Introduction

Abstract

What is geometry? According to Veblen and Young [8], geometry deals with the properties of figures in space. Etymologically, geometry means the practical science of measurement. No wonder geometry plays a fundamental role in mathematics, physics, astronomy, and engineering. Historically, as explained in more detail by Coxeter [1], geometry was studied in Egypt about 2000 B.C. Then, it was brought to Greece by Thales (640–456 B.C.). Thales also began the process of abstracting positions and straight edges as points and lines, and studying incidence properties. This line of work was greatly developed by Pythagoras and his disciples, among which we should distinguish Hippocrates. Indeed, Hippocrates attempted a presentation of geometry in terms of logical deductions from a few definitions and assumptions. But it was Euclid (about 300 B.C.) who made fundamental contributions to geometry, recorded in his immortal Elements, one of the most widely read books in the world.