Circle (EntityTopic, 15)
From Hi.gher. Space
A circle refers to the surface of a perfectly symmetrical planar object.
Sometimes, the word circle is used to refer to the edge, while the filled in version is called a disc.
Equations
- Variables:
r ⇒ radius of circle
- All points (x, y) that lie on the surface of a circle will satisfy the following equation:
x^{2} + y^{2} = r^{2}
- The hypervolumes of a circle are given by:
total edge length = 2πr
area = πr^{2}
- The linear cross-sections (n) of a circle are:
[!x,!y] ⇒ digon of length (rcos(πn/2))
Homology groups
Any unstated homology group is the trivial group 0.
- 0-frame
- N/A
- 1-frame (circle)
- H_{0} = ℤ, H_{1} = ℤ
- 2-frame (disc)
- H_{0} = ℤ
Use
Circular faces are found in these trishapes on FGwiki:
Notable Dishapes | |
Flat: | triangle • square • pentagon • hexagon • octagon • decagon |
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 |