Origins of Geometry
The study of geometry is extremely ancient, and has been carried on for many thousands of years, across all civilizations – Egypt, Babylonia, India, China, Greece, the Incas, etc. Problems of geometry are so fundamental to our lives that it is natural for this study to be almost as old as civilization itself.
In the ancient world, geometry was mostly a practical science. For example, the Egyptians used it in the construction of pyramids. For these civilizations, geometry consisted of a set of results which they could apply to guide and refine their constructions. However, with the coming of the Greeks, geometry turned into a more rigorous discipline, with more emphasis on reasoning rather than on results.
This was an important development in mankind’s progress, because without this shift in emphasis, geometry would have remained a collection of disparate, seemingly unrelated results. But with reasoning and deductive logic as their tools, the Greeks showed that geometry could be unified into a coherent and beautiful subject.
As we will discuss later, the Greeks were the first to systematically introduce the concept of proofs. A proof consists of a series of arguments, starting from an original assumption, and designed to show that a given assertion is true.
In your study of geometry, you will come across a lot of results and their proofs. You might be tempted to skip over the proofs and apply those results directly (this is what many students actually do). But you should follow the example of the ancient Greeks and always lay more emphasis on the reasoning (the proofs) behind the results. Otherwise, all the different results will be unconnected in your mind, and you will have a hard time remembering and applying them. But if your reasoning process (the ability to understand and construct proofs) is well-developed, you will see all these various results and their various interconnections effortlessly.