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The oldest known multiplication tables were used by the Babylonians about 4000 years ago. [2] However, they used a base of 60. [2] The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. [2] "Table of Pythagoras" on Napier's bones [3]
The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and inspection of the symmetry of their Cayley tables verifies this. In contrast, the smallest non-abelian group, the dihedral group of order 6, does not have a symmetric Cayley table.
A subtraction problem such as is solved by borrowing a 10 from the tens place to add to the ones place in order to facilitate the subtraction. Subtracting 9 from 6 involves borrowing a 10 from the tens place, making the problem into +. This is indicated by crossing out the 8, writing a 7 above it, and writing a 1 above the 6.
The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. [1] Named after mathematicians Paul Erdős , Gérald Tenenbaum , and Kevin Ford , it is defined as δ := 1 − 1 + log log 2 log 2 = 0.0860713320 … {\displaystyle \delta :=1-{\frac {1+\log \log 2}{\log 2}}=0.0860713320\dots }
A larger table of quarter squares from 1 to 100000 was published by Samuel Laundy in 1856, [9] and a table from 1 to 200000 by Joseph Blater in 1888. [ 10 ] Quarter square multipliers were used in analog computers to form an analog signal that was the product of two analog input signals.
In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n. [2] [10] [14] [15] For instance, the manuscript ...