# The Geometry of a Cycloid

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The circle has a radius of 8. As the circle rolls along the line, the point P (a pencil point) draws a curve.

a) Draw the curve for three complete revolutions of the circle.

b) Find the area between the curve (one loop) and the line.

c) Find the length of the curve - all three loops.

https://brainmass.com/math/geometry-and-topology/geometry-cycloid-36747

#### Solution Preview

The arc length of one hump of a cycloid is marked by:

L = 8r (where r is the radius of the circle)

The area under the curve is marked by:

A = ...

#### Solution Summary

The solution shows how to calculate the area of a cycloid and the length of three complete revolutions.

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