# Arc length

- Author:
- Šárka Voráčová

Arc length of one arch of cycloid X(t) = (

*rt*– sin*t*,*r*– cos t) is*8r*where*r*is radius of the rolling circle. Units of measurements are the same as axis units.For different values of c you get a various type of cycloid.

- Curtate cycloid: Here the point tracing out the curve is inside the circle, which rolls on a line.
- Prolate cycloid: Here the point tracing out the curve is outside the circle, which rolls on a line.

## When rectified, the curve gives a straight line segment with the same length as the curve's arc length.

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