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)
“Coming out, all the way out, is offered more and more as the political solution to our oppression. The argument goes that, if people could see just how many of us there are, some in very important places, the negative stereotype would vanish overnight. ...It is far more realistic to suppose that, if the tenth of the population that is gay became visible tomorrow, the panic of the majority of people would inspire repressive legislation of a sort that would shock even the pessimists among us.”
—Jane Rule (b. 1931)
“The truth of the thoughts that are here set forth seems to me unassailable and definitive. I therefore believe myself to have found, on all essential points, the final solution of the problems. And if I am not mistaken in this belief, then the second thing in which the value of this work consists is that it shows how little is achieved when these problems are solved.”
—Ludwig Wittgenstein (1889–1951)