A Discovery System for Trigonometric Functions

Tsuyoshi Murata, Masami Mizutani, Masamichi Shimura

This paper describes a discovery system for trigonometric fuctions (DST), which has abilities to acquire new knowledge in the form of theorems and formulas in a plane geometry domain. The system is composed of two subsystems: a plane geometry analysis system and a mathematical formula transformation system. The former changes the length and angles of a figure and extracts geometric relations, and the latter transforms the relations to acquire useful formulas. With little basic knowledge such as the definition of the congruence of triangles and the definition of fundamental trigonometric functions, our system has rediscovered many trigonometric formulas and geometric theorems, including the Pythagorean theorem.

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