Cylinder (EntityTopic, 14)
From Hi.gher. Space
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| - | {{Shape|Cylinder|http://img392.imageshack.us/img392/1103/cylinder8gi.png|3|3, 2, 0|0|N/A|N/A|[[Line (object)|E]][[Circle|L]]E|21 (x,y),z|N/A|N/A|N/A}} | + | {{Shape|Cylinder|http://img392.imageshack.us/img392/1103/cylinder8gi.png|3|3, 2, 0|0|N/A|N/A|[[Line (object)|E]][[Circle|L]]E|21 (x,y),z|N/A|N/A|N/A|11}} |
== Geometry == | == Geometry == | ||
A '''cylinder''' is a special case of a [[prism]] where the base is a [[circle]]. | A '''cylinder''' is a special case of a [[prism]] where the base is a [[circle]]. | ||
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{{Polyhedra}} | {{Polyhedra}} | ||
| - | {{ | + | {{Rotope Nav|10|11|12|(I'I)<br>Triangular torus|(II)I<br>Cylinder|(II)'<br>Cone}} |
Revision as of 12:13, 17 June 2007
Geometry
A cylinder is a special case of a prism where the base is a circle.
Equations
- Assumption: Cylinder is centered at the origin.
- Variables:
r ⇒ radius of cylinder
h ⇒ height of cylinder
- All points (x, y, z) that lie on the surface of a cylinder will satisfy the following equations:
x2 + y2 = r2
abs(z) ≤ h/2
-- or --
x2 + y2 < r2
abs(z) = h/2
- All points (x, y, z) that lie on the edges of a cylinder will satisfy the following equations:
x2 + y2 = r2
abs(z) = h/2
- The hypervolumes of a cylinder are given by:
total edge length = 4πr
surface area = 2πr(r+h)
volume = πr2h
- The planar cross-sections (n) of a cylinder are:
[!x,!y] ⇒ rectangle with width (2rcos(πn/2)), height (h)
[!z] ⇒ circle of radius (r)
| 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 |
