Chemistry, physics and biology are by their nature genuinely
difficult. Mathematics, however, is man-made, and therefore not as
complicated. Two ideas form the basis for this book: 1) to use
ordinary mathematics to describe the simplicity in the structure of
mathematics and 2) to develop new branches of mathematics to
describe natural sciences.
Mathematics can be described as the addition, subtraction or
multiplication of planes. Using the exponential scale the authors
show that the addition of planes gives the polyhedra, or any solid.
The substraction of planes gives saddles. The multiplication of
planes gives the general saddle equations and the multispirals. The
equation of symmetry is derived, which contains the exponential
scale with its functions for solids, the complex exponentials with
the nodal surfaces, and the GD (Gauss Distribution) mathematics
with finite periodicity.
Piece by piece, the authors have found mathematical functions for
the geometrical descriptions of chemical structures and the
structure building operations. Using the mathematics for
dilatation; twins, trillings, fourlings and sixlings are made, and
using GD mathematics these are made periodic. This description of a
structure is the nature of mathematics itself. Crystal structures
and 3D mathematics are synonyms. Mathematics are used to describe
rod packings, Olympic rings and defects in solids. Giant molecules
such as cubosomes, the DNA double helix, and certain building
blocks in protein structures are also described mathematically.
General
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