forward. That is, a checker on codice_19 can move to codice_20, codice_21 or codice_22. This problem exhibits optimal substructure. That is, the solution to the entire problem relies on solutions to subproblems. Let us define a function codice_23 as  Starting at rank codice_24 and descending to rank codice_25, we compute the value of this function for all the squares at each successive rank. Picking the square that holds the minimum value at each rank gives us the shortest path between rank codice_24 and rank codice_25.  The function codice_23 is equal to the minimum cost to get to any of the three squares below it (since those are the only squares that can reach it) plus codice_14. For instance:  Now, let us define codice_23 in somewhat more general terms:  The first line of this equation deals with a board modeled as squares indexed on codice_25 at the lowest bound and codice_24 at the highest bound. The second line specifies what happens at the last rank; providing a base case. The third line, the recursion, is the important part. It represents the codice_33 terms in the example. From this definition we can derive straightforward recursive code for codice_34. In the following pseudocode, codice_24 is the size of the board, codice_14 is the cost function, and codice_37 returns the minimum of a number of values:  This function only computes the path cost, not the actual path. We discuss the actual path below. This, like the Fibonacci-numbers example, is horribly slow because it too exhibits the overlapping sub-problems attribute. That is, it recomputes the same path costs over and over. However, we can compute it much faster in a bottom-up fashion if we store path costs in a two-dimensional array codice_38 rather than using a function. This avoids recomputation; all the values needed for array codice_38 are computed ahead of time only once. Precomputed values for codice_15 are simply looked-up whenever needed.  We also need to know what the actual shortest path is. To do this, we use another array codice_41; a "predecessor array". This array records the path to any square codice_42. The predecessor of codice_42 is modeled as an offset relative to the index (in codice_38) of the precomputed path cost of codice_42. To reconstruct the complete path, we lookup the predecessor of codice_42, then the predecessor of that square, then the predecessor of that square, and so on recursively, until we reach the starting square. Consider the following code:  Now the rest is a simple matter of finding the minimum and printing it.

Sequence alignment.

In genetics, sequence alignment is an important application where dynamic programming is essential. Typically, the problem consists of transforming one sequence into another using edit operations that replace, insert, or remove an element. Each operation has an associated cost, and the goal is to find the sequence of edits with the lowest total cost.  The problem can be stated naturally as a recursion, a sequence A is optimally edited into a sequence B by either:  The partial alignments can be tabulated in a matrix, where cell (i,j) contains the cost of the optimal alignment of A[1..i] to B[1..j]. The cost in cell (i,j) can be calculated by adding the cost of the relevant operations to the cost of its neighboring cells, and selecting the optimum.  Different variants exist, see Smith–Waterman algorithm and Needleman–Wunsch algorithm.

Tower of Hanoi puzzle.

The Tower of Hanoi or Towers of Hanoi is a mathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.  The objective of the puzzle is to move the entire stack to another rod, obeying the following rules:  The dynamic programming solution consists of solving the functional equation  where n denotes the number of disks to be moved, h denotes the home rod, t denotes the target rod, not(h,t) denotes the third rod (neither h nor t), ";" denotes concatenation, and  For n=1 the problem is trivial, namely S(1,h,t) = "move a disk from rod h to rod t" (there is only one disk left).  The number of moves required by this solution is 2 − 1. If the objective is to maximize the number of moves (without cycling) then the dynamic programming functional equation is slightly more complicated and 3 − 1 moves are required.

Egg dropping puzzle.

The following is a description of the instance of this famous puzzle involving N=2 eggs and a building with H=36 floors:  To derive a dynamic programming functional equation for this puzzle, let the state of the dynamic programming model be a pair s = (n,k), where  For instance, "s" = (2,6) indicates that two test eggs are available and 6 (consecutive) floors are yet to be tested. The initial state of the process is "s" = ("N","H") where "N" denotes the number of test eggs available at the commencement of the experiment. The process terminates either when there are no more test eggs ("n" = 0) or when "k" = 0, whichever occurs first. If termination occurs at state "s" = (0,"k") and "k" > 0, then the test failed.  Now, let  Then it can be shown that  with "W"("n",0) = 0 for all "n" > 0 and "W"(1,"k") = "k" for all "k". It is easy to solve this equation iteratively by systematically increasing the values of "n" and "k".

Faster DP solution using a different parametrization.

Notice that the above solution takes formula_88 time with a DP solution. This can be improved to formula_89 time by binary searching on the optimal formula_90 in the above recurrence, since formula_91 is increasing in formula_90 while formula_93 is decreasing in formula_90, thus a local minimum of formula_95 is a global minimum. Also, by storing the optimal formula_90 for each cell in the DP table and referring to its value for the previous cell, the optimal formula_90 for each cell can be found in constant time, improving it to formula_98 time. However, there is an even faster solution that involves a different parametrization of the problem:  Let formula_18 be the total number of floors such that the eggs break when dropped from the formula_18th floor (The example above is equivalent to taking formula_101).  Let formula_102 be the minimum floor from which the egg must be dropped to be broken.  Let formula_103 be the maximum number of values of formula_102 that are distinguishable using formula_13 tries and formula_19 eggs.  Then formula_107 for all formula_108.  Let formula_109 be the floor from which the first egg is dropped in the optimal strategy.  If the first egg broke, formula_102 is from formula_111 to formula_109 and distinguishable using at most formula_113 tries and formula_114 eggs.  If the first egg did not break, formula_102 is from formula_116 to formula_18 and distinguishable using formula_113 tries and formula_19 eggs.  Therefore, formula_120.  Then the problem is equivalent to finding the minimum formula_90 such that formula_122.  To do so, we could compute formula_123 in order of increasing formula_13, which would take formula_125 time.  Thus, if we separately handle the case of formula_126, the algorithm would take formula_127 time.  But the recurrence relation can in fact be solved, giving formula_128, which can be computed in formula_129 time using the identity formula_130 for all formula_131.  Since formula_132 for all formula_133, we can binary search on formula_13 to find formula_90, giving an formula_136 algorithm.

Matrix chain multiplication.

Matrix chain multiplication is a well-known example that demonstrates utility of dynamic programming. For example, engineering applications often have to multiply a chain of matrices. It is not surprising to find matrices of large dimensions, for example 100×100. Therefore, our task is to multiply matrices. As we know from basic linear algebra, matrix multiplication is not commutative, but is associative; and we can multiply only two matrices at a time. So, we can multiply this chain of matrices in many different ways, for example:  and so on. There are numerous ways to multiply this chain of matrices. They will all produce the same final result, however they will take more or less time to compute, based on which particular matrices are multiplied. If matrix A has dimensions m×n and matrix B has dimensions n×q, then matrix C=A×B will have dimensions m×q, and will require m*n*q scalar multiplications (using a simplistic matrix multiplication algorithm for purposes of illustration).  For example, let us multiply matrices A, B and C. Let us assume that their dimensions are m×n, n×p, and p×s, respectively. Matrix A×B×C will be of size m×s and can be calculated in two ways shown below:  Let us assume that m = 10, n = 100, p = 10 and s = 1000. So, the first way to multiply the chain will require 1,000,000 + 1,000,000 calculations. The second way will require only 10,000+100,000 calculations. Obviously, the second way is faster, and we should multiply the matrices using that arrangement of parenthesis.  Therefore, our conclusion is that the order of parenthesis matters, and that our task is to find the optimal order of parenthesis.  At this point, we have several choices, one of which is to design a dynamic programming algorithm that will split the problem into overlapping problems and calculate the optimal arrangement of parenthesis. The dynamic programming solution is presented below.  Let's call m[i,j] the minimum number of scalar multiplications needed to multiply a chain of matrices from matrix i to matrix j (i.e. A ×... × A, i.e. i<=j). We split the chain at some matrix k, such that i <= k < j, and try to find out which combination produces minimum m[i,j].  The formula is:  where "k" ranges from "i" to "j" − 1.  This formula can be coded as shown below, where input parameter "chain" is the chain of matrices, i.e. :  So far, we have calculated values for all possible, the minimum number of calculations to multiply a chain from matrix "i" to matrix "j", and we have recorded the corresponding "split point". For example, if we are multiplying chain, and it turns out that and, that means that the optimal placement of parenthesis for matrices 1 to 3 is and to multiply those matrices will require 100 scalar calculation.  This algorithm will produce "tables" "m"[, ] and "s"[, ] that will have entries for all possible values of i and j. The final solution for the entire chain is m[1, n], with corresponding split at s[1, n]. Unraveling the solution will be recursive, starting from the top and continuing until we reach the base case, i.e. multiplication of single matrices.  Therefore, the next step is to actually split the chain, i.e. to place the parenthesis where they (optimally) belong. For this purpose we could use the following algorithm:  Of course, this algorithm is not useful for actual multiplication. This algorithm is just a user-friendly way to see what the result looks like.  To actually multiply the matrices using the proper splits, we need the following algorithm:

History.

