Cone (EntityTopic, 11)
From Hi.gher. Space
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*Variables: | *Variables: | ||
<blockquote>''r'' ⇒ radius of base of cone<br> | <blockquote>''r'' ⇒ radius of base of cone<br> | ||
| - | ''h'' ⇒ height of cone</blockquote> | + | ''h'' ⇒ perpendicular height of cone</blockquote> |
*All points (''x'', ''y'', ''z'') that lie on the surface of a cone will satisfy the following equations: | *All points (''x'', ''y'', ''z'') that lie on the surface of a cone will satisfy the following equations: | ||
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*The [[planar]] [[cross-section]]s (''n'') of a cone are: | *The [[planar]] [[cross-section]]s (''n'') of a cone are: | ||
| - | <blockquote>[!x,!y] ⇒ '' | + | <blockquote>[!x,!y] ⇒ isosceles [[triangle]] of base length 2''r'' and perpendicular height ''h''<br> |
| - | [!z] ⇒ circle of radius (''r'' − '' | + | [!z] ⇒ circle of radius (''r'' − {{Over|''nr''|''h''}})</blockquote> |
== Arrinder == | == Arrinder == | ||
Revision as of 12:34, 18 November 2011
A cone is a special case of a pyramid where the base is a circle.
The cone is one of the few curved polyhedra that satisfy Euler's F + V = E + 2.
Equations
- Variables:
r ⇒ radius of base of cone
h ⇒ perpendicular height of cone
- All points (x, y, z) that lie on the surface of a cone will satisfy the following equations:
Unknown
- All points (x, y, z) that lie on the edges of a cone will satisfy the following equations:
x2 + y2 = r2
z = 0
- The hypervolumes of a cone are given by:
total edge length = 2πr
surface area = πr(r + √(r2 + h2))
volume = π∕3 · r2h
- The planar cross-sections (n) of a cone are:
[!x,!y] ⇒ isosceles triangle of base length 2r and perpendicular height h
[!z] ⇒ circle of radius (r − nr∕h)
Arrinder
An arrinder is the surface of revolution of an arrow, just as a cone is the surface of revolution of a triangle. It can also be thought of as a cone with a smaller cone removed from the base. As such, this shape's volume is the difference between the volume of the two aforementioned cones.
| 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 |
| 7. 111 Cube | 8. 21 Cone | 9. [11]1 Square pyramid |
| List of tapertopes | ||
