Circle

A circle is a rotatope with no flat dimensions and two round dimensions. It is, therefore, the 2D hypersphere. It can also be considered as the set of all points that are the same distance from a point (the center of a circle) in the plane.

In the plane, a circle will roll, as it is completely round. The proof of this is that if you trace the path the middle of a circle takes when it rolls, that that is straight. Circle could not roll on other surfaces smoothly.

Equation

A circle with a diameter of

$l$ can be constructed by drawing the line that satisfies

$2\sqrt { { x }^{ 2 }+{ y }^{ 2 } } ={ l }$ .

Hypervolumes

• vertex count =$N/A$
• edge length (circumference) =$\pi l$
• surface area =$\frac { \pi }{ 4 } { l }^{ 2 }$

Subfacets

• 1 circle (1D)

A circle has no zero-dimensional subfacets. Its only one-dimensional subfacet is its edge, which is also, quite confusingly, called a circle. To unambiguously distinguish between the 1D length and the 2D area, the area can be called a "disc".

See also

	Zeroth	First	Second	Third	Fourth	Fifth	Sixth	Seventh	Eighth	Ninth	Tenth
Simplex	Point	Line	Triangle	Tetrahedron	Pentachoron	Hexateron	Heptapeton	Octaexon	Enneazetton	Decayotton	Hendecaxennon
Hypercube	Point	Line	Square	Cube	Tesseract	Penteract	Hexeract	Hepteract	Octeract	Enneract	Dekeract
Cross	Point	Line	Square	Octahedron	Hexadecachoron	Pentarss	Hexarss	Heptarss	Octarss	Ennearss	Decarss
Hypersphere	Point	Line	Circle	Sphere	Glome	Hyperglome	Hexaphere	Heptaphere	Octaphere	Enneaphere	Decaphere