A Geometrical Picture Book

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.

I Finite Geometries.- 1 Introduction via the Fano Plane.- 2 Designs.- 3 Configurations.- 4 Generalized Quadrangles.- 5 The Smallest Three-Dimensional Projective Space.- 6 The Projective Plane of Order 3.- 7 The Projective Plane of Order 4.- 8 The Projective Plane of Order 5.- 9 Stargazing in Affine Planes up to Order 8.- 10 Biplanes.- 11 Semibiplanes.- 12 The Smallest Benz Planes.- 13 Generalized Polygons.- 14 Colour Pictures and Building the Models.- 15 Some Fun Games and Puzzles.- II Geometries on Surfaces.- 16 Introduction via Flat Affine Planes.- 17 Flat Circle Planes—An Overview.- 18 Flat Projective Planes.- 19 Spherical Circle Planes.- 20 Cylindrical Circle Planes of Rank 3.- 21 Toroidal Circle Planes.- A Models on Regular Solids.- B Mirror Technique Stereograms.- B.1 The Generalized Quadrangle of Order (4,2).- B.3 The Smallest Projective Space.- References.