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The plane has length and width. The plane also refers to a hypothetical two-dimensional space of infinite extent; this use is used, for example, when describing tilings of the plane. Points on the plane can be shown using two coordinates, written as

${\displaystyle (x,y)}$ . In analogue with Space.

## Objects on the Plane

### Flexagons

A Polygon which has 3 or more faces is called a flexagon

### Polyominoes

Polyominoes are two-dimensional figures consisting of multiple squares fixed edge-to-edge. There are an infinite number of polyominoes, and the number of polyominoes increases with the amount of squares allowed.

## Coordinates on the Plane

There are two coordinate systems that can be used to define points on the plane - Cartesian coordinates, and polar coordinates.

Cartesian coordinates consist of two distances - the left-right distance from the origin, and the up-down distance from the origin. This is written as

${\displaystyle (x,y)}$ . Cartesian coordinates where either x or y are fixed trace out an infinite line. Cartesian coordinates where both are fixed trace out a point, and where none are fixed trace out a plane. Polar coordinates consist of a distance and an angle - the overall distance from the origin, and the angle of the point from horizontal. This is written as

${\displaystyle (x,\theta )}$ . Polar coordinates where x is fixed trace out a circle; polar coordinates where θ is fixed trace out an infinite line. Polar coordinates where both are fixed trace out a point, and where none are fixed trace out a plane. When converting from polar to Cartesian coordinates, the equations

${\displaystyle x\cos { \theta } =x}$ and

${\displaystyle x\sin{\theta } =y}$ can be used. When converting from Cartesian to polar coordinates, the equations

${\displaystyle \sqrt { { x }^{ 2 }+{ y }^{ 2 } } =x }$ and

${\displaystyle \tan ^{ -1 }{ (\frac { y }{ x } ) } =\theta }$ can be used.

## Dimension

Name: Polygon

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Next: Space