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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. [2] "Table of Pythagoras" on Napier's bones [3]
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It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base 10. A person doing long multiplication on paper will write down all the products and then add them together; an abacus-user will sum the products as soon as each one is computed.
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
The Erdős–Tenenbaum–Ford constant is a mathematical constant that appears in number theory. [1] Named after mathematicians Paul Erdős , Gérald Tenenbaum , and Kevin Ford , it is defined as δ := 1 − 1 + log log 2 log 2 = 0.0860713320 … {\displaystyle \delta :=1-{\frac {1+\log \log 2}{\log 2}}=0.0860713320\dots }
[f] [13] Therefore, the result of multiplication by 1:6:40 (4000) has the same Assyro-Babylonian representation as the result of multiplication by 1:6:40 (1/54). To convert from the former to the latter, the result's representation is interpreted as a number shifted three base-60 places to the right, reducing it by a factor of 60 3. [g]
The tables contain the prime factorization of the natural numbers from 1 to 1000. When n is a prime number, the prime factorization is just n itself, written in bold below. The number 1 is called a unit. It has no prime factors and is neither prime nor composite.
Mathematical tables are lists of numbers showing the results of a calculation with varying arguments.Trigonometric tables were used in ancient Greece and India for applications to astronomy and celestial navigation, and continued to be widely used until electronic calculators became cheap and plentiful in the 1970s, in order to simplify and drastically speed up computation.
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