A discovery system for trigonometric functions
Tsuyoshi Murata, Masami Mizutani, Masamichi Shimura · 1994
This paper describes a discovery system for trigonometric fuctions (DST), which has abili-ties to acquire new knowledge in the form of the-orcins ancl foriiialas ii1 a plant: geometry cloiiiaiil. The systcn1 is composed of two suhystenls: a plaiic: geonhry analysis systeiri ad a niatlicniat-ical fornda t,ratnsforlllat,ioll system. The former changes the length and angles of a figure and ex-tracts geouietric relations, and the lat,tcr trans-foriiis the relations to acquire nsefnl formnlas. With little lmsic: knowledge such as the clefini-tioii of the congruence of triangles aid the dcf-iiiition of fiuidameiit~al trigonometric fiuictions, our system has recliscovered many trigononietric formulas ant1 geometric theorems, including the Pythagorean tlieoreui.