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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.
The first edition was published in 1928. [4] Subsequent editions are: [5] Mathematical Tables from Handbook of Chemistry and Physics. 3rd edition (1933) 4th edition (1934) 5th edition (1936) 6th edition (1938) 7th edition (1941) 8th edition (1946, 1947) 9th edition (1952) CRC Standard Mathematical Tables. 10th edition (1956) 11th edition (1957 ...
For each positive integer , let () be the number of distinct integers in an multiplication table. In 1960, [ 5 ] Erdős studied the asymptotic behavior of M ( N ) {\displaystyle M(N)} and proved that
Area of a cloth 4.5m × 2.5m = 11.25m 2; 4 1 / 2 × 2 1 / 2 = 11 1 / 4 Multiplication (often denoted by the cross symbol × , by the mid-line dot operator ⋅ , by juxtaposition, or, on computers, by an asterisk * ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition ...
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]
For q = 2 2 = 4, it can be checked case by case using the above multiplication table that all four elements of F 4 satisfy the equation x 4 = x, so they are zeros of f. By contrast, in F 2 , f has only two zeros (namely 0 and 1 ), so f does not split into linear factors in this smaller field.
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