Geometry and its Applications in Arts, Nature and Technology

Inhaltsverzeichnis

Introduction.- An idealized world out of simple elements: Points, straight lines and circles in the drawing plane. Special points inside the triangle. Elemental building blocks in space. Euclidean space. Polarity, duality and inversion. Projective and non-euclidean geometry.- Projections and shadows - Reduction of the dimension: The principle of the central projection. Through restrictions to parallel projection and normal projection. Assigned normal projections. The difference about technical drawing.- Polyhedra: Multiple faced and multi-sided: Congruence transformations. Convex polyhedral. Platonic solids. Other special classes of polyhedral. Planar sections of prisms and pyramids.- Curved but simple: Planar and spatial curves. The sphere. Cylinder surfaces. The ellipse as a planar section of a cylinder of revolution.- More about conic sections and developable surfaces: Cone surfaces. Conic sections. General developables (torses). About maps and "sphere developments". The "physical" reflection in a circle, a sphere and a cylinder of revolution.- Prototypes: Second-order surfaces. Three types of spatial points. Surfaces of revolution. The torus as a prototype for all other surfaces of revolution. Pipe and duct surfaces.- Further remarkable classes of surfaces: Ruled surfaces. Helical surfaces. Different types of spiral surfaces. Minimal surfaces.- The endless variety of curved surfaces: Mathematical surfaces and free-form surfaces. Interpolating surfaces. Bézier- and B-spline-curves. Bézier- and B-spline-surfaces. Surface design, only differently.- Photographic image and individual perception: The human eye and the pinhole camera. Different techniques of perspective. Reconstruction of spatial objects. Other perspectives. Geometry at the water surface.- Everything is moving - Kinematics: The pole, about which everything revolves. Different mechanisms. Ellipse movement. Trochoid motion.- Movement in space: Movement on the sphere. Genmeral spatial movements. Where is the sun? About sundials.- A: The variety of tessellations.- B: A course in free hand drawing.- C: A geometrical course about photography.- D Nature of geometry and geometry of nature.

Geometry and its Applications in Arts, Nature and Technology

Buch (Gebundene Ausgabe)

61,99 €

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Beschreibung

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

12.12.2012

Verlag

Birkhäuser

Seitenzahl

512

Maße (L/B/H)

24,5/18/3 cm

Beschreibung

Rezension

From the reviews: "A marvelous book, abundantly illustrated. It contains many applications ... all with an underlying geometric flavor. ... What is immediately striking at first glance is the luxury of this publication: thick paper with hundreds of colorful glossy pictures and graphs. If you love books and geometry, this is one to fall in love with. ... This picture book is more than just a coffee-table book ... of a math department, because it contains not only many pictures, but also gives theorems and proofs(!)." (A. Bultheel, The European Mathematical Society, February, 2013)

Details

Einband

Gebundene Ausgabe

Erscheinungsdatum

12.12.2012

Verlag

Birkhäuser

Seitenzahl

512

Maße (L/B/H)

24,5/18/3 cm

Gewicht

1372 g

Auflage

1

Sprache

Deutsch, Englisch

ISBN

978-3-99043-528-1

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  • Geometry and its Applications in Arts, Nature and Technology
  • Introduction.- An idealized world out of simple elements: Points, straight lines and circles in the drawing plane. Special points inside the triangle. Elemental building blocks in space. Euclidean space. Polarity, duality and inversion. Projective and non-euclidean geometry.- Projections and shadows - Reduction of the dimension: The principle of the central projection. Through restrictions to parallel projection and normal projection. Assigned normal projections. The difference about technical drawing.- Polyhedra: Multiple faced and multi-sided: Congruence transformations. Convex polyhedral. Platonic solids. Other special classes of polyhedral. Planar sections of prisms and pyramids.- Curved but simple: Planar and spatial curves. The sphere. Cylinder surfaces. The ellipse as a planar section of a cylinder of revolution.- More about conic sections and developable surfaces: Cone surfaces. Conic sections. General developables (torses). About maps and "sphere developments". The "physical" reflection in a circle, a sphere and a cylinder of revolution.- Prototypes: Second-order surfaces. Three types of spatial points. Surfaces of revolution. The torus as a prototype for all other surfaces of revolution. Pipe and duct surfaces.- Further remarkable classes of surfaces: Ruled surfaces. Helical surfaces. Different types of spiral surfaces. Minimal surfaces.- The endless variety of curved surfaces: Mathematical surfaces and free-form surfaces. Interpolating surfaces. Bézier- and B-spline-curves. Bézier- and B-spline-surfaces. Surface design, only differently.- Photographic image and individual perception: The human eye and the pinhole camera. Different techniques of perspective. Reconstruction of spatial objects. Other perspectives. Geometry at the water surface.- Everything is moving - Kinematics: The pole, about which everything revolves. Different mechanisms. Ellipse movement. Trochoid motion.- Movement in space: Movement on the sphere. Genmeral spatial movements. Where is the sun? About sundials.- A: The variety of tessellations.- B: A course in free hand drawing.- C: A geometrical course about photography.- D Nature of geometry and geometry of nature.