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[[File:Axel_Helsted_-_Geometri_-_(gentagelse).png|thumb|[[Axel Helsted]], "Geometry"]]

'''Geometry''' (from [[Ancient Greek]]: Γεωμετρία ([[Romanization of Greek|romanized]]: ''Geometria'' ([[English language|English]]: "Land measurement") derived from Γη (romanized: Ge; English: "Earth" or "land") and also derived from Μέτρον) (romanized: ''Métron''; English: "A measure")) is a branch of [[mathematics]] that studies the [[size]], [[shape]]s, positions and dimensions of things. We can only see shapes that are [[flat|flat]] ([[2D]]) or solid ([[3D]]), but [[mathematician]]s (people who study math) are able to study shapes that are [[4D]], 5D, 6D, and so on.

[[square (geometry)|Squares]], [[circle]]s and [[triangle]]s are some of the simplest shapes in flat geometry. [[Cube]]s, [[cylinder]]s, [[cone]]s and [[sphere]]s are simple shapes in [[solid geometry]].
== Uses ==
Plane geometry can be used to [[measure]] the [[area]] and [[perimeter]] of a flat shape. Solid geometry can measure a [[solid]] shape's [[volume]] and [[surface area]].

Geometry can be used to calculate the size and shape of many things. For example, geometry can help people find:
* the surface area of a [[house]], so they can buy the right amount of [[paint]]
* the [[volume]] of a [[box]], to see if it is big enough to hold a [[litre|liter]] of [[food]]
* the area of a [[farm]], so it can be divided into equal parts
* the [[distance]] around the edge of a [[pond]], to know how much [[fence|fencing]] to [[buy]].
== Origins ==
Geometry is one of the oldest branches of mathematics. Geometry began as the art of [[surveying]] of [[land]] so that it could be shared fairly between people. The word "geometry" is from a Greek word that means "to measure the land". It has grown from this to become one of the most important parts of mathematics. The [[ancient Greece|Greek]] [[mathematician]] [[Euclid]] wrote the first book about geometry, a book called ''The Elements''.
== Non-Euclidean geometry ==
Plane and solid geometry, as described by Euclid in his textbook [[Euclid's Elements|Elements]], is called "Euclidean Geometry". This was simply called "geometry" for centuries. In the 19th century, mathematicians created several new kinds of geometry that changed the rules of Euclidean geometry. These and earlier kinds were called "non-Euclidean" (not created by Euclid). For example, [[hyperbolic geometry]] and elliptic geometry come from changing Euclid's [[parallel postulate]].

[[Non-Euclidean geometry]] is more complicated than Euclidean geometry but has many uses. [[Spherical geometry]] for example is used in [[astronomy]] and [[cartography]].
== Examples ==
Geometry starts with a few simple ideas that are thought to be true, called axioms. Such as:
* A '''[[point (geometry)|point]]''' is shown on [[paper]] by [[touch]]ing it with a [[pencil]] or [[pen]], without making any sideways movement. We know where the point is, but it has no [[size]].
* A '''[[straight]] [[line]]''' is the [[short]]est [[distance]] between two points. For example, Sophie pulls a piece of [[string|string]] from one point to another point. A straight line between the two points will follow the [[path|path]] of the tight string.
* A '''[[Plane (mathematics)|plane]]''' is a flat [[surface]] that does not [[stop|stop]] in any [[direction]]. For example, imagine a wall that extends in all directions infinitely.

== Geometry Media ==
<gallery widths='160px' heights='100%' mode='traditional' caption=''>
File:Westerner and Arab practicing geometry 15th century manuscript.jpg|A [[Ethnic groups in Europe|European]] and an [[Arab]] practicing geometry in the 15th century

File: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 ''[[Element (mathematics)|Elements]]'', 1570

File:Woman teaching geometry.jpg|''Woman teaching geometry''. Illustration at the beginning of a medieval translation of [[Euclid's Elements]], {{Circa|1310}}.

File:Parallel postulate en.svg|An illustration of Euclid's [[parallel postulate]]

File:Sphere wireframe.svg|A sphere is a surface that can be defined parametrically (by {{nowrap|''x'' {{=}} ''r'' sin ''θ'' cos ''φ'',}} {{nowrap|''y'' {{=}} ''r'' sin ''θ'' sin ''φ'',}} {{nowrap|''z'' {{=}} ''r'' cos ''θ'')}} or implicitly (by {{nowrap|''x''2 + ''y''2 + ''z''2 − ''r''2 {{=}} 0}}).

File:Blue ball.png|In [[Euclidean space]], a ball is the volume bounded by a sphere.

File:Angle obtuse acute straight.svg|Acute (a), obtuse (b), and straight (c) angles. The acute and obtuse angles are also known as oblique angles.

File:Chinese pythagoras.jpg|Visual checking of the [[Pythagorean theorem]] for the (3, 4, 5) [[triangle]] as in the [[Zhoubi Suanjing]] 500–200&nbsp;BC. The Pythagorean theorem is a consequence of the [[Euclidean metric]].

File:Von Koch curve.gif|The [[Koch snowflake]], with [[fractal dimension]]=log4/log3 and [[topological dimension]]=1

File:Order-3 heptakis heptagonal tiling.png|A [[Order-3 bisected heptagonal tiling|tiling]] of the [[Hyperbolic geometry|hyperbolic plane]]
</gallery>
== Related pages ==
* [[Topology]]
== References ==
{{Areas of mathematics}}
{{commonscat}}

[[Category:Geometry|*]]