A method of machine discovery based on geometrical structure
Tsuyoshi Murata, Masamichi Shimura · Systems and Computers in Japan · 1998
In the discovery of useful theorems or laws from the data of observed instances, structures that group instances often play an important role. Acquiring data from such structure avoids the combinatorial explosion of numerous instances and enables the discovery of generalized theorems. This paper proposes a method for discovering useful theorems in the domain of plane geometry by using data from triangles, that form the basic structure in figures. We have implemented DIGEST, a discovery system based on geometrical structure, which generates figures by itself and finds theorems by using the relations among the areas of observed triangles. DIGEST succeeds in discovering new useful theorems as well as rediscovering well-known theorems such as the Menelaus Theorem and the Ceva Theorem. © 1998 Scripta Technica, Syst Comp Jpn, 29(6): 74–81, 1998