Using Symbolic Computation to Inductively Prove Geometric Theorems And Its Implication to The Study of General Relativity

Abstract

One can reasonably say that we always prove geometric theorems using deductive method. The deductive method is too often used such that we get the impression that there is no other alternative appropriate method. In this paper we will use inductive method. We need many special cases to prove so that we will use the computer algebra system to assist us. We use symbolic computation (using CAS and Fortran) to compute with rational number. First we prove geometric theorems about triangles and conic sections. In those cases we only need linear algebra so that using rational numbers will eliminate rounding error. Every theorem can be proved with special cases using rational numbers. Then we move on to non- euclidean geometry which is one of the most important topics in general relativity. We need calculus so that we use real number with high precision to prove special cases. The main goal of this research is to make mathematics closer to physics and by doing that we get a deeper understanding of general relativity.