Teaching Materials/Cycloid calculus

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Title Cycloid Calculus
Description By parametrizing the cycloid, we can deduce many of the physical properties that are apparent by watching a bicycle wheel.
Concept Photographs of moving bicycles sometimes show a nice picture of the spokes at the bottom with a blur of spokes at the top. By considering the elementary calculus of the cycloid, we can discover an explanation of this phenomenon.
Goals To introduce a parametrization of the cycloid and use it to determine the tangent vector to the curve at various points.
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