Thread: Club 27
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Old 14-11-2012, 06:44 PM   #148
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The 27 real or imaginary lines which lie on the general cubic surface and the 45 triple tangent planes to the surface. All are related to the 28 bitangents of the general quartic curve...A characteristic property of hyperbolic geometry is that the angles of a triangle add to less than a straight angle. In the limit as the vertices go to infinity, there are even ideal hyperbolic triangles in which all three angles are 0°. In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai-Lobachevskian geometry) is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...A triangle immersed in a saddle-shape plane
Schoute (1910) showed that the 27 lines can be put into a one-to-one correspondence with the vertices of a particular polytope in six-dimensional space in such a manner that all incidence relations between the lines are mirrored in the connectivity of the polytope and conversely (Du Val 1933). A similar correspondence can be made between the 28 bitangents and a seven-dimensional polytope (Coxeter 1928) and between the tritangent planes of the canonical curve of genus four and an eight-dimensional polytope (Du Val 1933). In mathematics, the projective special linear group PSL(2,7) (isomorphic to GL(3,2)) is a finite simple group that has important applications in algebra, geometry, and number theory...

In Medieval Jewish, Christian and Islamic legends, the Seal of Solomon was a magical signet ring said to have been possessed by King Solomon, which variously gave him the power to command demons, genies (or jinni), or to speak with animals...

Last edited by lightgiver; 14-11-2012 at 06:57 PM.
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