A Topological Picturebook (Google eBook)

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Springer Science & Business Media, Oct 24, 2006 - Mathematics - 194 pages
1 Review

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 ``hands 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

  

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Contents

WIRE FRAMES
32
HIDDEN LINES
33
ELABORATIONS
34
SPINNING A PAIR OF PANTS
35
LAMINATION AND EIGHT KNOT
37
CABLE KNOT AND COMPANION
38
CABLING TEMPLATE
39
OCTAHEDRAL HYPERBOLIC MANIFOLD
40
CHAPEAU DIAGRAM
108
ASTROIDDELTOID
109
ASSEMBLING IMMERSIONS
111
MORIN EVERSION
113
TOBACCO POUCHES
115
ASTROID FAMILY
118
CATASTROPHE MACHINE
121
MORIN TWIST
123

TETRAHEDRAL HYPERBOLIC MANIFOLD
41
BORROMEAN ORBIFOLD
42
PICTURES IN PERSPECTIVE
43
LINEAR PERSPECTIVE
44
HORIZON AND ZENITH
47
RECIPE FOR A CUBE
49
CUBE IN 321 POINT PERSPECTIVE
50
LOOKING FOR A CUBE
53
DIAGONALS
55
WHEEL AND AXLE
57
AXONOMETRICS
58
CHIAROSCURO
61
THE IMPOSSIBLE TRIBAR
65
PENROSE TRIBAR
66
IMPOSSIBLE QUADRILATERAL
67
PIPELINE
69
DICE
70
POINCARE GROUP
71
CUBIC LATTICE
73
MAN IN A CUBE
74
LEFT HANDRIGHT HAND
76
SHADOWS FROM HIGHER DIMENSION
77
CROSSING A CHANNEL
79
PLUCKER CONOID
81
PINCHING A ROMAN SURFACE
84
GAUSS MAP AND CROSS CAP
87
BODY SURFACE
90
SLICE AND SHADOW
93
WHITNEY BOTTLE
94
ROMBOY DEFORMATION
95
SPHERE EVERSIONS
99
GOLDEN RECTANGLE
100
CROSS CAP AND HANDLE
101
FORBIDDEN EVERSION
103
BASEBALL MOVE
105
ORIGINAL DESIGN
124
GROUP PICTURES
125
ZIPPING UP A DOUBLE TORUS
127
PRESENTING THE DOUBLE TORUS
129
BRAIDING HOMEOMORPHISM
130
ARTIN SWAP
132
SPHERICAL BRAIDS
133
PLATE TRICK
135
WHORL AND CHIMNEY
137
SWAPPING HANDLE CORES
140
SWAP DIAGRAM
141
LICKORISH TWIST
142
KING SOLOMON SEAL
145
THE FIGURE EIGHT KNOT
149
PROJECTIONS OF THE KNOT
150
HEXAHEDRAL COMPLEMENT
152
HEXAHEDRAL GLUING DIAGRAM
154
SEIFERT SPANNING SURFACE
156
Six HAKEN SURFACES
158
FIBER MNEMONIC
159
THE OWL AND THE PUSSYCAT
161
ISOTOPIC SEIFERT SURFACES
163
TRIVIAL FIBRATION
164
DOUBLE TORUS KNOT
165
ONE
167
Two
168
TOROIDAL SHEAR ISOTOPY
170
CYLINDRICAL SHEAR ISOTOPY
171
COMPUTING THE MONODROMY
172
HOPF FIBRATION
173
POSTSCRIPT
176
BIBLIOGRAPHY
180
INDEX
186
Copyright

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