**Euclidean geometry** is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the *Elements*. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The *Elements* begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the *Elements* states results of what are now called algebra and number theory, couched in geometrical language.

For over two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that Euclidean space is a good approximation to the properties of physical space only where the gravitational field is weak.

Read more about Euclidean Geometry: *The Elements*, Methods of Proof, System of Measurement and Arithmetic, Some Important or Well Known Results, Applications, As A Description of The Structure of Space, Logical Basis

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### Famous quotes containing the word geometry:

“I am present at the sowing of the seed of the world. With a *geometry* of sunbeams, the soul lays the foundations of nature.”

—Ralph Waldo Emerson (1803–1882)