The term "dynamic programming" was originally used in the 1940s by Richard Bellman to describe the process of solving problems where one needs to find the best decisions one after another. By 1953, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions, and the field was thereafter recognized by the IEEE as a systems analysis and engineering topic. Bellman's contribution is remembered in the name of the Bellman equation, a central result of dynamic programming which restates an optimization problem in recursive form.  Bellman explains the reasoning behind the term "dynamic programming" in his autobiography, "Eye of the Hurricane: An Autobiography":  The word "dynamic" was chosen by Bellman to capture the time-varying aspect of the problems, and because it sounded impressive. The word "programming" referred to the use of the method to find an optimal "program", in the sense of a military schedule for training or logistics. This usage is the same as that in the phrases "linear programming" and "mathematical programming", a synonym for mathematical optimization.  The above explanation of the origin of the term is lacking. As Russell and Norvig in their book have written, referring to the above story: "This cannot be strictly true, because his first paper using the term (Bellman, 1952) appeared before Wilson became Secretary of Defense in 1953." Also, there is a comment in a speech by Harold J. Kushner, where he remembers Bellman. Quoting Kushner as he speaks of Bellman: "On the other hand, when I asked him the same question, he replied that he was trying to upstage Dantzig's linear programming by adding dynamic. Perhaps both motivations were true."

Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics.

Dynamische Programmierung ist eine Methode zum algorithmischen Lösen eines Optimierungsproblems durch Aufteilung in Teilprobleme und systematische Speicherung von Zwischenresultaten. Der Begriff wurde in den 1940er Jahren von dem amerikanischen Mathematiker Richard Bellman eingeführt, der diese Methode auf dem Gebiet der Regelungstheorie anwandte. In diesem Zusammenhang wird auch oft von "Bellmans Prinzip der dynamischen Programmierung" gesprochen.


Etymology.

The origin of the name Bengal ("Bangla" and "Bongo" in Bengali) is unknown. One theory suggests the word derives from "Bang", the name of a Dravidian tribe that settled the region around 1000BCE. The Bengali word "Bongo" might have been derived from the ancient kingdom of "Vanga" (or "Banga"). Although some early Sanskrit literature mentions the name "Vanga", the region's early history is obscure.  In 1947, at the end of British rule over the Indian subcontinent the Bengal Legislative Council and the Bengal Legislative Assembly voted on the Partition of Bengal along religious lines into two separate entities: West Bengal, which continued as an Indian state and East

History.

Ancient and classical period.

Stone Age tools dating back 20,000 years have been excavated in the state, showing human occupation 8,000 years earlier than scholars had thought. According to the Indian epic "Mahabharata" the region was part of the Vanga Kingdom. Several Vedic realms were present in the Bengal region, including Vanga, Rarh, Pundravardhana and the Suhma Kingdom. One of the earliest foreign references to Bengal is a mention by the Ancient Greeks around 100BCE of a land named Gangaridai located at the mouths of the Ganges. Bengal had overseas trade relations with Suvarnabhumi (Burma, Lower Thailand, the Lower Malay Peninsula and Sumatra). According to the Sri Lankan chronicle "Mahavamsa," Prince Vijaya (), a Vanga Kingdom prince, conquered Lanka (modern-day Sri Lanka) and named the country Sinhala Kingdom.  The kingdom of Magadha was formed in the 7thcentury BCE, consisting of the regions now comprising Bihar and Bengal. It was one of the four main kingdoms of India at the time of the lives of Mahavira, the principal figure of Jainism and Gautama Buddha, founder of Buddhism. It consisted of

Medieval and early modern periods.

Subsequent Muslim conquests helped spread Islam throughout the region. It was ruled by dynasties of the Bengal Sultanate and feudal lords under the Delhi Sultanate for the next few hundred years. The Bengal Sultanate was interrupted for twenty years by a Hindu uprising under Raja Ganesha. In the 16thcentury, Mughal general Islam Khan conquered

Colonial period.

Several European traders reached this area in the late 15thcentury. The British East India Company defeated Siraj ud-Daulah, the last independent Nawab, in the Battle of Plassey in 1757. The company gained the right to collect revenue in Bengal subah (province) in 1765 with the signing of the treaty between the East India company and the Mughal emperor following the Battle of Buxar in 1764. The Bengal Presidency was established in 1765; it later incorporated all British-controlled territory north of the Central Provinces (now Madhya Pradesh), from the mouths of the Ganges and the Brahmaputra to the Himalayas and the Punjab. The Bengal famine of 1770 claimed millions of lives due

Indian independence and afterwards.

When India gained independence in 1947, Bengal was partitioned along religious lines. The western part went to the Dominion of India and was named West Bengal. The eastern part went to the Dominion of Pakistan as a province called East Bengal (later renamed East Pakistan in 1956), becoming the independent nation of Bangladesh in 1971. In 1950 the Princely State of Cooch Behar merged with West Bengal. In 1955 the former French enclave of Chandannagar, which had passed into Indian control after 1950, was integrated into West Bengal; portions of Bihar were also subsequently merged with West Bengal. Both West and East Bengal experienced large influxes of refugees during and after partition in 1947. Refugee resettlement and related issues continued to play a significant role in the politics and socio-economic condition of the state. During the 1970s and 1980s, severe power shortages, strikes and a violent Naxalite movement damaged much of the state's infrastructure, leading to a period

Geography and climate.

West Bengal is on the eastern bottleneck of India, stretching from the Himalayas in the north to the Bay of Bengal in the south. The state has a total area of. The Darjeeling Himalayan hill region in the northern extreme of the state is a part of the eastern Himalayas mountain range. In this region is Sandakfu, which, at, is the highest peak in the state. The narrow Terai region separates the hills from the North Bengal plains, which in turn transitions into the Ganges delta towards the south. The Rarh region intervenes between the Ganges delta in the east and the western plateau and high lands. A small coastal region is in the extreme south, while the Sundarbans mangrove forests form a geographical landmark at the Ganges delta.  The main river in West Bengal is the Ganges, which divides into two branches. One branch enters Bangladesh as the "Padma", or "Pôdda", while the other flows through West Bengal as the Bhagirathi River and Hooghly River. The Farakka barrage over the Ganges feeds the Hooghly branch of the river by a feeder canal. Its water flow management has been a source of lingering dispute between India and Bangladesh. The

Flora and fauna.

The "India State of Forest Report 2017", recorded forest area in the state is, while in 2013, forest area was, which was 18.93% of the state's geographical area, compared to the then national average of 21.23%. Reserves and protected and unclassed forests constitute 59.4%, 31.8% and 8.9%, respectively, of forested areas, as of 2009. Part of the world's largest mangrove forest, the Sundarbans in southern West Bengal. From a phytogeographic viewpoint, the southern part of West Bengal can be divided into two regions: the Gangetic plain and the littoral mangrove forests of the Sundarbans. The alluvial soil of the Gangetic plain, combined with favourable rainfall, makes this region especially fertile. Much of the vegetation of the western part of the state has similar species composition with the plants of the Chota Nagpur plateau in the adjoining state of Jharkhand. The predominant commercial tree species is "Shorea robusta", commonly known as the sal tree. The coastal region of

Government and politics.

West Bengal is governed through a parliamentary system of representative democracy, a feature the state shares with other Indian states. Universal suffrage is granted to residents. There are two branches of government. The legislature, the West Bengal Legislative Assembly, consists of elected members and special office bearers such as the Speaker and Deputy Speaker, who are elected by the members. Assembly meetings are presided over by the Speaker or the Deputy Speaker in the Speaker's absence. The judiciary is composed of the Calcutta High Court and a system of lower courts. Executive authority is vested in the Council of Ministers headed by the Chief Minister although the titular head of government is the Governor. The Governor is the Head of State appointed by the President of India. The leader of the party or coalition with a majority in the Legislative Assembly is appointed as the Chief Minister

Districts.

