Geometry in nature

by Hansen, Vagn Lundsgaard

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Title Statements

Full title :Geometry in nature / Vagn Lundsgaard Hansen.

Edition Statements

Publication Date:©1993.

Publication Statements

Publisher(s):AK Peters
Place of Publication:Wellesley, Mass
Language:eng
Publication Date:©1993.

The Physical Object

Description:xiii, 238 pages : : illustrations ; : 22 cm

Edition Identifiers

ISBN:1568810059, 9781568810058, 1568810555, 9781568810553, 0867202386, 9780867202380
oclc:ocm27728082
LC Classification:QA445
Dewey Decimal:516

1. Geometric Forms in Nature. 1. Spirals and the Wonderful Snail. 2. The Helix and the Twining Vine. 3. The Geometry of Soap Films. 4. The Geometry of Tiled Surfaces. 5. The Regular Polyhedra -- 2. The Topology of Surfaces. 1. Some Familiar Surfaces. 2. The Projective Plane and the Klein Bottle. 3. What Is a Closed Surface? 4. Orientable and Non-Orientable Surfaces. 5. Connected Sum of Closed Surfaces. 6. Classification of Closed Surfaces. 7. Higher-Dimensional Manifolds and Poincare's Conjecture -- 3. The Topology of Catastrophes. 1. The Origin of Catastrophe Theory. 2. Singularities: Mappings of the Plane into the Plane. 3. The Fold Catastrophe. 4. The Cusp Catastrophe. 5. Thom's Theorem for Systems with Two Control Variables and One State Variable. 6. Some Applications of the Cusp Catastrophe. 7. The Mathematics behind the Models of Catastrophe Theory. 8. The Seven Elementary Catastrophes in Space-Time. 9. Some General Remarks concerning Applications -- 4. Geometry and the Physical World. 1. On Mathematics and Its Greek Legacy. 2. Greek Astronomy and the Ptolemaic System. 3. The Copernican World, Tycho Brahe and Kepler. 4. The Breakthrough of Modern Natural Science. 5. Newton a…