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Book Cover
E-book
Author Francis, George K.

Title A topological picturebook / George K. Francis
Edition First soft-cover edition
Published New York : Springer, [2007]
©2007
Online access available from:
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Description 1 online resource (xv, 194 pages, 4 unnumbered pages of plates) : illustrations (some color)
Contents I. Blackboard Dunce Cap -- II. Diapered Trefoil Knot -- III. Cross Cap and Limacon -- IV. Etruscan Venus -- Chapter 1. Descriptive Topology -- 1. Saddle in a Box -- 2. Saddle in a Drum -- 3. Whitney Umbrella -- 4. Cayley Cusp -- 5. Pinch Point/Branch Point -- Chapter 2. Methods and Media -- 1. Cubic Metaphor -- 2. Basic Surface Patterns -- 3. Triprong -- 4. Rounding a Polyhedral Saddle -- 5. Dunce Hat -- 6. Duns Egg -- 7. Mobius Bands -- Ink and Paper -- Chalk and Blackboard -- Slide and Transparency -- Computer and Drafting Table -- 8. Function Graphs -- 9. Cancelling Pinch Points: Wire Frames -- 10. Cancelling Pinch Points: Hidden Lines -- 11. Cancelling Pinch Points: Elaborations -- 12. Spinning a Pair of Pants -- 13. Lamination and Eight Knot -- 14. Cable Knot and Companion -- 15. Cabling Template -- 16. Octahedral Hyperbolic Manifold -- 17. Tetrahedral Hyperbolic Manifold -- 18. Borromean Orbifold -- Chapter 3. Pictures in Perspective -- 1. Linear Perspective -- 2. Horizon and Zenith -- 3. Recipe for a Cube -- 4. Cube in 3-2-1 Point Perspective -- 5. Looking for a Cube -- 6. Diagonals -- 7. Wheel and Axle -- 8. Axonometrics -- 9. Chiaroscuro -- Chapter 4. Impossible Tribar -- 1. Penrose Tribar -- 2. Impossible Quadrilateral -- 3. Pipeline -- 4. Dice -- 5. Poincare Group -- 6. Cubic Lattice -- 7. Man in a Cube -- 8. Left Hand/Right Hand -- Chapter 5. Shadows from Higher Dimension -- 1. Crossing a Channel -- 2. Plucker Conoid -- 3. Pinching a Roman Surface -- 4. Gauss Map and Cross Cap -- 5. Boy Surface -- 6. Slice and Shadow -- 7. Whitney Bottle -- 8. Romboy Deformation -- Chapter 6. Sphere Eversions -- 1. Golden Rectangle -- 2. Cross Cap and Handle -- 3. Forbidden Eversion -- 4. Baseball Move -- 5. Chapeau Diagram -- 6. Astroid/Deltoid -- 7. Assembling Immersions -- 8. Morin Eversion -- 9. Tobacco Pouches -- 10. Astroid Family -- 11. Catastrophe Machine -- 12. Morin Twist -- 13. Original Design -- Chapter 7. Group Pictures -- 1. Zipping up a Double Torus -- Presenting the Double Torus -- 2. Braiding Homeomorphism -- 3. Artin Swap -- 4. Spherical Braids -- 5. Plate Trick -- 6. Whorl and Chimney -- 7. Swapping Handle Cores -- 8. Swap Diagram -- 9. Lickorish Twist -- 10. King Solomon Seal -- Chapter 8. Figure Eight Knot -- 1. Projections of the Knot -- 2. Hexahedral Complement -- 3. Hexahedral Gluing Diagram -- 4. Seifert Spanning Surface -- 5. Six Haken Surfaces -- 6. Fiber Mnemonic -- 7. Owl and the Pussycat -- 8. Isotopic Seifert Surfaces -- 9. Trivial Fibration -- 10. Double Torus Knot -- 11. Tetrahedral Eight Knot: One -- 12. Tetrahedral Eight Knot: Two -- 13. Toroidal Shear Isotopy -- 14. Cylindrical Shear Isotopy -- 15. Computing the Monodromy -- 16. Hopf Fibration
Summary Praise for George Francis's A Topological Picturebook: Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what h̀̀ands on'' really means. - John Stillwell, University of San Francisco The Topological Picturebook has taught a whole generation of mathematicians to draw, to see, and to think. - Tony Robbin, artist and author of Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought The classic reference for how to present topological information visually, full of amazing hand-drawn pictures of complicated surfaces. - John Sullivan, Technische Universitat Berlin A Topological Picturebook lets students see topology as the original discoverers conceived it: concrete and visual, free of the formalism that burdens conventional textbooks. - Jeffrey Weeks, author of The Shape of Space A Topological Picturebook is a visual feast for anyone concerned with mathematical images. Francis provides exquisite examples to build one's "visualization muscles". At the same time, he explains the underlying principles and design techniques for readers to create their own lucid drawings. - George W. Hart, Stony Brook University In this collection of narrative gems and intriguing hand-drawn pictures, George Francis demonstrates the chicken-and-egg relationship, in mathematics, of image and text. Since the book was first published, the case for pictures in mathematics has been won, and now it is time to reflect on their meaning. A Topological Picturebook remains indispensable. - Marjorie Senechal, Smith College and co-editor of the Mathematical Intelligencer
Bibliography Includes bibliographical references (pages 180-185) and index
Notes Print version record
Subject Topology -- Graphic methods.
Form Electronic book
ISBN 0387681205 (electronic bk.)
9780387681207 (electronic bk.)