As of 2017, West Bengal is divided into 23 districts.  Each district is governed by a district collector or district magistrate, appointed by either the Indian Administrative Service or the West Bengal Civil Service. Each district is subdivided into sub-divisions, governed by a Sub-Divisional Magistrate, and again into blocks.

Economy.

, West Bengal has the sixth-highest GSDP in India. GSDP at current prices (base 2004–2005) has increased from Rs 2,086.56 billion in 2004–05 to Rs 8,00,868 crores in 2014–2015, reaching Rs 10,21,000 crores in 2017–18. GSDP percent growth at current prices varied from a low of 10.3% in 2010–2011 to a high of 17.11% in 2013–2014. The growth rate was 13.35% in 2014–2015. The state's per capita income has lagged the all India average for over two decades. As of 2014–2015, per capita NSDP at current prices was Rs78,903. Per-capita NSDP growth rate at current prices varied from 9.4% in 2010–2011 to a high of 16.15% in 2013–2014. The growth rate was 12.62% in 2014–2015.  In 2015–2016, percentage share of Gross Value Added (GVA) at factor cost by economic activity at constant price (base year 2011–2012) was Agriculture-Forestry and Fishery—4.84%, Industry 18.51% and Services 66.65%. It has been observed that there has been a slow but steady decline in the percentage share of industry and agriculture over the years. Agriculture is the leading economic sector in West Bengal. Rice is the state's principal food crop. Rice, potato, jute, sugarcane and wheat are the state's top five crops. Tea is produced commercially in northern districts; the region is well known for Darjeeling and other high-quality teas. State industries are localised in the Kolkata region, the mineral-rich western highlands, and the Haldia Port region. The Durgapur-Asansol colliery belt is home to a number of steel plants. Important

Transport.

As of 2011, the total length of surface roads in West Bengal was over ; national highways comprise and state highways. As of 2006, the road density of the state was, higher than the national average of.  As of 2011, the total railway route length was around. Kolkata is the headquarters of three zones of the Indian Railways—Eastern Railway and South Eastern Railway and the Kolkata Metro, which is the newly formed 17thzone of the Indian Railways. The Northeast Frontier Railway (NFR) serves the northern parts of the state. The Kolkata metro is the country's first underground railway. The Darjeeling Himalayan Railway, part of NFR, is a UNESCO World Heritage Site.  Netaji Subhas Chandra Bose International Airport at Dum Dum, Kolkata, is the state's largest airport. Bagdogra Airport near Siliguri is a customs airport that offers international

Demographics.

According to the provisional results of the 2011 national census, West Bengal is the fourth-most-populous state in India with a population of 91,347,736 (7.55% of India's population). Bengalis, consisting of Bengali Hindus, Bengali Muslims, Bengali Christians and a few Bengali Buddhists, comprise the majority of the population. Marwari, Maithil and Bhojpuri speakers are scattered throughout the state; various indigenous ethnic Buddhist communities such as the Sherpas, Bhutias, Lepchas, Tamangs, Yolmos and ethnic Tibetans can be found in the Darjeeling Himalayan hill region. Native Magahi speakers are found in Malda district. Surjapuri, a language considered to be a mix of Maithili and Bengali, is spoken across northern parts of the state. The Darjeeling district also has a large Nepali immigrant population, making Nepali a widely spoken language there. West Bengal is also home to indigenous tribal Adivasis such as: Santhal, Munda, Oraon, Bhumij, Lodha, Kol and Toto tribe. There are a small number of ethnic minorities primarily in the state capital, including : Chinese, Tamils, Maharashtrians, Odias, Assamese, Malayalis, Gujaratis, Anglo-Indians, Armenians, Jews, Punjabis and Parsis. India's sole Chinatown is in eastern Kolkata.  The state's official languages are Bengali and English; Nepali has additional official status in the three subdivisions of Darjeeling district. In 2012, the state government passed a bill granting additional official status to Hindi, Odia, Punjabi, Santali and Urdu in areas where speakers exceed 10% of the population. In 2019, another bill was passed by the government to include Kamtapuri, Kurmali and Rajbanshi as additional official languages in blocks, divisions or districts where the speakers exceed 10% of the population. As of 2001, in decreasing order of number of speakers, the languages of the state are: Bengali (85.27%), Hindi (7.17%), Santali (2.80%), Urdu (2.06%), and

Culture.

Literature.

The Bengali language boasts a rich literary heritage it shares with neighbouring Bangladesh. West Bengal has a long tradition of folk literature, evidenced by the "Charyapada", a collection of Buddhist mystic songs dating back to the 10th and 11thcenturies; "Mangalkavya", a collection of Hindu narrative poetry composed around the 13thcentury; "Shreekrishna Kirtana", a pastoral Vaishnava drama in verse composed by Boru Chandidas; "Thakurmar Jhuli", a collection of Bengali folk and fairy tales compiled by Dakshinaranjan Mitra Majumder; and stories of Gopal Bhar, a court jester in medieval Bengal. In the 19th and 20thcenturies, Bengali literature was modernised in the works of authors such as Bankim Chandra Chattopadhyay, whose works marked a

Music and dance.

A notable music tradition is the Baul music, practised by the Bauls, a sect of mystic minstrels. Other folk music forms include Gombhira and Bhawaiya. Folk music in West Bengal is often accompanied by the ektara, a one-stringed instrument. Shyama Sangeet is a genre of devotional songs, praising the Hindu goddess Kali; kirtan is devotional group songs dedicated to the god Krishna. Like other states in northern India, West

Films.

West Bengali films are shot mostly in studios in the Kolkata neighbourhood of Tollygunge; the name "Tollywood" (similar to Hollywood and Bollywood) is derived from that name. The Bengali film industry is well known for its art films, and has produced acclaimed directors like Satyajit Ray who is widely

Fine arts.

There are significant examples of fine arts in Bengal from earlier times, including the terracotta art of Hindu temples and the Kalighat paintings. Bengal has been in the vanguard of modernism in fine arts. Abanindranath Tagore, called the father of modern Indian art, started the Bengal School of Art,

Reformist heritage.

The capital, Kolkata, was the workplace of several social reformers, including Raja Ram Mohan Roy, Iswar Chandra Vidyasagar and Swami Vivekananda. Their social reforms eventually led

Cuisine.

Rice and fish are traditional favourite foods, leading to a saying in Bengali, ""machhe bhate bangali"", that translates as "fish and rice make a Bengali". Bengal's vast repertoire of fish-based dishes includes hilsa preparations, a favourite among Bengalis. There are numerous ways of cooking fish depending on its texture, size, fat content and bones. Most of the people also consume eggs, chicken, mutton, and shrimp. "Panta bhat" (rice soaked overnight in water)

Clothing.

Bengali women commonly wear the "sari", often distinctly designed according to local cultural customs. In urban areas, many women and men wear western attire. Among men, western dress has greater acceptance. Particularly on cultural occasions, men also wear traditional costumes such as the "panjabi" with "dhuti"

Festivals.

Durga Puja is the biggest, most popular and widely celebrated festival in West Bengal. The five-day-long colourful Hindu festival includes intense celebration across the state. Pandals are erected in various cities, towns, and villages throughout West Bengal. The city of Kolkata undergoes a transformation during Durga Puja. It is decked up in lighting decorations and thousands of colourful pandals are set up where effigies of the goddess Durga and her four children are displayed and worshipped. The idols of the goddess are brought in from Kumortuli, where idol-makers

Education.

West Bengal schools are run by the state government or private organisations, including religious institutions. Instruction is mainly in English or Bengali, though Urdu is also used, especially in Central Kolkata. Secondary schools are affiliated with the Council for the Indian School Certificate Examinations (CISCE), the Central Board for Secondary Education (CBSE), the National Institute of Open School (NIOS), West Bengal Board of Secondary Education, or the West Bengal Board of Madrasah Education.  As of 2016 85% of children within the 6 to 17-year age group attend school (86% do so in urban areas and 84% in rural areas). School attendance is almost universal among the 6 to 14-year age group then drops to 70% with the 15 to 17-year age group. There is a gender disparity in school attendance in the 6 to 14-year age group, more girls than boys are attending school. In Bengal, 71% of women aged 15–49 years and 81% of men aged 15–49 years are literate. Only 14% of women aged 15–49 years in West Bengal have completed 12 or more years of schooling, compared with 22% of men. 22% of women and 14% of men age 15–49 years have never attended school. Some of the notable schools in the city are: Ramakrishna Mission Narendrapur, Baranagore Ramakrishna Mission, Sister Nivedita Girls' School, Hindu School, Hare School, La Martiniere Calcutta, Calcutta Boys' School, St. James' School (Kolkata), South Point School, St. Xavier's Collegiate School, and Loreto House, Loreto Convent, Asansol some of which rank amongst the best schools in the country. Many of the schools in Kolkata and Darjeeling are colonial-era establishments housed in buildings that are exemplars of neo-classical architecture. Darjeeling's schools include: St. Paul's, St. Joseph's North Point, Goethals Memorial School, and Dow Hill in Kurseong.  West Bengal has eighteen universities. Kolkata has played a pioneering role in the development of the modern education system in India. It was the gateway to the revolution of European education during the British Raj. Sir William Jones established the Asiatic Society in 1794 to promote oriental studies. People such as Ram Mohan Roy, David Hare, Ishwar Chandra Vidyasagar, Alexander Duff and William Carey played leading roles in setting up modern schools and colleges in

Media.

In 2005 West Bengal had 505 published newspapers, of which 389 were in Bengali. "Ananda Bazar Patrika", published in Kolkata with 1,277,801 daily copies, has the largest circulation for a single-edition, regional language newspaper in India. Other major Bengali newspapers are: "Bartaman", "Sangbad Pratidin", "Aajkaal", "Jago Bangla", "Uttarbanga Sambad" and "Ganashakti". Major English language newspapers include "The Telegraph", "The Times of India", "Hindustan Times", "The Hindu", "The Statesman", "The Indian Express" and "Asian Age". Some prominent financial dailies such as: "The Economic Times", "Financial Express", "Business Line" and "Business Standard" are widely circulated.

Sports.

Cricket and association football are popular sports in the state. West Bengal, unlike most other states of India, is noted for its passion and patronage of football. Kolkata is one of the major centres for football in India and houses top national clubs such as Mohun Bagan Athletic Club, East Bengal Club and Mohammedan Sporting Club.  West Bengal has several large stadiums. Eden Gardens was one of only two 100,000-seat cricket stadiums in the world; renovations before the 2011 Cricket World Cup reduced the capacity to 66,000. The stadium is the home to various cricket teams such as the Kolkata Knight Riders, the Bengal cricket team and the East Zone. The 1987 Cricket World Cup final was hosted in Eden Gardens. The Calcutta Cricket and Football Club is the second-oldest cricket club in the world.  Vivekananda Yuba Bharati Krirangan (VYBK), is a multipurpose stadium in Kolkata, with a current capacity of 85,000. It is the largest stadium in India by seating capacity. Before its renovation in 2011, it was the second largest football stadium in the world, having a seating capacity of 120,000. It has hosted many national and international sporting events like the SAF Games of 1987 and the 2011 FIFA friendly football match between Argentina and Venezuela featuring Lionel Messi. In 2008 legendary German goalkeeper, Oliver Kahn played his farewell match on this ground. The stadium hosted the final match of the 2017 FIFA U-17 World Cup. Notable sports persons from West Bengal include former Indian national cricket team captain Sourav Ganguly, Pankaj Roy, Olympic tennis bronze medallist Leander Paes and chess grand master Dibyendu Barua.

West Bengal () is a state in the eastern region of India along the Bay of Bengal. With over 91million inhabitants (as of 2011), it is India's fourth-most populous state. West Bengal is also the world's seventh-most populous subnational entity. West Bengal is the thirteenth-largest Indian state, with an area of. Part of the ethno-linguistic Bengal region of the Indian subcontinent, it borders Bangladesh in the east, and Nepal and Bhutan in the north. It also borders the Indian states of Odisha, Jharkhand, Bihar, Sikkim and Assam. The state capital is Kolkata (Calcutta) the seventh-largest city in India, and center of the third-largest metropolitan area in the country. West Bengal includes the Darjeeling Himalayan hill region, the Ganges delta, the Rarh region and the coastal Sundarbans. The main ethnic group is the Bengalis, with Bengali Hindus forming the demographic majority.

Westbengalen (bengalisch:,, "Pashchimbanga"; Englisch: "West Bengal") ist ein indischer Bundesstaat mit einer Fläche von 88.752 km2 und 91 Millionen Einwohnern (Volkszählung 2011). Die Hauptstadt Westbengalens ist Kolkata (Kalkutta) im Süden des Bundesstaates. Die vorherrschende Sprache des Bundesstaates ist Bengalisch.


Early history of the discipline.

In late-nineteenth-century Germany, scholars at a number of universities, led by Gustav von Schmoller, developed the historical school of economic history. It argued that there were no universal truths in history, emphasizing the importance of historical context without quantitative analysis. This historical approach dominated German and French scholarship for most of the 20th century. The historical school of economics included other economists such as Max Weber and Joseph Schumpeter who reasoned that careful analysis of human actions, cultural norms, historical context, and mathematical support was key to historical analysis. The approach was spread to Great Britain by William Ashley (University of Oxford) and dominated British economic history for much of the 20th century. Britain's first professor in the subject was George Unwin at the University of Manchester. Meanwhile, in France, economic history was heavily influenced by the Annales School from the early 20th century to the present. It exerts a worldwide influence through its journal "Annales. Histoire, Sciences Sociales."  Treating economic history as a discrete academic discipline has been a contentious issue for many years. Academics at the London School of Economics and the University of Cambridge had numerous disputes over the separation of economics and economic history in the interwar era. Cambridge economists believed that pure economics involved a component of economic history and that the two were inseparably entangled. Those at the LSE believed that economic history warranted its own courses, research agenda and academic chair separated from mainstream economics. In the initial period of the subject's development, the LSE position of separating economic history from economics won out. Many universities in the UK developed independent programmes in economic history rooted in the LSE model. Indeed, the Economic History Society had its inauguration at LSE in 1926 and the University of Cambridge eventually established its own economic history programme.  In the United States, the field of economic history was largely subsumed into other fields of economics following the cliometric revolution of the 1960s. To many it became seen as a form of applied economics rather than a stand-alone discipline. Cliometrics, also known as the New Economic History, refers to the systematic use of economic theory and econometric techniques to the study of economic history. The term was originally coined by Jonathan R. T. Hughes and Stanley Reiter and refers to Clio, who was the muse of history and heroic poetry in Greek mythology. One of the most famous cliometric economic historians is Douglass North, who argued that it is the task of economic history to elucidate the historical dimensions of economies through time. Cliometricians argue their approach is necessary because the application of theory is crucial in writing solid economic history, while historians generally oppose this view warning against the risk of generating anachronisms.  Early cliometrics was a type of counterfactual history. However, counterfactualism was not its distinctive feature; it combines neoclassical economics with quantitative methods in order to explain human choices based on constraints. Some have argued that cliometrics had its heyday in the 1960s and 1970s and that it is now neglected by economists and historians. In response to North and Robert Fogel's Nobel Memorial Prize in Economics in 1993, Harvard University economist Claudia Goldin argued that:economic history is not a handmaiden of economics but a distinct field of scholarship. Economic history was a scholarly discipline long before it became cliometrics. Its practitioners were economists and historians studying the histories of economies... The new economic history, or cliometrics, formalized economic history in a manner similar to the injection of mathematical models and statistics into the rest of economics.The relationship between economic history, economics and history has long been the subject of intense discussion, and the debates of recent years echo those of early contributors. There has long been a school of thought among economic historians that splits economic history—the study of how economic phenomena evolved in the past—from historical economics—testing the generality of economic theory using historical episodes. US economic historian Charles P. Kindleberger explained this position in his 1990 book "Historical Economics: Art or Science?". Economic historian Robert Skidelsky (University of Cambridge) argued that economic theory often employs ahistorical models and methodologies that do not take into account historical context. Yale University economist Irving Fisher already wrote in 1933 on the relationship between economics and economic history in his "Debt-Deflation Theory of Great Depressions":  The study of dis-equilibrium may proceed in either of two ways. We may take as our unit for study an actual historical case of great dis-equilibrium, such as, say, the panic of 1873; or we may take as our unit for study any constituent tendency, such as, say, deflation, and discover its general laws, relations to, and combinations with, other tendencies. The former study revolves around events, or facts; the latter, around tendencies. The former is primarily economic history; the latter is primarily economic science. Both sorts of studies are proper and important. Each helps the other. The panic of 1873 can only be understood in light of the various tendencies involved—deflation and other; and deflation can only be understood in the light of various historical manifestations—1873 and other.

