Geometry and its Applications in Arts, Nature and Technology

2. Auflage 2020
ISBN: 978-3-030-61397-6
Verlag: Springer International Publishing

Buch, Englisch, 694 Seiten, Paperback, Format (B × H): 168 mm x 240 mm, Gewicht: 1330 g

This book returns geometry to its natural habitats: the arts, nature and technology. Throughout the book, geometry comes alive as a tool to unlock the understanding of our world.

Assuming only familiarity with high school mathematics, the book invites the reader to discover geometry through examples from biology, astronomy, architecture, design, photography, drawing, engineering and more. Lavishly illustrated with over 1200 figures, all of the geometric results are carefully derived from scratch, with topics from differential, projective and non-Euclidean geometry, as well as kinematics, introduced as the need arises. The mathematical results contained in the book range from very basic facts to recent results, and mathematical proofs are included although not necessary for comprehension.

With its wide range of geometric applications, this self-contained volume demonstrates the ubiquity of geometry in our world, and may serve as a source of inspiration for architects, artists, designers, engineers, and natural scientists. This new edition has been completely revised and updated, with new topics and many new illustrations.

Zielgruppe

Popular/general

Autoren/Hrsg.

Glaeser, Georg

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Technische Wissenschaften Technik Allgemein Konstruktionslehre und -technik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau Konstruktionslehre, Bauelemente, CAD
• Geisteswissenschaften Kunst Kunst, allgemein
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie
• Geisteswissenschaften Design Design: Allgemeines & Theorie

Inhaltsverzeichnis

1 An idealized world made of simple elements.- 2 Projections and shadows: Reduction of the dimension.- 3 Polyhedra: multi-faced and multi-sided.- 4 Curved but simple.- 5 More about conic sections and developable surfaces.- 6 Prototypes.- 7 Further remarkable classes of surfaces.- 8 The endless variety of curved surfaces.- 9 Photographic image and individual perception.- 10 Kinematics: Geometry in motion.- 11 Spatial motions.- 12 A variety of filling patterns.- 13 The nature of geometry and the geometry of nature.- 14 More applications.- A Geometrical freehand drawing.- B Geometry and photography.- Bibliography.- Index.

Über Autor(innen)

Georg Glaeser, born in 1955, obtained his PhD and habilitation in geometry at the Vienna University of Technology. Since 1998, he is full professor of geometry at the University of Applied Arts Vienna. He is the author or coauthor of more than twenty books on geometry, mathematics, computer graphics, evolutionary biology, and photography.