# Geometry

**Geometry** is the part of mathematics that studies the size, shapes, positions and dimensions of things. We can only see or make shapes that are flat (2D) or solid (3D), but mathematicians (people who study math) are able to study shapes that are 4D, 5D, 6D, and so on.

Squares, circles and triangles are some of the simplest shapes in flat geometry. Cubes, cylinders, cones and spheres 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 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 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 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 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**is shown on paper by touching 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 shortest distance between two points. For example, Sophie pulls a piece of string from one point to another point. A straight line between the two points will follow the path of the tight string. - A
**plane**is a flat surface that does not stop in any direction. For example, imagine a wall that extends in all directions infinitely.