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'''Geometry''' is the part of [[mathematics]] that studies the [[size]], [[shape]]s, positions and dimensions of things. We can only see or make shapes that are [[wikt: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 also 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 [[wikt:string|string]] from one point to another point. A straight line between the two points will follow the [[wikt:path|path]] of the tight string.
* A '''[[Plane (mathematics)|plane]]''' is a flat [[surface]] that does not [[wikt:stop|stop]] in any [[direction]]. For example, imagine a wall that extends in all directions infinitely.

== Related pages ==
* [[Topology]]

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Geometry - Revision history

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