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Geometry

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Geometry arose as the field of knowledge dealing with spatial relationships. Geometry is one of the two fields of pre-modern mathematics, the other being the study of numbers.

In modern times, geometric concepts have been extended. They sometimes show a high level of abstraction and complexity. Geometry now uses methods of calculus and abstract algebra, so that many modern branches of the field are not easily recognizable as the descendants of early geometry. (See areas of mathematics.) A geometer is one who works or is specialized in geometry.

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Title page of Sir Henry Billingsley's first English version of Euclid's Elements, 1570 (560x900).jpg
The frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570

Euclid's Elements (Greek: Στοιχεῖα) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Egypt during the early 3rd century BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems) and proofs thereof. Euclid's books are in the fields of Euclidean geometry, as well as the ancient Greek version of number theory. The Elements is one of the oldest extant axiomatic deductive treatments of geometry, and has proven instrumental in the development of logic and modern science.

It is considered one of the most successful textbooks ever written: the Elements was one of the very first books to go to press, and is second only to the Bible in number of editions published (well over 1000). For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century did it cease to be considered something all educated people had read. It is still (though rarely) used as a basic introduction to geometry today.

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Euclid of Alexandria

Euclid (also referred to as Euclid of Alexandria) (Greek: Εὐκλείδης) (c. 325–c. 265 BC), a Greek mathematician, who lived in Alexandria, Hellenistic Egypt, almost certainly during the reign of Ptolemy I (323 BC283 BC), is often considered to be the "father of geometry". His most popular work, Elements, is thought to be one of the most successful textbooks in the history of mathematics. Within it, the properties of geometrical objects are deduced from a small set of axioms, thereby founding the axiomatic method of mathematics.

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The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page.

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Construction of an astroid

One way of constructing an astroid, by tracking the path a point on the smaller circle follows as it is rolled round within the larger circle. Hence, an astroid is a hypocycloid.

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Basic topics Trigonometry Euclidean geometry Other geometries
Differential geometry Riemannian geometry Algebraic geometry Other

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