Geometry and Its Applications in Arts, Nature and Technology

ISBN-13: 9783030613976 / Angielski / Miękka / 2020 / 694 str.

Georg Glaeser

Recenzje

"I liken this book to a fine museum providing a curated selection of exhibits that both informs and delights. ... The book's most distinctive and attractive aspects-- its wealth of examples and illustrations--make it a good supplement for geometry courses, providing inspiration for projects and reports. ... In summary, this book is a celebration of geometric form, and its cornucopia of examples an excellent resource for sharpening geometric reasoning and nurturing fascination with geometric form in all its guises." (Jer-Chin Chuang, MAA Reviews, June 6, 2021)

Spis treści

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.

O autorze

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.

Blurb

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.