Circle (EntityTopic, 15)
From Hi.gher. Space
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Revision as of 17:10, 18 November 2011
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
- The hypervolumes of a circle are given by:
total edge length = 2πr
area = πr2
- The linear cross-sections (n) of a circle are:
[!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: | 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 | ||
