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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. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations ...
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.
The Tsinghua Bamboo Slips, containing the world's earliest decimal multiplication table, dated 305 BC during the Warring States period. The Chinese multiplication table is the first requisite for using the Rod calculus for carrying out multiplication, division, the extraction of square roots, and the solving of equations based on place value decimal notation.
The Babylonians used pre-calculated tables to assist with arithmetic, including multiplication tables, tables of reciprocals, and tables of squares (or, by using the same table in the opposite way, tables of square roots). Their multiplication tables were not the tables that one might expect by analogy to decimal multiplication tables.
An extension of the above example for Orders 8 and 12 First generate a pattern table, where a '1' indicates selecting from the square where the numbers are written in order 1 to n 2 (left-to-right, top-to-bottom), and a '0' indicates selecting from the square where the numbers are written in reverse order n 2 to 1.
Download as PDF; Printable version; In other projects ... 100x100 pixels, white background. ... bidderID, bid times, and opening prices. ~ 550 Text Regression ...
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