[□=□]
[lemma=□]
We also defined differentiability of a function , and computed the derivatives of the identity and squaring functions . Volume I contains : The divisions of mathematics ; mathematics in Greek education ; calculation ; arithmetical notation and operations , including square root and cube root ; Pythagorean arithmetic , including properties of numbers ; square root of 2 ; proportion and means ; algebraic equations ; Proclus ; Thales ; Pythagorean geometry ; Democritus ; Hippocrates of Chios ; duplicating the cube and squaring the circle ; trisecting angles ; Theaetetus ; Plato ; Eudoxus of Cnidus ( pyramid , cone , etc. ) ; Aristotle ( the infinite , the lever ) ; Euclid . " " His book contains a huge number of problems and their various solutions , covering everything from squares and triangles , to stars , Maltese crosses and tessellations , to how to cheat in solving puzzles . For example , if x represents height , then is the expected value of height squared , that is , the mean value of the population obtained by squaring every value in the population of heights . The sum of the squared values in each column is the single-degree-of-freedom sum of squares for the corresponding column of the model matrix . Stationary stochastic processes ; autocovariance function ; spectral density function ; Wiener and Khinchin relation ; linear filtering ; estimation of the mean function , the autocovariance function and the spectral density function ; linear time series models including autoregressive models , moving average models and autoregressive / moving average models ; time series modelling including model identification , parameter estimation and diagnostic checks ; non-stationary time series ; differencing operation ; cointegration ; nonlinear time series models ; least squares forecasting . Einstein 's equation , E = mc ^ 2 , shows that matter that is transformed into energy may yield a total energy equivalent to the mass multiplied by the square of the velocity of light . The need for a program to build so many square meters of warehouses each year can be clearly seen , not to meet needs in 6 months or a year , but to meet needs at least in 5 or 10 . The yield surface , sigma subscript Y , equals negative pressure , P , times the sine of the angle of friction , phi , plus the square root of the sum of the second invariant of the stress deviator , J subscript 2 , times the function of the angle in the deviatoric plane , K of theta , squared , plus the product of the Drucker-Prager coefficient , AHYP , squared , times the sine , squared , of phi . Note that this operation reveals nothing to the outside world , because the probabilities - - that is , the squares of the probability amplitudes - - remain unchanged . We learned of this trade pattern at the California Islands Symposium in 1999 from Camp Trail guide Mark Raab , a professor at CSU Northridge who was surprised to see that the unusual squared shell beads made on San Clemente as a form of money were also showing up in excavations in the eastern Sierras . ) Have students crumple their squares into a ball , and then smooth them out again . If some students put the square and parallelogram together TTW ask the students to explain why ( Some students may remember that a square is a parallelogram ) . ( Our computation of the derivative of the squaring function actually used continuity of the identity function . Such proofs are like Bryson 's method of squaring the circle ; for they operate by taking as their middle a common character-a character , therefore , which the subject may share with another-and consequently they apply equally to subjects different in kind . Have students cut the squares , turn them over so the blank side of the paper is facing up , and mix up the squares to create a game board . Computation for too simple an implementation may be order N squared . When activated in accordance with Massachusetts Building Codes , the voice / alarm signaling system shall automatically sound an alert signal to all occupants within the building on a general or selective basis to the following terminal areas : elevators , elevator lobbies , corridors , exit stairways , rooms and tenant spaces exceeding 1,000 square feet in area ; dwelling units in occupancies in R-1 Use Groups . This is opposed to the K value of 1.36 x 10-6 m / sec with a 95 % confidence interval of 3.40 x 10-7 m / sec that included the data for the ratio of 5 ( VH / VL ) that was found to be inconsistent with the mathematical model ( r squared of .944 ) developed due to the assumption that concentration was constant on each side of the system .