| Geometry is the study of shape, form, and space, and is of interest for its own sake as well as for its many applications in the sciences and the arts. Geometry is an integral part of mathematics, drawing upon all other areas in its development, and in turn contributing to the development of other parts of mathematics.
The roots of geometry lie in many different cultures, including the ancient Vedic, Egyptian, Babylonian, Chinese, and Greek civilizations. The development of geometry as a deductive science began with Thales and reached maturity with the Elements of Euclid around 300 B.C.E.
In the Elements, Euclid sets out a list of statements called postulates and common notions, which are fundamental, self-evident truths of geometry. These statements express common experiences and intuitions about space: It is flat, it extends infinitely in all directions, and it has everywhere the same structure.
From the postulates and common notions, Euclid derives 465 proposition that form the body of Euclidean geometry. Euclid’s presentation is systematic, beginning with simple statements that depend only on the postulates and common notions and concluding with intricate and exquisite propositions. Each proposition is supported by a logical deduction or proof, based only on the postulates, the common notions, and other propositions that have already been proved. |
