1 - Introduction

Abstract

This chapter discusses tools required in order to build and describe structures with the use of mathematics. The daily use of mathematics involved somewhat heavy, such as the differential geometry, Riemann surfaces or Bonnet transformations. It is found that the 3D representations of the hyperbolic functions are the concave adding of planes and the convex subtraction of planes. These give polyhedra in the first case and saddles in the second. It is observed that the multiplication of planes gives the general saddle equations and the multispirals. The simplest complex exponential in 3D is a fundamental nodal surface, within 0.5% the same as the famous Schwartz minimal surface as found by Schwartz himself. This surface is in a way identical to a classical chemical structure. It is noted that the functions can be dissecting into planes or lines, which may be the roots that build the fundamental theorem of algebra and finite periodicity. The equation of symmetry is derived which really contains the exponential scale with its functions for solids, the complex exponentials with all the nodal surfaces, and the gauss distribution mathematics.