# Portal:Geometry

## Geometry

**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.

## Selected article

All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. |

The **trigonometric functions** are functions of an angle; they are most important when studying triangles and modeling periodic phenomena, among many other applications. They are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to positive and negative values and even to complex numbers.

The study of trigonometric functions dates back to Babylonian times, and a considerable amount of fundamental work was done by ancient Greek, Indian and Arab mathematicians.

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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 picture

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 number of 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.

## Categories

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 |
---|---|---|---|

Differential geometry | Riemannian geometry | Algebraic geometry | Other |

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