Circle (EntityTopic, 15)
From Hi.gher. Space
(Difference between revisions)
Username5243 (Talk | contribs) (Let's try this...) |
Username5243 (Talk | contribs) |
||
| Line 2: | Line 2: | ||
{{STS Shape | {{STS Shape | ||
| dim=2 | | dim=2 | ||
| - | | elements=1, 0 | + | | elements=1 circular edge, 0 |
| genus=0 | | genus=0 | ||
| ssc=(xy) | | ssc=(xy) | ||
| Line 24: | Line 24: | ||
A '''circle''' refers to the surface of a perfectly symmetrical [[planar]] object. | 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 == | == Equations == | ||
| Line 37: | Line 39: | ||
*The [[linear]] [[cross-section]]s (''n'') of a circle are: | *The [[linear]] [[cross-section]]s (''n'') of a circle are: | ||
| - | <blockquote>[!x,!y] ⇒ [[ | + | <blockquote>[!x,!y] ⇒ [[digon]] of length (''r''cos(π''n''/2))</blockquote> |
== Homology groups == | == Homology groups == | ||
Latest revision as of 16:21, 25 March 2017
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:
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] ⇒ digon 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 | ||
