Euclidean biography definition

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Euclid

Ancient Greek mathematician (fl. BC)

For the philosopher, see Euclid of Megara. For other uses, see Euclid (disambiguation).

Euclid (; Ancient Greek: Εὐκλείδης; fl.&#; BC) was an ancient Greekmathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around BC, after Plato's students and before

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Euclidean geometry

Mathematical model of the physical space

"Plane geometry" redirects here. For other uses, see Plane geometry (disambiguation).

Euclidean geometry is a mathematical system attributed to ancient Greek mathematicianEuclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,^[1] Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.^[2]

The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. 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, explained in geometrical language.^[1]

For more than two thousand years, the adjective "Euclidean" was unnecessary because Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that theorems proved from them were deemed absolut