Scope and focus of the discipline today.

The past three decades have witnessed the widespread closure of separate economic history departments and programmes in the UK and the integration of the discipline into either history or economics departments. Only the LSE retains a separate economic history department and stand-alone undergraduate and graduate programme in economic history. Cambridge, Glasgow, the LSE, Oxford and Queen's University Belfast together train the vast majority of economic historians coming through the British higher education system today, but do so as part of economics or history degrees. Meanwhile, there have never been specialist economic history graduate programs at universities anywhere in the US. However, economic history remains a special field component of leading economics PhD programs, including University of California, Berkeley, Harvard University, Northwestern University, Princeton University, the University of Chicago and Yale University.  Despite the pessimistic view on the state of the discipline espoused by many of its practitioners, economic history remains an active field of social scientific inquiry. Indeed, it has seen something of a resurgence in interest since 2000, perhaps driven by research conducted at universities in continental Europe rather than the UK and the US.  Part of the growth in economic history is driven by the continued interest in big policy-relevant questions on the history of economic growth and development. MIT economist Peter Temin noted that development economics is intricately connected with economic history, as it explores the growth of economies with different technologies, innovations, and institutions. Studying economic growth has been popular for years among economists and historians who have sought to understand why some economies have grown faster than others. Some of the early texts in the field include Walt Whitman Rostow's "The Stages of Economic Growth: A Non-Communist Manifesto" (1971) which described how advanced economies grow after overcoming certain hurdles and advancing to the next stage in development. Another economic historian, Alexander Gerschenkron, complicated this theory with works on how economies develop in non-Western countries, as discussed in "Economic Backwardness in Historical Perspective: A Book of Essays" (1962). A more recent work is Daron Acemoglu and James A. Robinson's "" (2012) which pioneered a new field of persistence studies, emphasizing the path-dependent stages of growth. Other notable books on the topic include Kenneth Pomeranz's "The Great Divergence: China, Europe, and the Making of the Modern World Economy" (2000) and David S. Landes's "The Wealth and Poverty of Nations: Why Some are So Rich and Some So Poor" (1998).  In recent decades, and notably since the global financial crisis of 2007–2008, scholars have recently become more interested in a field which may be called "new" new economic history. Scholars have tended to move away from narrowly quantitative studies toward institutional, social, and cultural history affecting the evolution of economies. Columbia University economist Charles Calomiris argued that this new field showed 'how historical (path-dependent) processes governed changes in institutions and markets.' However, this trend has been criticized, most forcefully by Francesco Boldizzoni, as a form of economic imperialism "extending the neoclassical explanatory model to the realm of social relations."  Conversely, economists in other specializations have started to write a new kind of economic history which makes use of historical data to understand the present day. A major development in this genre was the publication of Thomas Piketty's "Capital in the Twenty-First Century" (2013). The book described the rise in wealth and income inequality since the 18th century, arguing that large concentrations of wealth lead to social and economic instability. Piketty also advocated a system of global progressive wealth taxes to correct rising inequality. The book was selected as a "New York Times" best seller and received numerous awards. The book was well received by some of the world's major economists, including Paul Krugman, Robert Solow, and Ben Bernanke. Books in response to Piketty's book include "After Piketty: The Agenda for Economics and Inequality", by Heather Boushey, J. Bradford DeLong, and Marshall Steinbaum (eds.) (2017), "Pocket Piketty" by Jesper Roine (2017), and "Anti-Piketty: Capital for the 21st Century", by Jean-Philippe Delsol, Nicolas Lecaussin, Emmanuel Martin (2017). One economist noted that Piketty's book was "Nobel-Prize worthy" and had changed the global discussion on how economic historians study inequality. It has also sparked new conversations in the disciplines of public policy.  In addition to the mainstream in economic history, there is a parallel development in the field influenced by Karl Marx and Marxian economics. Marx used historical analysis to interpret the role of class and class as a central issue in history. He debated with the "classical" economists (a term he coined), including Adam Smith and David Ricardo. In turn, Marx's legacy in economic history has been to critique the findings of neoclassical economists. Marxist analysis also confronts economic determinism, the theory that economic relationships are the foundation of political and societal institutions. Marx abstracted the idea of a "capitalist mode of production" as a way of identifying the transition from feudalism to capitalism. This has influenced some scholars, such as Maurice Dobb, to argue that feudalism declined because of peasants' struggles for freedom and the growing inefficiency of feudalism as a system of production. In turn, in what was later coined the Brenner debate, Paul Sweezy, a Marxian economist, challenged Dob"s definition of feudalism and its focus only on western Europe."

History of capitalism.

A new field calling itself the "history of capitalism" has emerged in US history departments since about the year 2000. It includes many topics traditionally associated with the field of economic history, such as insurance, banking and regulation, the political dimension of business, and the impact of capitalism on the middle classes, the poor and women and minorities. The field has particularly focused on the contribution of slavery to the rise of the US economy in the nineteenth century. The field utilizes the existing research of business history, but has sought to make it more relevant to the concerns of history departments in the United States, including by having limited or no discussion of individual business enterprises.  Scholars have critiqued the history of capitalism because it does not focus on systems of production, circulation, and distribution. Some have criticized its lack of social scientific methods and its ideological biases. As a result, a new academic journal, "Capitalism: A Journal of History and Economics", was founded at the University of Pennsylvania under the direction of Marc Flandreau (University of Pennsylvania), Julia Ott (The New School, New York) and Francesca Trivellato (Institute for Advanced Study, Princeton) to widen the scope of the field. The journal's goal is to bring together "historians and social scientists interested in the material and intellectual aspects of modern economic life." Historians of capitalism have countered these critiques, citing the issues with economic history. As University of Chicago professor of history Jonathan Levy states, "modern economic history began with industrialization and urbanization, and, even then, environmental considerations were subsidiary, if not nonexistent."

Academic journals and societies.

The first journal specializing in the field of economic history was "The Economic History Review", founded in 1927, as the main publication of the Economic History Society. The first journal featured a publication by Professor Sir William Ashley, the first Professor of Economic History in the English-speaking world, who described the emerging field of economic history. The discipline existed alongside long-standing fields such as political history, religious history, and military history as one that focused on humans' interactions with 'visible happenings'. He continued, '[economic history] primarily and unless expressly extended, the history of actual human practice with respect to the material basis of life. The visible happenings with regard-to use the old formula-to "the production, distribution, and consumption of wealth" form our wide enough field'.  Later, the Economic History Association established another academic journal, "The Journal of Economic History", in 1941 as a way of expanding the discipline in the United States. The first president of the Economic History Association, Edwin F. Gay, described the aim of economic history was to provide new perspectives in the economics and history disciplines: 'An adequate equipment with two skills, that of the historian and the economist, is not easily acquired, but experience shows that it is both necessary and possible'. Other related academic journals have broadened the lens with which economic history is studied. These interdisciplinary journals include the "Business History Review", "European Review of Economic History", "Enterprise and Society", and "Financial History Review".  The "International Economic History Association", an association of close to 50 member organizations, recognizes some of the major academic organizations dedicated to study of economic history: the Business History Conference, Economic History Association, Economic History Society, European Association of Business Historians, and the International Social History Association.

Economic history is the academic study of economies or economic events of the past. Research is conducted using a combination of historical methods, statistical methods and the application of economic theory to historical situations and institutions. The field can encompass a wide variety of topics, including equality, finance, technology, labor, and business. It emphasizes historicizing the economy itself, analyzing it as a dynamic force and attempting to provide insights into the way it is structured and conceived.

