Photos of Interactive Mathematics Miscellany and Puzzles
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Dear Alexander Bogomolny, I am very happy to say that I have found a new property of the Tetrahedron. In fact, this is a 3D generalization of theorem 1 in my paper "A Note on Reflection", published by Forum Geometricorum. Consider any Tetrahedron ABCD. Take an arbitrary point P on the space. Now, reflect P around the four centroids of the four triangular faces of the Tetrahedron. Then, the line segments joining the vertices with the symmetry image of P corresponding to the opposite faces of the vertices are concurrent. I took a photo with my smartphone since I could not find a way save the diagram in my pc. |
