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Feynman's Triangle Problem

Inspired by this thread on /r/math ==> This comment has some interesting links and further readings: Apparently this started as a dinnertime conversation with Richard Feynman: According to R.J. Cook & G.V. Wood (2004). Feynman's Triangle. Mathematical Gazette 88:299-302, this triangle result puzzled famous physicist Richard Feynman in a dinner conversation: For a triangle ABC in the plane, if each vertex is joined to the point (1/3) along the opposite side (measured say anti-clockwise), then area ABC = 7 x area UWV (the inner triangle formed by these lines).