Die Wirtschaftsgeschichte ist eine Brückendisziplin zwischen den Wirtschaftswissenschaften und der Geschichtswissenschaft. Je nach Betrachtungsweise können die Volks- und Betriebswirtschaftslehre sowie die Geschichtswissenschaft der Wirtschaftsgeschichte als Hilfswissenschaften dienen. Oder aber die Wirtschaftsgeschichte wird zur Hilfswissenschaft der erstgenannten Fächer, beispielsweise zur Untersuchung der epochenübergreifenden Gültigkeit von Theorien. Die Wirtschaftsgeschichte untersucht die Entwicklung, die Organisation und die Handlungslogiken von bzw. in Volkswirtschaften, Branchen, Unternehmen, Akteuren und Akteursgruppen in historischer Perspektive.


History.

Its etymology is uncertain. It may derive from "newie", which is attested in U.S. and Australian sources of the 1850s, meaning a neophyte in a place or situation; alternatively, it may derive from the British public school slang "new boy" or "new blood", which is attributed to the same era and was applied to a schoolboy in his first term.  In the 1960s and 1970s the term "newbie" had a limited usage among U.S. troops in the Vietnam War as a slang term for a new man in a unit.  Another use of the term newbee was the moniker given to new U.S. Navy recruit students attending Basic Electricity and Electronics school by more senior students, a requisite course prior to enrollment in the A-school course at Naval Air Technical Training Center, Millington, Tennessee.  Its earliest known usage on the internet may have been on the Usenet newsgroup "talk.bizarre". The term is believed to have entered online usage by 1981.  Coming from an oral tradition, the term has various spellings. Among alternative forms are "newby", "nubie", and "newbee" (e.g. "Los Angeles Times" of August 1985: "It had to do with newbees. I could be wrong on the spelling, but newbees are the rookies among the Blue Angels.").  In 2009, "noob" was among candidates for the one-millionth English word selection by the Global Language Monitor.

Connotations of variants.

Different spellings can have quite different connotations; so in some contexts a "newb" refers to a beginner who is willing to learn; while a "noob", refers disparagingly to an inexperienced or under-talented hacker or gamer who lacks the determination to learn.

Newbie, newb, noob, nub, or n00b is a slang term for a novice or newcomer, or somebody inexperienced in a profession or activity. Contemporary use can particularly refer to a beginner or new user of computers, often concerning internet activity, such as online gaming or Linux use. Depending on the context and spelling variant used, the term can have derogatory connotations (and be used as a term of abuse in internet-based games)—but is also often used for descriptive purposes only, without any value judgment.

Ein Neuling ist eine Person, die sich in ein Sachgebiet einarbeitet oder neu in eine Gemeinschaft aufgenommen wird und sich noch nicht so gut auskennt wie Personen, die schon länger damit Kontakt haben; andere Ausdrücke sind ‚Anfänger‘ und ‚Neueinsteiger‘.


Definition as locus of points.

An ellipse can be defined geometrically as a set or locus of points in the Euclidean plane:  The midpoint formula_11 of the line segment joining the foci is called the "center" of the ellipse. The line through the foci is called the "major axis", and the line perpendicular to it through the center is the "minor axis". The major axis intersects the ellipse at the "vertex" points formula_12, which have distance formula_13 to the center. The distance formula_14 of

In Cartesian coordinates.

Standard equation.

The standard form of an ellipse in Cartesian coordinates assumes that the origin is the center of the ellipse, the "x"-axis is the major axis, and:  For an arbitrary point formula_29 the distance to the focus formula_30 is formula_31 and to the other focus formula_32. Hence the point formula_33 is on the ellipse whenever:  Removing

Parameters.

Semi-major and semi-minor axes.

Throughout this article formula_13 is the semi-major axis, i.e. formula_44 In general the canonical ellipse equation formula_45 may have formula_46 (and hence the ellipse would be

Linear eccentricity.

This is the distance

Eccentricity.

The eccentricity can be expressed as:  assuming formula_54

Semi-latus rectum.

The length of the chord through one focus, perpendicular to the major axis, is called the "latus rectum". One half of it is the "semi-latus rectum" formula_56. A calculation shows:  The semi-latus rectum formula_56 is equal to the radius of curvature at the vertices (see section curvature).

Tangent.

An arbitrary line formula_59 intersects an ellipse at 0, 1, or 2 points, respectively called an "exterior line", "tangent" and "secant". Through any point of an ellipse there is a unique tangent. The tangent at a point formula_60 of the ellipse formula_61 has the coordinate equation:  A vector parametric equation of the tangent is:  Proof:

Shifted ellipse.

If the standard ellipse is shifted to have center formula_88,

General ellipse.

In analytic geometry, the ellipse is defined as a quadric: the set of points formula_90 of the Cartesian plane that, in non-degenerate cases, satisfy the implicit equation  provided formula_92  To distinguish the degenerate cases from the non-degenerate case, let "∆" be the determinant  Then the ellipse is a non-degenerate real ellipse if and only if "C∆" < 0. If

Parametric representation.

Standard parametric representation.

Using trigonometric functions, a parametric representation of the standard ellipse formula_103 is:  The parameter "t" (called the

Rational representation.

With the substitution formula_106 and trigonometric formulae one obtains  and the "rational" parametric equation of an ellipse  which covers any point of the ellipse formula_61 except the

Tangent slope as parameter.

A parametric representation, which uses the slope formula_114 of the tangent at a point of the ellipse can be obtained from the derivative of the standard representation formula_115:  With help of trigonometric formulae one obtains:  Replacing formula_118 and formula_119 of the standard representation yields:  Here formula_114 is the slope of the tangent at the corresponding ellipse

General ellipse.

Another definition of an ellipse uses affine transformations:  An affine transformation of the Euclidean plane has the form formula_131, where formula_132 is a regular matrix (with non-zero determinant) and formula_133 is an arbitrary vector. If formula_134 are the column vectors of the matrix formula_132, the unit circle formula_136, formula_137, is mapped onto the ellipse:  Here formula_133 is the center and formula_140 are the directions of two conjugate diameters, in general

Polar forms.

Polar form relative to center.

In polar coordinates, with the origin at the center of the

Polar form relative to focus.

If instead we use polar coordinates with the origin at one focus, with the angular coordinate formula_158 still measured from the major axis, the ellipse's equation is  where the sign in the denominator is negative if the reference direction formula_158 points towards the center

Eccentricity and the directrix property.

Each of the two lines parallel to the minor axis, and at a distance of formula_165 from it, is called a "directrix" of the ellipse (see diagram).  The proof for the pair formula_168 follows from the fact that formula_169 and formula_170 satisfy the equation  The second case is proven analogously.  The converse is also true and can be used to define an ellipse (in a manner similar to the definition of a parabola):  The choice formula_179, which is the eccentricity of a circle, is not

Focus-to-focus reflection property.

An ellipse possesses the following property:  Because the tangent is perpendicular to the normal, the statement is true for the tangent and the supplementary angle of the angle between the lines to the foci (see diagram), too.  Let formula_207 be the point on the line formula_208 with the distance formula_6 to the focus formula_19, formula_13 is the semi-major axis of the ellipse. Let line formula_212 be the bisector of the supplementary angle to the angle between

Conjugate diameters.

A circle has the following property:  An affine transformation preserves parallelism and midpoints of line segments, so this property is true for any ellipse. (Note that the parallel chords and the diameter are no longer orthogonal.)  Two diameters formula_226 of an ellipse are "conjugate" if the midpoints of chords parallel to formula_227 lie on formula_228  From the diagram one finds:  Conjugate diameters in an ellipse generalize orthogonal diameters in a circle.  In the parametric equation for a general ellipse given above,  any pair of points formula_234 belong to a diameter, and the pair formula_235 belong to its conjugate diameter.

Theorem of Apollonios on conjugate diameters.

For an ellipse with semi-axes formula_196 the following is true:  Let the ellipse be in the canonical form with parametric equation  The two points formula_244 are on

Orthogonal tangents.

For the ellipse formula_251 the intersection points of "orthogonal" tangents lie on the circle formula_252.

Drawing ellipses.

