Automated Reasoning in Differential Geometry and Mechanics Using Characteristic Method

This paper reports the study of properties of the curve pairs of the Bertrand types using our automated reasoning program based on Wu's method of mechanical theorem proving for differential geometry. A complete list of results about Bertrand curves in metric and affine spaces is derived mechanically. The list includes most of the known results of various Bertrand curves. We also derive some new results about Bertrand curves. Keywords Mechanical theorem proving, metric differential geometry, affine differential geometry, Bertrand curves. Abbreviated title: Automated Reasoning in Differential Geometry 1 The work reported here was supported in part by the NSF Grant CCR-8702108. 1 

• Type: Conference
• Year: 1992
• Where: IWAR
• Authors: Shang-Ching Chou, Xiao-Shan Gao
• Keywords: Automated Reasoning, Bertrand Curves, IWAR 1992, Theorem Proving, Various Bertrand Curves