# Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322

## Abstract

The mathematical cuneiform tablet Plimpton 322 is one of the most important source materials in history of mathematics. It lists fifteen Pythagorean triples together with a certain table which suggests that one of the angles of a right-angled triangle decreases from \( 45^\circ\ \text{to}\ 31^\circ, \) as O. Neugebauer explained in detail. However, we do not know the principle of constructing the fifteen triples and the true purpose of the table.

In this paper I shall clarify the mathematical meanings of a few technical terms which occur in the headings of the four columns of the tablet, and also the constructing principle of the listed numbers by analyzing Babylonian calculation methods. As a result, we can conclude that the Babylonian scribe of our tablet calculated the fifteen Pythagorean triples using the trigonometric table of the first column which was made by a kind of linear-interpolation.

## Keywords

Trigonometric Function Technical Term Arithmetic Sequence Pythagorean Triple Trigonometric Table## Preview

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