Solution
Clearly triangles ACO and ADO are congruent right angled triangles, as are triangles BEO and BFO. In addition, triangles ACO and BEO are similar. Therefore angles CAO, DAO, EBO and FBO are all equal. Denoting this angle by, the length of the belt is
This uses the fact that the length of an arc = the radius × the measure of the angle facing the arc in radians.
To find we see from the similarity of triangles ACO and BEO that
For fixed P the length of the belt depends only on the sum of the radius values r1 + r2, and not on their individual values.
Read more about this topic: Belt Problem
Famous quotes containing the word solution:
“Any solution to a problem changes the problem.”
—R.W. (Richard William)
“There’s one solution that ends all life’s problems.”
—Chinese proverb.
“What is history? Its beginning is that of the centuries of systematic work devoted to the solution of the enigma of death, so that death itself may eventually be overcome. That is why people write symphonies, and why they discover mathematical infinity and electromagnetic waves.”
—Boris Pasternak (1890–1960)