thomas@utah-gr.UUCP (Spencer W. Thomas) (12/01/83)
Here's another neat one. Solution is not trivial, but can supposedly be done from Euclid (I say supposedly because I solved it with vector arithmetic). Given ANY (scalene) triangle (the set of scalene triangles is dense in the set of all triangles, so you will pick one with probability 1, right?) erect equilateral triangles on all three sides (on the outside). Show that the triangle formed by connecting the centers of the equilateral triangles is itself equilateral. Have fun! (Please don't post solutions to the net, let people work on it. Thanks.) =Spencer