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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 ...
Thus, the Cayley table of a group is an example of a latin square. An alternative and more succinct proof follows from the cancellation property . This property implies that for each x in the group, the one variable function of y f(x,y)= xy must be a one-to-one map.
A square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes. From Gulley (2010).The n th coloured region shows n squares of dimension n by n (the rectangle is 1 evenly divided square), hence the area of the n th region is n times n × n.
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In prehistoric time, quarter square multiplication involved floor function; that some sources [7] [8] attribute to Babylonian mathematics (2000–1600 BC). Antoine Voisin published a table of quarter squares from 1 to 1000 in 1817 as an aid in multiplication.
This page was last edited on 6 June 2004, at 11:02 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply ...