Authors: Antony Ryan
Comments: 7 Pages.
Kissing Numbers (1) appear to be the product of dimension number and the dimension’s simplex vertex number for 0-3 Euclidean spatial dimensions, but depart from the linear product of dimension and dimension+1 relationship at 4-dimensions and above increasing away from this exponentially. For 0-8 dimensions there is a Coxeter Number root system type relationship. The author proposes a very simple relationship which satisfies both aforementioned patterns, but extends from dimension 0 infinitely upwards. The conjecture is seen to satisfy the non-root system 24-dimensions and leads to prediction. The simplex nature of this work may be utilised in Quantum Gravity theories similar to Causal Dynamical Triangulation.
Comments: 3 Pages. No Comments
Once the famous French mathematician Lagrange remarked that as long as algebra and geometry are not inter linked,one can not expect good results. Keeping this in mind, the author has attempted to establish an interesting classical Euclidean theorem by applying the algebra of matrices.