Cylinder (EntityTopic, 14)

From Hi.gher. Space

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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)

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