Prolate Cycloid
The path traced out by a fixed point at a radius 
, where 
is the radius
of a rolling circle, also sometimes called an extended
cycloid. The prolate cycloid contains loops, and has parametric
equations
 |  |  |
(1)
|
 |  |  |
(2)
|
The arc length from 
is
 |
(3)
|
where
 |
(4)
|
 |
(5)
|
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