A Geometrical Picture Book

Front Cover
Springer Science & Business Media, Sep 17, 2012 - Mathematics - 292 pages
How do you convey to your students, colleagues and friends some of the beauty of the kind of mathematics you are obsessed with? If you are a mathematician interested in finite or topological geometry and combinatorial designs, you could start by showing them some of the (400+) pictures in the "picture book". Pictures are what this book is all about; original pictures of everybody's favorite geometries such as configurations, projective planes and spaces, circle planes, generalized polygons, mathematical biplanes and other designs which capture much of the beauty, construction principles, particularities, substructures and interconnections of these geometries. The level of the text is suitable for advanced undergraduates and graduate students. Even if you are a mathematician who just wants some interesting reading you will enjoy the author's very original and comprehensive guided tour of small finite geometries and geometries on surfaces This guided tour includes lots of sterograms of the spatial models, games and puzzles and instructions on how to construct your own pictures and build some of the spatial models yourself.
 

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Contents

Introduction via the Fano Plane
3
Designs
19
Configurations
27
Generalized Quadrangles
39
The Smallest ThreeDimensional Projective Space
67
The Projective Plane of Order 3 93
92
The Projective Plane of Order 4
107
The Projective Plane of Order 5
117
Generalized Polygons 173
172
Colour Pictures and Building the Models
185
Some Fun Games and Puzzles
197
Introduction via Flat Affine Planes
205
Flat Circle PlanesAn Overview
219
Spherical Circle Planes 231
230
Cylindrical Circle Planes of Rank 3
245
Toroidal Circle Planes
259

Stargazing in Affine Planes up to Order 8
125
Biplanes
135
Semibiplanes
155
The Smallest Benz Planes
161
A Models on Regular Solids
267
References
279
Index
287
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