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 $(x,y)$.

Objects on the Plane

List of Uniform Polygons

• Henagon
• Digon
• Triangle
• Square
• Pentagram
• Pentagon
• Hexagon
• Apeirogon

List of Curved Polygons

• Circle
• Semicircle

Flexagons

Polygon has 3 or more faces called 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 $x\cos { \theta } =x$ and $x\sin{\theta } =y$ can be used. When converting from Cartesian to polar coordinates, the equations $\sqrt { { x }^{ 2 }+{ y }^{ 2 } } =x$ and $\tan ^{ -1 }{ (\frac { y }{ x } ) } =\theta$ can be used.

Dimension

Name: Polygon

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