A geometrical link between the circle and sexagesimal system

TL;DR

This paper reveals a simple geometric fact linking the circle to sexagesimal divisions, illustrating historical and astronomical connections, and providing methods to represent time and numbers in base 60.

Contribution

It introduces a geometric approach to understanding the origin of sexagesimal divisions and their relation to astronomical timekeeping and number representation.

Findings

Shows a geometric link between the circle and multiples of 6

Provides a method to represent time and numbers in base 60

Suggests a geometric basis for dividing the circle into 360 parts

Abstract

This paper presents a simple geometrical fact which could relate to the history of mathematics and astronomy. This fact shows a natural link between the circle and the multiples of 6 and it makes it possible to obtain a simple representation of the 12 months of the year, the 24 hours of the day, the 30 days (average number) of the month and the 360 days (approximate number) of the year, which brings us closer to the sexagesimal division of time. Moreover this representation reminds one of the movement of the planets around a centre. Using this fact one will be able also to find geometrically the principal divisor of number 60, to represent numbers in base 60 with a kind of abacus or calculation table and to make a division of the circle into 6 and 12 equal parts. Afterwards one will be able to obtain a division in 360 unequal parts but relatively close to one another, and the goal isn't precisely to obtain an optimal division of the circle in 360 equal parts but to prove that the idea to divide the circle in 360 equal parts can subsequently be suggested by these geometrical facts that have been showed. In this article the author will not answer the following questions: a) What is the origin of the sexagesimal system? b) By which way could one manage to adopt the sexagesimal system starting from the knowledge of the facts exposed in this article and starting from the knowledge of the astronomical data? These questions could be treated, using information of this article, by the readers or later on by the author.