The Figurate Numbers of the Greeks

The figurate numbers of the Greeks go back to the time of Pythagoras and are frequently referred to by Greek authors. The natural way to represent numbers was by a set of units, shown by dots in sand or by pebbles, and these were arranged in patterns of geometrical figures. In writing, a dot or the letter α would be used for each unit. The figurate numbers and various relations and problems concerning them form a substantial part of Greek number theory (arithmetic). Surviving works which treat figurate numbers are by Nicomachus of Gerasa (c. 100 A.D.), Theon of Smyrna (c. 130 A.D.),99 Diophantus of Alexandria (c. 250 A.D.),100 and Iamblichus (c. 283–330 A.D.).101 Summaries are given by Heath and Dickson, and some relevant extracts by Cohen and Drabkin.102 This section will review some of this material, with some added matter, before presenting the text of the second part of the manuscript, which deals with figurate numbers.