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A cycloid is a curve representing the path of a point of a circle as it rolls along the ground.

## Definition

$x(\theta) = a(t-\sin \theta)$
$y(\theta) = a(1-\cos \theta)$

## Properties

Arc length[1]:

$s = \int\limits_0^{2\pi} 2a \sin (\theta/2) dt = 8a$

## References

1. ProofWiki - Length of Arc of Cycloid