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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 multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC).
One of the main properties of multiplication is the commutative property, which states in this case that adding 3 copies of 4 gives the same result as adding 4 copies of 3: 4 × 3 = 3 + 3 + 3 + 3 = 12. {\displaystyle 4\times 3=3+3+3+3=12.}
The first tables of trigonometric functions known to be made were by Hipparchus (c.190 – c.120 BCE) and Menelaus (c.70–140 CE), but both have been lost. Along with the surviving table of Ptolemy (c. 90 – c.168 CE), they were all tables of chords and not of half-chords, that is, the sine function. [1]
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.
1 Multiplication table problem. 2 References. 3 External links. Toggle the table of contents. Erdős–Tenenbaum–Ford constant. ... [3] [4] Multiplication table problem
The History of Mathematical Tables: from Sumer to Spreadsheets is an edited volume in the history of mathematics on mathematical tables.It was edited by Martin Campbell-Kelly, Mary Croarken, Raymond Flood, and Eleanor Robson, developed out of the presentations at a conference on the subject organised in 2001 by the British Society for the History of Mathematics, [1] [2] and published in 2003 ...
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