Publisher's Synopsis
This book is about constructing number arrangements in a two dimensional space. It illustrates many ways to place numbers on matrices of different shapes, so that their sum can be represented by mathematical equations. The use of color enhances the visibility of the number partitions according to the recurrence level or just the different classes. Many of the arrangements based on equations can be extended to larger size without the need to change existing number placements, resulting in a truly scalable number arrangement. The book starts with number arrangements based on least common multiples, Cartesian products, averages, and recursive product arrangements. The LCM based arrangements result in the total value for all cells of each color to be equal. The Cartesian product arrangements illustrate a way to generate a two dimensional matrix from linear number series representing any equation. So it is possible to create (1+3+5+...) crossed with (1+2+3+4+5+...) to get a value for f(n) = n^2 × n(n+1)/2. The arrangements based on average are meant to generate additional matrices using simple average generation rules. The book then illustrates numerous ways to construct matrices of different shapes for a total sum of n^3 or n^4. They include different types of matrices such as rectangular, square, hexagonal, pentagonal, triangular, among others. In addition, a few regular matrices have also been generated with help from the computer to identify increasing levels for square matrices such that they have interesting number patterns for the different levels. Number arrangements based on factorials, exponentials, permutations, combinations, and Pascal's triangle are also presented. Finally, a step by step method is provided to generate a matrix representation based on any arbitrary number. The topographical charts shown for many of the arrangements clearly illustrate that the number placements are orderly and quite varied even for different arrangements for the same function. Two such arrangements can be compared at a glance by comparing their 3-dimensional charts. The book also shows that there exist exact equations to represent number arrangements in two dimensional space, i.e., the equation defines each number in the matrix. Such equations are based on multiple variables and helped create arrangements for n^3, n^4, and other summations. It should be noted that the subject matter in this book, albeit provided with visual illustrations - is not meant for casual reading - but for those wearing 'mathematical glasses' - with a view towards future research scholars to publish and flourish. Also available directly from the publisher, an Amazon company, at: CreateSpace eStore: https: //www.createspace.com/4173844
