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By George K. Francis

Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this exact and gorgeous publication! It not just reminds the older new release of the pleasures of doing arithmetic by means of hand, but in addition exhibits the hot new release what ``hands on'' quite means.

- John Stillwell, college of San Francisco

The Topological Picturebook has taught a complete new release of mathematicians to attract, to work out, and to think.

- Tony Robbin, artist and writer of Shadows of fact: The Fourth size in Relativity, Cubism, and sleek Thought

The vintage reference for a way to offer topological details visually, choked with extraordinary hand-drawn photos of complex surfaces.

- John Sullivan, Technische Universitat Berlin

A Topological Picturebook shall we scholars see topology because the unique discoverers conceived it: concrete and visible, freed from the formalism that burdens traditional textbooks.

- Jeffrey Weeks, writer of The form of Space

A Topological Picturebook is a visible ceremonial dinner for a person concerned about mathematical photos. Francis presents beautiful examples to construct one's "visualization muscles". while, he explains the underlying rules and layout strategies for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this number of narrative gemstones and fascinating hand-drawn photos, George Francis demonstrates the chicken-and-egg dating, in arithmetic, of picture and textual content. because the e-book used to be first released, the case for images in arithmetic has been received, and now it's time to think of their which means. A Topological Picturebook is still indispensable.

- Marjorie Senechal, Smith university and co-editor of the Mathematical Intelligencer

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Extra info for A Topological Picturebook

Example text

This initiates two contours, 4(23), which, in this case, cannot merge smoothly into a border or into each other. Hence they meet at a cusp, 4(33). For simplicity and optical coherence of the various parts I have not used perspective in this drawing. " Thickening the facing borders, as in 4(33) helps decide which view is intended, 4(43). The other three corners, left column, present fewer graphical problems. No contours are generated when two face edges meet, 4(21). Only one contour is generated in 4( 11) and 4(31), and it can merge with a border in both cases.

Since the solvent of many inks will smear adjacent pigments already applied, I sometimes color on alternating sides of the sheet. When using several overlays, it pays to tape the sheets together, so that they fit correctly. COMPUTER AND DRAFfING TABLE. Computer-generated visual displays certainly are marvelous aids to the imagination. This spectacular new medium has been used by Tom Banchoff [1977] and Nelson Max [1977] to produce films of great beauty and lucidity in geometry and topology, respectively.

Push the small loops (cuts 2 and 3) out from the plane of cut 1 by changing the contour cusps from 6(42) to 6(41). Next, bend the edge sharply into the keel of a hemisphere to bring the border into the equatorial plane, 6(43). CHAPTER Figure 6 2 METHODS AND MEDIA DUNS EGG 23 24 MOBIUS BAND. A TOPOLOGICAL PICTUREBOOK Figure 7. This picture shows two solutions to the the problem of visualizing a Mobius band whose border is a plane circle. It also illustrates two different graphical techniques for constructing such visualizations.

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