# Sphere (EntityTopic, 15)

(Difference between revisions)
 Revision as of 07:15, 20 June 2007 (view source)Keiji (Talk | contribs)m← Older edit Revision as of 08:09, 25 June 2007 (view source)Keiji (Talk | contribs) m (rm per FGwiki:Shape assumptions)Newer edit → Line 4: Line 4: === Equations === === Equations === - *Assumption: Sphere is centered at the origin. *Variables: *Variables:
''r'' ⇒ radius of sphere
''r'' ⇒ radius of sphere

## Geometry

A sphere refers to the surface of a perfectly symmetrical realmic object.

### Equations

• Variables:
r ⇒ radius of sphere
• All points (x, y, z) that lie on the surface of a sphere will satisfy the following equation:
x2 + y2 + z2 = r2
total edge length = 0
surface area = 4πr2
volume = 4πr33-1
[!x,!y,!z] ⇒ circle of radius (rcos(πn/2))

### Mapping

When the surface of a sphere is mapped onto a rectangle {(-1,-1),(1,-1),(1,1),(-1,1)}, the surface will be horizontally stretched such that the further away from the equator of the sphere a point is, the more it is stretched. The top and bottom edges of the rectangle will converge into a single point. Leaving the top edge of the rectangle will continue entering from the top edge at the position (x±1,1). Similarly, leaving the bottom edge of the rectangle will continue entering from the bottom edge at the position (x±1,-1).

 Notable Trishapes Regular: tetrahedron • cube • octahedron • dodecahedron • icosahedron Direct truncates: tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate Mesotruncates: stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron Snubs: snub staurohedron • snub rhodohedron Curved: sphere • torus • cylinder • cone • frustum • crind
 12. (z)Narrow crind 13. (xyz)Sphere 14. [xyzw]Tesseract List of bracketopes