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

. In analogue with Space.

## Contents

## Objects on the Plane

### List of Uniform Polygons

- Henagon
- Digon
- Triangle
- Square
- Pentagram
- Pentagon
- Hexagon
- Heptagon
- Octagon
- Nonagon
- Decagon
- ...
- Apeirogon

### List of Curved Shapes

- Circle
- Semicircle

### 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

. 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

. 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

and

can be used. When converting from Cartesian to polar coordinates, the equations

and

can be used.

## Dimension

Name: Polygon

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