In 1899, Frank Morley (1860-1937) professor of mathematics at John Hopkins University discovered a novel theorem for 2-dimensional plane geometry http://en.wikipedia.org/wiki/Frank_Morley. It states that if the angle trisectors are drawn at each vertex of any scalene triangle, adjacent trisectors meet at the vertices of a smaller equilateral triangle found within the plane figure, see http://mathworld.wolfram.com/MorleysTheorem.html.

The trillion dollars question: Is there a multidimensional extension of Morley’s theorem? The answer could possibly help clarify the differences between general relativity and quantum mechanics and subsequently their possible unification. In the theory of elementary particles, strongly interacting particles are called hadrons and they are subdivided into baryons and mesons. The fundamental structure of all baryons is the quark triplet configuration. This is topologically equivalent to an equilateral triangle at the infinitesimal Planck scale of internal composite structures of quarks which in 3-space is that of a tetrahedron in contrast to the cubic structures of all leptons. However, at irreducible constant multiples of Planck length the tetrahedron is more compact than the cube. On the other hand, the same cannot be said about the metric tensors of non-Euclidean spacetime structure of general relativity.