𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A method of machine discovery based on geometrical structure

✍ Scribed by Tsuyoshi Murata; Masamichi Shimura

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
113 KB
Volume
29
Category
Article
ISSN
0882-1666

No coin nor oath required. For personal study only.

✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Applications in intelligent systems of k
Applications in intelligent systems of knowledge discovery methods based on human–machine interaction
✍ Vladimir Jotsov; Vassil Sgurev πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 193 KB

Contemporary knowledge discovery systems are mainly quantitative. This part of the research could be successfully combined with the considered qualitative research in acquisition, elicitation, and discovery of logic-based rules and patterns. The paper introduces a synthetic metamethod (SMM), which i

A geometrical non-linear brick element b
A geometrical non-linear brick element based on the EAS-method
✍ S. Klinkel; W. Wagner πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 210 KB πŸ‘ 2 views

This paper presents the development of a 3-D brick element with enhanced assumed strains for a geometrically non-linear theory. Some linear and non-linear examples show that this element can be used successfully in the whole range of solid structures. Thin 2-D-and 3-D-beam and shell structures are c