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zhizhin g non euclidean geometry materials living 2022

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Textbook in PDF format 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 Blank Page

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zhizhin g non euclidean geometry materials living 2022