An introduction to Pythagorean Arithmetic

This thesis provides a look at some aspects of Pythagorean Arithmetic. The topic is introduced by looking at the historical context in which the Pythagoreans nourished, that is at the arithmetic known to the ancient Egyptians and Babylonians. The view of mathematics that the Pythagoreans held is introduced via a look at the extraordinary life of Pythagoras and a description of the mystical mathematical doctrine that he taught. His disciples, the Pythagoreans, and their school and history are briefly mentioned. Also, the lives and works of some of the authors of the main sources for Pythagorean arithmetic and thought, namely Euclid and the Neo-Pythagoreans Nicomachus of Gerasa, Theon of Smyrna, and Proclus of Lycia, are looked at in more detail. Finally, an overview of the content of the arithmetic of the Pythagoreans is given, with particular attention paid to their relationship to incommensurable or irrational numbers. With this overview in hand, the topics of Perfect and Friendly Numbers, Figurate Numbers, Relative Numbers (the Pythagorean view of ratios and fractions), and Side and Diagonal numbers are explored in more detail. In particular, a selection of the works of Nicomachus, Theon, and Proclus that deal with these topics are analyzed carefully, and their content is reformulated and commented upon using clearer and more modern terminology.Science, Faculty ofMathematics, Department ofGraduat