Ellipses appear in descriptive geometry as images (parallel or central projection) of circles. There exist various tools to draw an ellipse. Computers provide the fastest and most accurate method for drawing an ellipse. However, technical tools ("ellipsographs") to draw an ellipse without a computer exist. The principle of ellipsographs were known to Greek mathematicians such as Archimedes and Proklos.  If there is no ellipsograph available, one can draw an ellipse using an approximation by the four osculating circles at the vertices.  For any method described below, knowledge of the axes and the semi-axes is necessary (or equivalently: the foci and the semi-major axis). If this presumption is not fulfilled one has to know at least two conjugate diameters. With help of Rytz's construction the axes and semi-axes can be retrieved.

de La Hire's point construction.

The following construction of single points of an ellipse is due

Pins-and-string method.

The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string, and a pencil. In this method, pins are pushed into the paper at two points, which become the ellipse's

Paper strip methods.

The two following methods rely on the parametric representation (see section "parametric representation", above):  This representation can be modeled technically by two simple methods. In both cases center, the axes and semi axes formula_260 have to be known.  The first method starts with  The point, where the semi axes meet is marked by formula_7. If the strip slides with both ends on the axes of the desired ellipse, then point P traces the ellipse. For the proof one shows that point formula_7 has the parametric representation formula_253, where parameter formula_265 is the angle of the slope of the paper strip.  A technical realization of the motion of the paper strip can be achieved by a Tusi couple (see animation). The device is able to draw any ellipse with a "fixed" sum formula_261, which is the radius of the large circle. This restriction may be a disadvantage in real

Approximation by osculating circles.

From "Metric properties" below, one obtains:  The diagram shows an easy way to find the centers of curvature formula_283 at vertex formula_284 and

Steiner generation.

The following method to construct single points of an ellipse relies on the Steiner generation of a conic section:  For the generation of points of the ellipse formula_61 one uses the pencils at the vertices formula_279. Let formula_299 be an upper co-vertex of the ellipse and formula_300.  formula_7 is the center of the rectangle formula_302. The side formula_303 of the rectangle is divided into n equal spaced line segments and this division is projected parallel with the diagonal formula_304 as

As hypotrochoid.

The ellipse is a special case of the hypotrochoid when "R" = 2"r", as shown in

Inscribed angles and three-point form.

Circles.

A circle with equation formula_313 is uniquely determined by three points formula_314 not on a line. A simple way to determine the parameters formula_315 uses the "inscribed angle theorem" for circles:  Usually one measures inscribed angles by a degree or radian "θ," but here the following measurement is more convenient:

Inscribed angle theorem for circles.

For four points formula_316 no three of them on a line, we have the following (see

Three-point form of circle equation.

For example, for formula_327 the three-point equation is:  Using vectors, dot products and determinants this formula can be arranged more clearly, letting formula_330:  The center of the circle formula_88 satisfies:  The radius is the distance between any of the three points and the center.

Ellipses.

This section, we consider the family of ellipses defined by equations formula_335 with a "fixed" eccentricity "e". It is convenient to use the parameter:  and to write the ellipse equation as:  where "q" is fixed and formula_338 vary over the real numbers. (Such ellipses have their axes parallel to the coordinate axes: if formula_339, the major axis is parallel to the "x"-axis; if formula_340, it is parallel to the "y"-axis.) Like a circle, such an ellipse is determined by three points not on a line.  For this family of ellipses, one introduces the following q-analog angle measure, which is "not" a function of the usual angle measure "θ":

Inscribed angle theorem for ellipses.

At first the measure is available only for chords which are not parallel to the y-axis. But the final formula works for

Three-point form of ellipse equation.

For example, for formula_350 and formula_351 one obtains the three-point form  Analogously to the circle case, the equation can be written more clearly using vectors:  where formula_355 is the modified dot product formula_356

Pole-polar relation.

Any ellipse can be described in a suitable coordinate system by an equation formula_61. The equation of the tangent at a point formula_358 of the ellipse is formula_359 If one allows point formula_358 to be an arbitrary point different from the origin, then

Metric properties.

All metric properties given below refer to an ellipse with equation formula_376.

Area.

The area formula_377 enclosed by an ellipse is:  where formula_13 and formula_47 are the lengths of the semi-major and semi-minor axes, respectively. The area formula formula_381 is intuitive: start with a circle of radius formula_47 (so its area is formula_383) and stretch it by a factor formula_384 to make an ellipse. This scales the area by the same factor: formula_385 It is also easy to rigorously

Circumference.

The circumference formula_11 of an ellipse is:  where again formula_13 is the length of the semi-major axis, formula_400 is the eccentricity, and the function formula_401 is the complete elliptic integral of the second kind,  The circumference of the ellipse may be evaluated in terms of formula_403 using Gauss's arithmetic-geometric mean; this is a quadratically converging iterative method.  The exact infinite series is:  where formula_405 is the double factorial. This series converges, but by expanding in terms of formula_406 James Ivory and Bessel derived an expression that converges much more rapidly:  Srinivasa Ramanujan gives two close approximations for the circumference in §16 of "Modular Equations and Approximations to formula_294"; they are  and  The

Curvature.

The curvature is given by formula_426 radius of curvature at point formula_29:  Radius of curvature

In triangle geometry.

Ellipses appear

As plane sections of quadrics.

Ellipses appear as plane

Applications.

Physics.

Elliptical reflectors and acoustics.

If the water's surface is disturbed at one focus of an elliptical water tank, the circular waves of that disturbance, after reflecting off the walls, converge simultaneously to a single point: the "second focus". This is a consequence of the total travel length being the same along any wall-bouncing path between the two foci.  Similarly, if a light source is placed at one focus of an elliptic mirror, all light rays on the plane of the ellipse are reflected to the second focus. Since no other smooth curve has such a property, it can be used as an alternative definition of an ellipse. (In the special case of a circle with a source at its center all light would be reflected back to the center.) If the ellipse is rotated along its major axis to produce an ellipsoidal

Planetary orbits.

In the 17th century, Johannes Kepler discovered that the orbits along which the planets travel around the Sun are ellipses with the Sun [approximately] at one focus, in his first law of planetary motion. Later, Isaac Newton explained this as a corollary of his law of universal gravitation.  More generally, in the gravitational two-body problem, if the two bodies are bound to each other (that is, the total energy is negative), their orbits are similar ellipses with the common barycenter being one of the foci of each ellipse. The other focus of either ellipse

Harmonic oscillators.

The general solution for a harmonic oscillator in two or more dimensions is also an ellipse. Such is the case, for instance, of a long pendulum that is free to move in two dimensions; of a mass attached

Phase visualization.

In electronics, the relative phase of two sinusoidal signals can be compared by feeding them to the vertical

Elliptical gears.

Two non-circular gears with the same elliptical outline, each pivoting around one focus and positioned at the proper angle, turn smoothly while maintaining contact at all times. Alternatively, they can be connected by a link chain or timing belt, or in the case of a bicycle the main chainring may be elliptical, or an ovoid similar to an ellipse in form. Such elliptical gears may be used in mechanical equipment to produce variable angular speed or torque from a constant rotation of the driving axle, or in the case of a bicycle to allow a varying crank rotation speed with inversely varying mechanical advantage.  Elliptical bicycle gears make it easier for the chain to slide off the cog when changing gears.  An example gear application would be a device that winds thread onto a conical bobbin on a spinning machine. The bobbin would need to wind faster when the thread is near the apex than when it is near the base.

Statistics and finance.

In statistics, a bivariate random vector ("X", "Y") is jointly elliptically distributed if its iso-density contours—loci of equal values of the density function—are ellipses. The concept extends to an arbitrary number of elements of the random vector, in which case in

Computer graphics.

Drawing an ellipse as a graphics primitive is common in standard display libraries, such as the MacIntosh QuickDraw API, and Direct2D on Windows. Jack Bresenham at IBM is most famous for the invention of 2D drawing primitives, including line and circle drawing, using only fast integer operations such as addition and branch on carry bit. M. L. V. Pitteway extended Bresenham's algorithm for lines to conics in 1967. Another efficient generalization to draw ellipses was invented in 1984 by Jerry Van Aken.  In 1970 Danny Cohen presented at the "Computer Graphics 1970"

Optimization theory.

It is sometimes useful to find the minimum bounding ellipse

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity "e", a number ranging from "e =" 0 (the limiting case of a circle) to "e" = 1 (the limiting case of infinite elongation, no longer an ellipse but a parabola).

