Circle (EntityTopic, 15)
From Hi.gher. Space
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Any unstated homology group is the trivial group 0. | Any unstated homology group is the trivial group 0. | ||
| - | 0-frame: N/A | + | ;0-frame:N/A |
| - | + | ;1-frame (circle):H<sub>0</sub> = ℤ, H<sub>1</sub> = ℤ | |
| - | 1-frame (circle): | + | ;2-frame (disc):H<sub>0</sub> = ℤ |
| - | H<sub>0</sub> = | + | |
| - | + | ||
| - | 2-frame ( | + | |
| - | H<sub>0</sub> = | + | |
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== Use == | == Use == | ||
Revision as of 14:11, 24 November 2009
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 |
| 3. Diamond | 4. (xy) Circle | 5. [xyz] Cube |
| List of bracketopes | ||
