Cylinder (EntityTopic, 14)

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{{Rotope Nav|10|11|12|(I'I)<br>Triangular torus|(II)I<br>Cylinder|(II)'<br>Cone}}
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{{Bracketope Nav|6|7|8|[<xy>z]<br>Cuboid|[(xy)z]<br>Cylinder|<[xy]z><br>Wide octahedron|hedra}}

Revision as of 07:15, 20 June 2007

Template:Shape

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
total edge length = 4πr
surface area = 2πr(r+h)
volume = πr2h
[!x,!y] ⇒ rectangle with width (2rcos(πn/2)), height (h)
[!z] ⇒ circle of radius (r)




Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind

Template:Rotope Nav

6. [z]
Cuboid
7. [(xy)z]
Cylinder
8. <[xy]z>
Wide octahedron
List of bracketopes