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Multiplication table from 1 to 10 drawn to scale with the upper-right half labeled with prime factorisations. In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.
So for example, for a promptuary capable of multiplying two five-digit numbers together, the strips should 6 times as long as they are wide, with 50 number strips and 50 mask strips. Napier's example specified strips 1 finger (19mm) wide and 11 fingers (209mm) long, enabling the device to multiply two 10-digits numbers to produce a 20-digit result.
Napier gave details of a scheme for arranging the tables so that no rod has two copies of the same table, enabling every possible four-digit number to be represented by 4 of the 10 rods. A set of 20 rods, consisting of two identical copies of Napier's 10 rods, allows calculation with numbers of up to eight digits, and a set of 30 rods can be ...
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 hexidecimal multiplication table. Date: 22 November 2009, 02:19 (UTC) ... (possibly using MediaWiki's special syntax for tables, ... 20, 22 November 2009: