Circle (EntityTopic, 15)

From Higher Dimensions Database


A circle refers to the surface of a perfectly symmetrical planar object.

Equations

  • Variables:
r ⇒ radius of circle
  • All points (x, y) that lie on the surface of a circle will satisfy the following equation:
x2 + y2 = r2
total edge length = 2πr
area = πr2
[!x,!y] ⇒ line of length (rcos(πn/2))

Homology groups

Any unstated homology group is the trivial group 0.

0-frame
N/A
1-frame (circle)
H0 = ℤ, H1 = ℤ
2-frame (disc)
H0 = ℤ

Use

Circular faces are found in these trishapes on FGwiki:


Notable Dishapes
Flat: trianglesquarepentagonhexagonoctagondecagon
Curved: circle


1. 1
Digon
2. 2
Circle
3. 11
Square
List of tapertopes


a. b. 1a. II
Square
1b. (II)
Circle
2a. III
Cube
2b. (III)
Sphere
List of toratopes


2. [II]
Square
3. (II)
Circle
4. [III]
Cube
List of bracketopes