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cycloid

Cycloid: equation, length of arc, area

Problem
A circle of radius r rolls along a horizontal line without skidding.

  1. Find the equation traced by a point on the circumference of the circle.
  2. Determine the length of one arc of the curve.
  3. Calculate the area bounded by one arc of the curve and the horizontal line.
cycloid_small_02.gif

 

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