Spirals, Helical Lines, and Spiral-Like Figures : Mathematical Playfulness in Two and Three Dimensions

• Autore: Walser Hans
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin / Heidelberg, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (157 pages)
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Rotating and Growing -- 1.1.1 Archimedean Spirals -- 1.1.2 Logarithmic Spirals -- 1.1.3 Asymptotes -- 1.2 Winding and Unwinding -- 1.3 Seeing Spirals -- 1.4 Number Spiral -- References -- 2 The Logarithmic Spiral -- 2.1 Polar Equation -- 2.2 Standardized Representation -- 2.3 Rotation and Scaling -- 2.4 Angular Logarithmic Spirals -- 2.5 Jacob Bernoulli -- 2.6 Constant Angle of Intersection -- 2.6.1 Approximation of the Logarithmic Spiral -- 2.6.2 Special Case -- 2.7 Number of Data -- 2.8 Examples of Logarithmic Spirals -- 2.8.1 Exponential Growth -- 2.8.2 Optical illusion -- 2.9 Cube Doubling with Star and Spiral -- References -- 3 The Archimedean Spiral -- 3.1 Linear Radius Function -- 3.2 Interstice -- 3.3 The Parabola Comes into Play -- 3.4 Offset Circles -- 3.5 Coloring -- 3.6 Unwinding and Winding -- 3.7 Circle Evolute -- 3.7.1 Cartography -- 3.7.2 Gears -- 3.7.3 Optical Effects -- 3.8 Examples from Everyday Life -- 3.9 The Spirals of Pythagoras -- 3.10 The Beard of Archimedes -- Reference -- 4 Screws -- 4.1 Helical Lines -- 4.2 Helix on Helix -- 4.3 Accelerated Slope -- 4.4 Screw Surfaces -- 4.5 Disaxial Helical Lines -- 4.6 On the Cone -- 4.7 Archimedean Screw -- 4.8 Curved Screw Surfaces -- 5 Angular Logarithmic Spirals -- 5.1 In the Triangle -- 5.2 In the Square -- 5.3 Quadrilateral Spirals -- 5.4 Spirals in Rectangles -- 5.4.1 DIN Rectangle -- 5.4.2 Golden Rectangle -- 5.4.3 Silver Rectangle -- 5.4.4 Arbitrary Rectangle -- 5.4.5 Pythagorean Triangles -- 5.5 Spirals in Parallelograms -- 5.6 Right-Angled Isosceles Triangles -- 5.7 Game with Squares -- 5.8 Endless Pythagoras -- 5.9 Folding Spiral -- 5.10 Similar Right-Angled Triangles -- 5.11 Witch Spiral -- 5.12 The Fibonacci Spiral -- References -- 6 Angular Archimedean Spirals -- 6.1 A Number Spiral -- 6.2 Tri-Bar Spiral. ; 6.3 Root Spirals -- 6.4 The Root Pyramid -- 6.5 Sum of Odd Numbers -- 6.6 Semi-Regular Pentagon -- References -- 7 Curvature -- 7.1 Folding Ruler -- 7.2 Curvature -- 7.3 The Clothoid -- 7.4 Road and Railway Construction -- 7.5 Another Optical Illusion -- 7.6 All Clothoids are Similar -- 7.7 Increasing Curvature -- 8 Golden Spirals -- 8.1 In the Golden Rectangle -- 8.2 The Fibonacci Curve -- References -- 9 Optical Illusions -- 9.1 Horizontal Wave Lines -- 9.2 Cylinder, Torus and Sphere -- 9.3 Circular Waves -- 9.4 Radial Wave Lines -- 9.5 Other Complex Mappings -- 10 Spherical Spirals -- 10.1 Flat Map -- 10.2 Mercator Map -- 10.3 Stereographic Projection -- 10.4 Map of Archimedes and Lambert -- 10.5 Screw Surface and Sphere -- Reference.
• Titolo autorizzato: Spirals, Helical Lines, and Spiral-Like Figures
• ISBN: 3-662-68931-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910857781903321
• Lo trovi qui: Univ. Federico II