Circle (EntityTopic, 15)
From Hi.gher. Space
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*The [[linear]] [[cross-section]]s (''n'') of a circle are: | *The [[linear]] [[cross-section]]s (''n'') of a circle are: | ||
<blockquote>[!x,!y] ⇒ [[line (object)|line]] of length (''r''cos(π''n''/2))</blockquote> | <blockquote>[!x,!y] ⇒ [[line (object)|line]] of length (''r''cos(π''n''/2))</blockquote> | ||
| + | |||
| + | |||
| + | == Homology Groups == | ||
| + | Any unstated homology group is the trivial group 0. | ||
| + | |||
| + | 0-frame: N/A | ||
| + | |||
| + | 1-frame (circle): | ||
| + | H<sub>0</sub> = Z, H<sub>1</sub> = Z | ||
| + | |||
| + | 2-frame (disk): | ||
| + | H<sub>0</sub> = Z | ||
| + | |||
== Use == | == Use == | ||
Revision as of 07:38, 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 (disk): 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 | ||
