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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 ...
Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
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 ...
together with a table of reciprocals. Numbers whose only prime factors are 2, 3 or 5 (known as 5-smooth or regular numbers) have finite reciprocals in sexagesimal notation, and tables with extensive lists of these reciprocals have been found. Reciprocals such as 1/7, 1/11, 1/13, etc. do not have finite representations in sexagesimal notation.
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.
In the example movement above, Tables 1, 2, 7, and 8 would use one set of boards, with boards entering at Table 2 and exiting at Table 7, and Tables 3, 4, 5, and 6 would use the other, with boards entering at Table 6 and exiting at Table 3. The remaining boards of each set usually are placed on stands next to the table where they will enter.
Fano planes for the two multiplication tables used here. Two different multiplication tables have been used in this article, and there are more. [5] [13] These multiplication tables are characterized by the Fano plane, [14] [15] and these are
While the entire Legion mourns Superboy's death, four members are particularly outraged: Saturn Girl, one of the three founders who invited Superboy to join; [8] Brainiac 5, who realizes that all of his theories about time travel are incorrect; [9] Mon-El, who regards Superboy as a brother; [10] and Duo Damsel, who previously had an unrequited crush on him. [11]