AUTOMATED PRODUCTION OF TRADITIONAL PROOFS IN SOLID GEOMETRY

This paper presents a method of producing readable proofs for theorems in solid geometry. The method is for a class of constructive geometry statements about straight lines, planes, circles, and spheres. The key idea of the method is to eliminate points from the conclusion of a geometric statement using several (fixed) high-level basic propositions about the signed volumes of tetrahedrons and Pythagorean differences of triangles. We have implemented the algorithm, and more than 80 examples from solid geometry have been used to test the program. Our program is efficient and the proofs produced by it are generally short and readable.