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Preface
Euclidean Geometry and Non-Euclidean Geometry
Abstract
Introduction
Euclidean Geometry
Non-Euclidean Hyperbolic Geometry
Non-Euclidean Eleptical Geometry
Non-Euclidean Geometry of the Higher Dimension Polytopes
Conclusion
Geometry of the Polytopes of Higher Dimensions
Abstract
Introduction
Structure of the Polytope Higher Dimension
The Structure of a N-Cube
The Structure of a N-Simplex
The Structure of a N-Cross-Polytope
Reconstruction of the Geometry of Polytopes of Higher Dimension
The Structure of the Cube with Center
The Structure of the Octahedron with Center
The Structure of the Tetrahedron with Center
Polytopic Prismahedrons
Structure of Polytopic Prisms
The Incidence Values in the Polytopic Prismahedrons
Poly-Incident and Dual Polytopes
Polytope Dual to the Product of Two Triangles
Conclusion
Non-Euclidean Properties of the Geometry of Polytopes of Higher Dimension
Abstract
Introduction
Axioms of Multidimensional Euclidean Geometry
Connection Axioms
About the Impossibility of the Axiom Systems of the N-Dimensional Geometry of Euclides for Higher Dimensional Popytopes
Inappropriatness of the Basic Principles of Classical Mechanics for the Analysis of Motion in a Space of Higher Dimensions
Movement of a Material Point in Four – Dimensional Spaces
Movement of a Material Point in a 4-Cube
Movement of a Material Point in a 4-Simplex
Movement of a Material Point in a 4-Cross-Polytope
Movement of a Material Point in n – Dimensional Spaces (n >4 )
On the Possibile Electronic Structure of Atoms in a Space of Higher Dimension
The Stationary Schrödinger Equation in a P – Dimensional Metric Space
The Decision of the Stationary Schrödinger Equation in a P – Dimension Metric Space
Quantum Numbers of Solutions of the Schrödinger Equation in a Space of Higher Dimension
Conclusion
Polytopes of the Highest Dimension of Inert Substances
Abstract
Introduction
The Dimension of Adamantane Molecules and Methods of Molecules Connecting with Each Other
The Dimension of the Adamantine Molecule
Connection Types of Adamantane Molecules
The Structure of Binary Natural Compounds
The Dimension of the Wurtzite
The Dimension of the Fluorite
The Structure of Natural Compounds with a Large Number Types of Atoms
Pomegranate Texture
Conclusion
“Inert” Substances as a Self-Regulating Medium Tending to Capture Space
Abstract
Introduction
Geometric Growth Models of Dissipative Systems
The Dimension of Clusters of Several Shells in the Form of Plato’s Bodies
Filling the Space with Simplices of Increasing Dimension
Filling the Space with Cross-Polytopes of Increasing Dimension
Clusters on an Octahedron
Conclusion
Spatial Models of Sugars and Their Compounds
Abstract
Introduction
Spatial Structure of Stereoisomers of Glyceraldehyde and Dihydroxyacetone
The Dimension of Linear Molecules of Monosaccharides with a Carbon Length from 4 to 7
Functional Dimension of Monosaccharides with a Closed Carbon Chain with Trhee Chiral Carbon Atoms
Functional Dimension of Monosaccharides with a Closed Carbon Chain with Four Chiral Carbon Atoms
3D Simplified Image of Pyranose Monosaccharide Molecules
Monosaccharide Chains
Conclusion
The Theory of the Folder and Native Structures of the Proteins
Abstract
Introduction
Dimensions of Protein Molecules
Linear Polypeptide Chain Structure
Turns of Polypeptie Chains
Spiral Polypeptide Chains
Folder Structures of the Amino Acids
Native Structure of Globular Proteins with Parallel Arrangement of Amino Acid Residues
Native Structure of Globular Proteins with Antiparallel Arangement of Aminoacide Residues
Native Structure of Globular Proteins with Parallel and Antiparallel Arragement of Amino Acid Residie, and α-Spirals
Globular Proteins as Molecular Machines
Conclusion
Geometry of the Structure of Nucleic Acids in the Space of the Highest Dimension
Abstract
Introduction
The Dimension of Phosphoric Acid and Its Residue
The Dimension of the Molecules Deribose and Deoxyribose
The Structure of the α-D-Ribose and 2-Deoxy α-D-Ribose Nucleic Acids
The Three-Dimensional Model of the Nucleic Acid Molecule
Conclusion
Interaction of Nucleic Acids in the Space of Higher Dimension and the Transmission of Hereditary Information
Abstract
Introduction
Polytopes with Antiparallel Edges
The Polytope of Hereditary Information
Hidden Nucliec Acid Bond Order
The Law of Conservation of Incidents in Polytope of Hereditary Information
Theorem
Proof
Methylated Polytope of Hereditary Information
Nucliec Acids Methylation
The Law of Conservation of Incidents in the Methylated Polytope of Hereditary Information
Conclusion
Dimension of Substances and Life
Abstract
Introduction
The Structure of Water
The Dimensional of Biomolecules
The Memory of Water
Chelated Compounds
Dimension and Genes
Conclusion
Summary
References
About the Author
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