An algorithm of developing of all the numerals from the relation of equality and Plato's Ideal numbers

Abstract

Andrej I. Schetnikov (ΣΙΓΜΑ: The Centre for Educational Projects, Novosibirsk), on the basis of testimonies by Nicomachus of Gerasa, Theon of Smyrna and other later authors, reconstructs an algorithm of developing all the numerals (provisionally called the ‘algorithm of Nicomachus’) and demonstrates how this algorithm could be found in the background of the so-called Plato’s ideal numbers. Besides, he suggests that the Platonicus by Erathosthenes, preserved in a fragmentary form by Theon, could be used as a supplementary source for reconstructing the content of the famous lecture of Plato On the Good.

Keywords

• Ancient mathematics
• Plato's unwritten doctrine
• Old Academy
• Eratosthenes
• Platonism
• Nicomachus