The Universe of Conics : From the ancient Greeks to 21st century developments （Softcover Reprint of the Original 1st 2016）

Glaeser, Georg/ Stachel, Hellmuth/ Odehnal, Boris

Springer Spektrum（2018/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 488 p.
• 言語 ENG
• 商品コード 9783662568811
• DDC分類 516.2152

Full Description

This text presents the classical theory of conics in a modern form. It includes many novel results that are not easily accessible elsewhere. The approach combines synthetic and analytic methods to derive projective, affine and metrical properties, covering both Euclidean and non-Euclidean geometries.

With more than two thousand years of history, conic sections play a fundamental role in numerous fields of mathematics and physics, with applications to mechanical engineering, architecture, astronomy, design and computer graphics.

This text will be invaluable to undergraduate mathematics students, those in adjacent fields of study, and anyone with an interest in classical geometry.

Augmented with more than three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.

Contents

1 Introduction.- 2 Euclidean plane.- 3 Differential Geometry.- 4 Eucledian 3-space.- 5 Projective Geometry.- 6 Projective conics.- 7 Polarities and pencils.- 8 Affine Geometry.- 9 Special problems.- 10 Other geometries.- Index.