Number Magic

This book is all original. Unlike so many other books on the topic, it is not a compilation of the works of others. Most of the number tables are so perfect that they have never even been seen before this. In fact, hardly anybody has gotten the tables to be perfect beyond squares of sizes 5 for odd sizes and 8 for even; that's how limited this area of knowledge is. The perfect size-9 has never even been seen before and it took a special transformation in 5-dimensions to manifest it.Everybody feigned from manifesting the size-6 square because it could never be found to be perfect. Actuality it is found to be at best only near-perfect (one minor step away from perfect) and that is the normal state of affairs for every magic square whose size is 2 times an odd number.Yet this is all small stuff. The book goes light years beyond these myopic topics by consecutively depicting and describing every magic square one by one up thru size-31 and sequentially, chapter by chapter, up thru the 5th dimension. The treatment deals with every possible rectangular magic number table that can be printed legibly, making the book a seminal work as well as a keepsake. It introduces a wholly new type of magic square never observed before that has its own totally independent properties, called the Matchmaker's Magic Square, yet is generalized (in the Appendix) by the same formulas as for the other magic number tables. The book introduces depth-sum tables derived from collapsing a table of higher dimension to one of lower dimension to readily observe the equal planar and linear equalities along the axes of collapse.It shows certain perfect squares to also have dual simultaneous tiling patterns in which each interlocking tile also sums to the square's characteristic number, dubbed 'ultra-perfect'.It introduces dual loom tables derived from the modulus and integer functions applied to these ultra-perfect squares. These lead directly to the original square's ultra-perfect dual square which shares the same characteristic dual tiling patterns as the original!The book introduces characteristic circles in squares, spheres in cubes and toruses in hypercubes whose incident number cells also sum to the table's characteristic number.The book uses all of these amazing yet simply-observed equality patterns to explain the distribution and count of electrons in the nested electron-shells of atoms! This solid mathematical demonstration proves the existence of actual geometrical patterns within Science itself that can only be explained by fundamental numerical patterns.All the formal math has been placed in the Appendix with the purpose of making the subject continuously readable without distractions like proofs and derivations.The book also introduces magic diamonds, two distinctly different types of magic number table whose existence has never even been surmised before. These tables are enumerated up thru size 27 for both types of diamond. And surprisingly, although comprised of a different range of numbers, still satisfies the formulas in the Appendix for regular magic squares. The book also introduces for the first time anywhere magic triangles. These are shown from size 1 thru 18. The book shows a direct 1-to-1 correlation between the numbers in a triangle and the characteristic number of magic squares.The book offers guidance to discovering additional number tables that are pentagonal and hexagonal. It shows perfect hexagons up to size 7 where every linear slice through the hexagon, parallel to one of its sides, sums to the same number!Having observed some amazing patterns in this enumeration process, the book then takes the topic on numbers and converts it into a topic on the structure of virtual space with some startling predictions for real space as described in both the Postscript and the Epilogue. It's a real mind-trip without the need for hallucinogens.