Note: Front Cover -- Biomathematics: Mathematics of Biostructures and Biodynamics -- Copyright Page -- Contents -- Chapter 1. Introduction -- References -- Chapter 2. Counting, Algebra and Periodicity - the Roots of Mathematics are the Roots of Life -- 2.1 Counting and Sine -- 2.2 Three Dimensions -- Planes and Surfaces, and Surface Growth -- 2.3 The Growth of Nodal Surfaces - Molecules and Cubosomes -- References 2 -- Chapter 3. Nodal Surfaces of Tetragonal and Hexagonal Symmetry, and Rods -- 3.1 Non Cubic Surfaces -- 3.2 Tetragonal Nodal Surfaces and their Rod Structures -- 3.3 Hexagonal Nodal Surfaces and their Rod Structures -- References 3 -- Chapter 4. Nodal Surfaces, Planes, Rods and Transformations -- 4.1 Cubic Nodal Surfaces -- 4.2 Nodal Surfaces and Planes -- 4.3 Cubic Nodal Surfaces and Parallel Rods -- 4.4 Transformations of Nodal Surfaces -- References 4 -- Chapter 5. Motion in Biology -- 5.1 Background and Essential Functions -- 5.2 The Control of Shape - the Natural Exponential or cosh in 3D -- 5.3 The Gauss Distribution (GD) Function and Simple Motion -- 5.4 More Motion in 3D -- References 5 -- Chapter 6. Periodicity in Biology - Periodic Motion -- 6.1 The Hermite Function -- 6.2 Flagella- Snake and Screw Motion -- 6.3 Periodic Motion with Particles in 2D or 3D -- 6.4 Periodic Motion with Rotation of Particles in 2D -- References 6 -- Chapter 7. Finite Periodicity and the Cubosomes -- 7.1 Periodicity and the Hermite Function -- 7.2 Cubosomes and the Circular Functions -- 7.3 Cubosomes and the GD-Function - Finite Periodicity and Symmetry P -- 7.4 Cubosomes and the GD-Function - Symmetry G -- 7.5 Cubosomes and the GD Function - Symmetry D -- 7.6 Cubosomes and the Handmade Function -- References 7 -- Chapter 8. Cubic Cell Membrane Systems/Cell Organelles and Periodically Curved Single Membranes -- 8.0 Introduction -- 8.1 Cubic Membranes. , 8.2 The Endoplasmatic Reticulum -- 8.3 Protein Crystallisation in Cubic Lipid Bilayer Phases and Cubosomes - Colloidal Dispersions of Cubic Phases -- 8.4 From a Minimal Surface Description to a Standing Wave Dynamic Model of Cubic Membranes -- 8.5 Periodical Curvature in Single Membranes -- References 8 -- Chapter 9. Cells and their Division - Motion in Muscles and in DNA -- 9.1 The Roots and Simple Cell Division -- 9.2 Cell Division with Double Membranes -- 9.3 Motion in Muscle Cells -- 9.4 RNA and DNA Modelling -- References 9 -- Chapter 10. Concentration Gradients, Filaments, Motor Proteins and again- Flagella -- 10.1 Background and Essential Functions -- 10.2 Filaments -- 10.3 Microtubulus and Axonemes -- 10.4 Motor Proteins and the Power Stroke -- 10.5 Algebraic Roots Give Curvature to Flagella -- References 10 -- Chapter 11. Transportation -- 11.1 Background - Examples of Docking and Budding with Single Plane Layers, and Other Simple Examples -- 11.2 Docking and Budding with Curved Single Layers -- 11.3 Transport Through Double Layers -- References 11 -- Chapter 12. Icosahedral Symmetry, Clathrin Structures, Spikes, Axons, the Tree, and Solitary Waves -- 12.1 The icosahedral symmetry -- 12.2 Hyperbolic Polyhedra, Long Cones, Cylinders and Catenoids -- 12.3 Cylinder Division and Cylinder Fusion - Cylinder Growth -- 12.4 Solitary Waves, Solitons and Finite Periodicity -- References 12 -- Chapter 13. Axon Membranes and Synapses - A Role of Lipid Bilayer Structure in Nerve Signals -- 13.1 The Nerve Impulse -- 13.2 At the Action Potential Region of the Membrane there is a Phase Transition in the Lipid Bilayer -- 13.3 A Model of a Phase-Transition/Electric Signal Coupling at Depolarisation and its Physiological Significance -- 13.4 Transmission of the Nerve Signal at the Terminal Membrane of the Neurons - Synaptic Transmission. , 13.5 Synchronisation of Muscle Cell Activation -- 13.6 The General Anaesthetic Effect -- 13.7 Physiological Significance of Involvement of a Lipid Bilayer Phase Transition in Nerve Signal Conduction -- References 13 -- Chapter 14. The Lung Surface Structure and Respiration -- 14.1 The Alveolar Surface -- 14.2 Lung Surfactant -- 14.3 Structure of Tubular Myelin - A Bilayer arranged as the Classical CLP-Surface -- 14.4 The Existence of a Coherent Surface Phase Lining the Alveoli -- 14.5 Respiration -- 14.6 Physiological Significance of the Existence of an Organised Surface Phase at the Alveolar Surface -- References 14 -- Chapter 15. Epilogue -- Acknowledgement -- References 15 -- Appendix 1. The Plane, the Cylinder and the Sphere -- Appendix 2. Periodicity -- Appendix 3. The Exponential Scale, the GD function, Cylinder and Sphere Fusion -- Appendix 4. The Exponential Scale, the Planes and the Natural Function, Addition and Subtraction 409 -- Appendix 5. Multiplication of Planes, Saddles and Spirals -- Appendix 6. Symmetry -- Appendix 7. The Complex Exponential, the Natural Exponential and the GD- Exponential - General Examples and Finite Periodicity -- Appendix 8. Classical Differential Geometry and the Exponential Scale -- Appendix 9. Mathematica (Contains the Mathematica scripts used for calculating the equations for the figures in this book.) -- Subject Index.