Ellipsen sind in der Geometrie spezielle geschlossene ovale Kurven. Sie zählen neben den Parabeln und den Hyperbeln zu den Kegelschnitten. Eine anschauliche Definition ist die Definition der Ellipse als Punktmenge.


Biography.

Born in Paris, a descendant of an aristocratic (yet obscure) Picard family, he was educated at the Lycée Janson de Sailly and the Sainte-Croix boarding school at Neuilly-sur-Seine. Henry's father was a hard-line reactionary (to the extent of despising the post-Dreyfus Affair army as too subservient to the Republic, and refusing to have electricity or the telephone installed in his house). His mother, a formerly lively socialite, became chronically ill due to the difficult childbirth, being bedridden most of the time, and dying at the young age of 43.  Since 7 or 8 years old, Henry was enthusiastic about literature and began writing. In 1905 reading "Quo Vadis" by Henryk Sienkiewicz caused him a lifelong fascination with Ancient Rome and a proficient interest in Latin. He also was enthusiastic about school comradeship, sports and bullfighting. When he was 15 his parents sent him alone to Spain where got initiated in the "corrida", killing two young bulls. He was also a talented draughtsman and since 1913 he resorted to hiring young people in the street for nude modelling.  On 5 April 1912, aged almost 17, Henry was expelled from the Catholic Sainte-Croix de Neuilly school for being a «corruptor of souls». Together with other five youngsters he had founded a group called 'La Famille' (the Family), a kind of order of chivalry whose members were bonded by an oath of fidelity and mutual assistance. A member of that group was Philippe Jean Giquel (1897–1977), Montherlant's two year junior "special friend", with whom he was madly in love although it never became physical. According to Montherlant this "special friendship" had raised the fierce and jealous opposition of abbé de La Serre, who managed to get the older boy expelled. This incident (and Giquel) became a lifelong obsession of Montherlant's that would depict it in the 1952 play "La Ville dont le prince est un enfant" and his 1969 novel "Les Garçons". Later, in his adult years, he would resume his platonic friendship with Giquel, who would invite the writer to be the godfather of his daughter Marie-Christine.  After the deaths of his father and mother in 1914 and 1915, he went to live with his doting grandmother and eccentric uncles. Mobilised in 1916, he was wounded and decorated. Marked by his experience of war, he wrote "Songe" ('Dream'), an autobiographic novel, as well as his "Chant funèbre pour les morts de Verdun" ("Funeral Chant for the Dead at Verdun"), both exaltations of heroism during the Great War.  Montherlant first achieved critical success with the 1934 novel "Les Célibataires", and sold millions of copies of his tetralogy "Les Jeunes Filles", written from 1936 through 1939. In these years Montherlant, a well-to-do heir, traveled extensively, mainly to Spain (where he met and worked with bullfighter Juan Belmonte), Italy, and Algeria, giving vent to his passion of street boys. During the Second World War after the fall of France in 1940 he remained in Paris and continued to write plays, poems, essays, and worked as a war correspondent.  Some time in 1968, according to Roger Peyrefitte, outside a movie theatre in Paris, 72 years old Montherlant was attacked and beaten up by a group of youths because he had groped the younger brother of one them. Montherlant was seriously injured and blinded in one eye as a result. The British writer Peter Quennell, who edited a collection of translations of his works, recalled that Montherlant attributed the eye injury to "a fall" instead; and mentions in confirmation that Montherlant suffered from vertigo.  After going almost blind in his later years and becoming the target of scorners like Peyrefitte, Montherlant died from a self-inflicted gunshot wound to the head after swallowing a cyanide capsule in 1972. His ashes were scattered in Rome, at the Forum, among the Temple of Portunus and into the Tiber, by Jean-Claude Barat and Gabriel Matzneff.  His standard biography was written by Pierre Sipriot, and published in two volumes (1982 and 1990), revealing the full extent of Montherlant's sexual habits.

Works.

His early successes were works such as "Les Célibataires" ("The Bachelors") in 1934, and the highly anti-feminist tetralogy "Les Jeunes Filles" ("The Young Girls") (1936–1939), which sold millions of copies and was translated into 13 languages. His late novel "Chaos and Night" was published in 1963. The novels were praised by writers as diverse as Aragon, Bernanos, and Malraux. Montherlant was well known for his anti-feminist and misogynistic views, as exemplified particularly in "The Girls". Simone de Beauvoir considered his attitudes about women in detail in her "The Second Sex".  He wrote plays such as "Pasiphaé" (1936), "La Reine morte" (1942, the first of a series of historical dramas), "Malatesta" (1946), "Le Maître de Santiago" (1947), "Port-Royal" (1954) and "Le Cardinal d'Espagne" (1960). He is particularly remembered as a playwright. In his plays as well as in his novels he frequently portrayed heroic characters displaying the moral standards he professed, and explored the 'irrationality and unpredictability of human behaviour'.  He worked as an essayist also. In the collection "L'Equinoxe de septembre" (1938) he deplored the mediocrity of contemporary France and in "Le solstice de Juin", (1941), he expressed his admiration for Wehrmacht and claimed that France had been justly defeated and conquered in 1940. Like many scions of the old aristocracy, he had hated the Third Republic, especially as it had become in the aftermath of the Dreyfus Affair. He was in a ""round-table"" of French and German intellectuals who met at the Georges V Hotel in Paris in the 1940s, including, the writers Ernst Junger, Paul Morand and Jean Cocteau, the publisher Gaston Gallimard and the Nazi legal scholar Carl Schmitt. Montherlant wrote articles for the Paris weekly, "La Gerbe", directed by the pro-Nazi novelist and Catholic reactionary Alphonse de Châteaubriant. After the war, he was thus viewed as a collaborationist, and was punished by a one-year restriction on publishing.  A closeted pederast, Montherlant treated boy-love themes in his work, including his play "La Ville dont le prince est un enfant" (1952) and novel "Les Garçons" (The Boys), published in 1969 but written four or five decades earlier. He maintained a private and coded correspondence with fellow boy-lover Roger Peyrefitte — author of "Les Amitiés particulières" (Special Friendships, 1943), also about relationships between boys at a Roman Catholic boarding school. Peyrefitte would later mercilessly mock and out Montherlant in his 1970 novel "Des Français" (under the alias "Lionel de Beauséant") and in his memoirs "Propos secrets" (1977).  Montherlant is remembered for his aphorism "Happiness writes in white ink on a white page", often quoted in the shorter form "Happiness writes white".

Honours and awards.

"Les célibataires" was awarded the Grand prix de littérature de l'Académie française in 1934, and the English Northcliffe Prize. In 1960 Montherlant was elected a member of the Académie française, taking the seat which had belonged to André Siegfried, a political writer. He was an Officer of the French Ordre national de la Légion d'honneur.  Reference is made to "Les Jeunes Filles" in two films by West German director Rainer Werner Fassbinder: "Das kleine Chaos" (1967) and "Satansbraten" (1977). In the short film "Das kleine Chaos" the character portrayed by Fassbinder himself reads aloud from a paperback German translation of "Les Jeunes Filles" which he claims to have stolen.

Translations and adaptations.

Terence Kilmartin, best known for revising the Moncrieff translation of Proust, translated some of Montherlant's novels into English, including a 1968 edition of the four volumes of "Les Jeunes Filles", in English called simply "The Girls".  In 2009, New York Review Books returned Montherlant to print in English by issuing Kilmartin's translation of "Chaos and Night" (1963) with a new introduction by Gary Indiana.  Christophe Malavoy directed and starred in a 1997 television movie adaption of "La Ville dont le prince est un enfant".

Illustrated works.

Some works of Henry de Montherlant were published in illustrated editions, today commanding high prices at book auctions and in book specialists. Examples include "Pasiphaé," illustrated by Henri Matisse, "Les Jeunes Filles", illustrated by Mariette Lydis, and others illustrated by Jean Cocteau, Robert Cami, Édouard Georges Mac-Avoy and Pierre-Yves Tremois.

Henry Marie Joseph Frédéric Expedite Millon de Montherlant (; 20 April 1895 – 21 September 1972) was a French essayist, novelist, and dramatist. He was elected to the Académie française in 1960.

Henry de Montherlant (* 20. April 1895 in Paris; † 21. September 1972 ebenda) war ein französischer Schriftsteller, Dramatiker und Essayist.