Circle (EntityTopic, 15)

From Hi.gher. Space

Revision as of 13:38, 3 January 2012

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:

• Cylinder (or Frustum) (2×, 67%)
• Cone (1×, 50%)