Portal:Geometry
Introduction
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.
Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists preserved Greek ideas and expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since then, and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience.
Selected articles
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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Selected biography
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 BC–283 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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Selected images
The above shows an example of doubly ruled surface – the hyperboloid of one sheet. Although the wires are straight lines, they are lying within the surface. Through any point on this surface pass two straight lines, so it is doubly ruled.
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Did you know?
- ...that the hyperboloid of one sheet is a doubly ruled surface?
- ...that as the dimension of a hypersphere tends to infinity, its "volume" (content) tends to 0?
- ...that a nonconvex polygon with three convex vertices is called a pseudotriangle?
- ...that a regular heptagon is the regular polygon with the fewest sides which is not constructible with a compass and straightedge?
- ...that it is possible for a three-dimensional figure to have a finite volume but infinite surface area? An example of this is Gabriel's Horn.
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Algebraic geometry •
Classical geometry
Conformal geometry •
Convex geometry
Coordinate systems •
Differential geometry
Digital geometry •
Dimension •
Discrete geometry
Duality theories •
Figurate numbers
Frames of reference •
Geometers
Geometric algorithms •
Geometric graph theory
Geometric group theory •
Geometric shapes
Homogeneous spaces •
Incidence geometry
Integral geometry •
Metric geometry
Symmetry •
Trigonometry
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Topics in Geometry
Basic topics | Trigonometry | Euclidean geometry | Other geometries |
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Differential geometry | Riemannian geometry | Algebraic geometry | Other |
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Logic | Mathematics |
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Physics | Science | Set theory | Statistics |