chapter  12
14 Pages

Shapely Numbers and Mr. Waring

WithMalcolm E Lines

Ancient Greek mathematicians, and especially the followers of Pythagoras and his school, were entranced by numbers which could be made up by arranging points in regular patterns on a plane or in space. We are already familiar with the ‘square numbers’ (i.e. the squares of the integers) beginning 1, 4, 9, 16, 25, … and these particular numbers can be given a picturesque representation by building up bigger and bigger squares on a plane in the following manner; * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *