Plane

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

$(x,y)$ . In analogue with Space.

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

$(x,y)$ . 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

$(x,\theta )$ . 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