Arc length of the cycloid corresponding to a complete rotation
Answers
Answered by
0
Answer:
The arc length of the cycloid is 4 times the diameter of the rolling circle.
For an insightful explanation of this (and much more!) free from painful calculus, have a look at section 3.6 "Arclength of Cyclogonal Arches" of the book "New Horizons in Geometry" by T. M. Apostol and M. A. Mnatsakanian. This section deals with rolling general (so not necessarily regular) polygons around other polygons. A circle rolling on a line is then just a limiting case.
Similar questions