What mathematical tabular system was invented in 1614 by John Napier that changes calculations of, for example, multiplication and finding square roots to addition and division respectively?
History of computing hardware combinatorics. This idea was taken up by Leibniz centuries later, and is thus one of the founding elements in computing and information science. Scottish mathematician and physicist John Napier discovered that the multiplication and division of numbers could be performed by the addition and subtraction, respectively, of the logarithms of those numbers. While producing the first logarithmic tables, Napier needed to perform many tedious multiplications. It was at this point that he designed his 'Napier's bones', an abacus-like device that greatly simplified calculations that involved multiplication and division. Since real numbers can be represented as distances or intervals on a
Multiplication and repeated addition Once 0 is brought in, it affects no significant change because which is 0, and the commutative property would lead us also to define Thus, repeated addition extends to the whole numbers (0, 1, 2, 3, 4, ...). The first challenge to the belief that multiplication is repeated addition appears when students start working with fractions. From the mathematical point of view, multiplication as repeated addition can be "extended" into fractions. For example, literally calls for “one and three-fourths of the five-sixths.” This is later significant because students are taught that, in word problems, the word “of” usually indicates a