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Cycloid

Cycloid

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

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