Cylinder (EntityTopic, 14)
From Hi.gher. Space
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<blockquote>[!x,!y] ⇒ [[rectangle]] with width (2''r''cos(π''n''/2)), height (''h'')<br> | <blockquote>[!x,!y] ⇒ [[rectangle]] with width (2''r''cos(π''n''/2)), height (''h'')<br> | ||
[!z] ⇒ [[circle]] of radius (''r'')</blockquote> | [!z] ⇒ [[circle]] of radius (''r'')</blockquote> | ||
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== Cylindrogram == | == Cylindrogram == | ||
A ''cylindrogram'' is the [[surface of revolution]] of a [[parallelogram]], just as a [[cylinder]] is the surface of revolution of a [[rectangle]]. It can also be thought of as a cylinder with a cone removed from one end and placed on the other. As such, this shape has the same [[volume]] as a cylinder with the same radius and height. | A ''cylindrogram'' is the [[surface of revolution]] of a [[parallelogram]], just as a [[cylinder]] is the surface of revolution of a [[rectangle]]. It can also be thought of as a cylinder with a cone removed from one end and placed on the other. As such, this shape has the same [[volume]] as a cylinder with the same radius and height. | ||
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{{Trishapes}} | {{Trishapes}} | ||
Revision as of 14:04, 3 November 2009
A cylinder is a special case of a prism where the base is a circle.
Equations
- 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)
Cylindrogram
A cylindrogram is the surface of revolution of a parallelogram, just as a cylinder is the surface of revolution of a rectangle. It can also be thought of as a cylinder with a cone removed from one end and placed on the other. As such, this shape has the same volume as a cylinder with the same radius and height.
| 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 |
| 6. [ Cuboid | 7. [(xy)z] Cylinder | 8. <[xy]z> Wide octahedron |
| List of bracketopes | ||
