Monday, July 12, 2010

Fox 299

1 comment:

  1. From #160 we know the four legs meet in one point, say P.

    Let k', l', m', n' be the four legs from outer corners to P. From Thales theorem we get k'/k = l'/l = m'/m = n'/n. Hence problem is equivalent to k'^2+m'^2 = l'^2+n'^2.

    From Julian's solution to #160 we can view this figure as the orthogonal projection of a square-based pyramid having P as vertex.

    Solution to #243 ( shows that any rectangular based skewed pyramid obeys the above law if we name k, l, m, n the four edges from P.

    Since this law is true for "any" 3D pyramid, it is also true for a flat pyramid (vertex P is on the base plane).