UID:
almahu_9947367880502882
Format:
1 online resource (355 p.)
ISBN:
1-281-12005-7
,
9786611120054
,
0-08-053734-0
Content:
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 multip
Note:
Description based upon print version of record.
,
Front Cover; The Nature of Mathematics and the Mathematics of Nature; Copyright Page; Contents; Chapter 1. Introduction; References 1; Publications on 'The Exponential Scale'; Chapter 2. The Roots of Mathematics - the Roots of Structure; 2.1 Multiplication of Polynomials; 2.2 Addition of Polynomials; 2.3 Saddles; Exercises 2; References 2; Chapter 3. The Natural Function and the Exponential Scale; 3.1 Polygons and Planar Geometry; 3.2 Polyhedra and Geometry; 3.3 Curvature; 3.4 The Fundamental Polyhedra- and Others; 3.5 Optimal Organisation and Higher Exponentials; Exercises 3; References 3
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Chapter 4. Periodicity and the Complex Exponential4.1 The Translation Vector; 4.2 The Complex Exponential and Some Variants; 4.3 Some Other Exponentials; Exercises 4; References 4; Chapter 5. The Screw and the Finite Periodicity with the Circular Punctions; 5.1 Chirality, the Screw and the Multi Spiral; 5.2 The Bending of a Helix; 5.3 Finite Periodicity- Molecules and the Larsson Cubosomes; Exercises 5; References 5; Chapter 6. Multiplication, Nets and Planar Groups; 6.1 Lines and Saddles; 6.2 Nets with Two Planes, and Variations; 6.3 Nets with Three Planes, and Variations
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6.4 Nets with Four Planes, and Variations6.5 Structures in 3D from the Nets; 6.6 Quasi; Exercises 6; References 6; Chapter 7. The Gauss Distribution Function; 7.1 The GD Function and Periodicity; 7.2 The GD Function and Periodicity in 3D; 7.3 The BCC and Diamond Symmetries; 7.4 The Link to Cosine; Exercises 7; References 7; Chapter 8. Handmade Structures and Periodicity; 8.1 Prelude; 8.2 Simplest of Periodic Structures; 8.3 Contact of Spheres in Space- Structures and Surfaces; 8.4 How Tetrahedra and Octahedra meet in Space; Exercises 8; References 8; Chapter 9. The Rods in Space
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9.1 Primitive Packing of Rods9.2 Body Centred Packing of Rods; 9.3 Tetragonal and Hexagonal Packing of Rods; 9.4 Larsson Cubosomes of Rods; 9.5 Packing of Rods, and their Related Surfaces; Exercises 9; References 9; Chapter 10. The Rings, Addition and Subtraction; 10.1 Some Simple Examples of Subtraction and Addition in 3D; 10.2 The Rings; 10.3 More Ways to make Rings; 10.4 More Subtraction- Hyperbolic Polyhedra; Exercises 10; References 10; Chapter 11. Periodic Dilatation- Concentric Symmetry; 11.1 Dilatation and Translation in 2D; 11.2 Dilatation and Translation in 3D; 11.3 Pure Dilatation
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Exercises 11References 11; Appendix 1. Mathematica; Appendix 2. Curvature and Differential Geometry; Appendix 3. Formal Way to Derive the Shapes of Polyhedra; Appendix 4. More Curvature; Appendix 5. Raison d'etre; Subject Index
,
English
Additional Edition:
ISBN 0-444-82994-6
Language:
English
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