A Method of Machine Discovery Based on Geometric Constraints

DOI Web Site 1 Citations 12 References
  • MURATA Tsuyoshi
    Dept. of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology
  • SHIMURA Masamichi
    Dept. of Computer Science, Graduate School of Information Science and Engineering, Tokyo Institute of Technology

Bibliographic Information

Other Title
  • 計算機による図形的制約に基づく発見手法
  • ケイサンキ ニヨル ズケイテキ セイヤク ニ モトズク ハッケン シュホウ

Search this article

Description

<p>This paper describes a new method of discovering theorems in a plane geometry domain. In order to discover useful theorems from a figure, the following subjects should be discussed : the contents of acquired data by observing the figure, the techniques for avoiding combinatorial explosion of expressions, and the criteria for choosing useful theorems from generated expressions. Our discovery method is based on the sides in a given figure. All the geometric relations among sides are observed from a figure. Deduced expression which shows the relation of closely located sides in the figure are regarded as a useful theorem. It is because a human often considers such an expression to be an important theorem. Observed geometric relations among sides are used for both choosing useful theorems and avoiding combinatorial explosion of generated expressions. Although most of the methods of previous discovery systems such as AM, KEKADA and IDS require much initial knowledge for evaluating the usefulness of generated knowledge, our method needs little initial knowledge about plane geometry. Our discovery method has been implemented in a system called PLANET, a discovery system for plane geometry theorems. PLANET has succeeded in discovering many useful geometry theorems and trigonometric formulas, including Menelaus' theorem, Ceva's theorem, and addition theorems of trigonometric functions, through trial and error.</p>

Journal

Citations (1)*help

See more

References(12)*help

See more

Keywords

Details 詳細情報について

Report a problem

Back to top