Circle (EntityTopic, 15)
From Hi.gher. Space
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| extra={{STS Matrix| | | extra={{STS Matrix| | ||
0 0 | 0 0 | ||
| - | 2 1}}{{STS | + | 2 1}}{{STS Tapertope |
| - | | | + | | order=1, 0 |
| - | | notation=2 ( | + | | notation=2 |
| - | | index= | + | | index=2 |
| + | }}{{STS Toratope | ||
| + | | holeseq=[1] | ||
| + | | notation=(II) | ||
| + | | index=1b | ||
}}{{STS Bracketope | }}{{STS Bracketope | ||
| index=4 | | index=4 | ||
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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 == | == Homology groups == | ||
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{{Dishapes}} | {{Dishapes}} | ||
| - | {{ | + | {{Tapertope Nav|1|2|3|1<br>Digon|2<br>Circle|11<br>Square|gons}} |
| + | {{Toratope Nav B||1|2|||II<br>Square|(II)<br>Circle|III<br>Cube|(III)<br>Sphere|gons}} | ||
{{Bracketope Nav|3|4|5|<xy><br>Diamond|(xy)<br>Circle|[xyz]<br>Cube|gons}} | {{Bracketope Nav|3|4|5|<xy><br>Diamond|(xy)<br>Circle|[xyz]<br>Cube|gons}} | ||
Revision as of 16:20, 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 |
| 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 | |||||
| 3. Diamond | 4. (xy) Circle | 5. [xyz] Cube |
| List of bracketopes | ||
