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By George K. Francis

Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this particular and gorgeous e-book! It not just reminds the older new release of the pleasures of doing arithmetic through hand, but in addition indicates the hot iteration what ``hands on'' fairly means.

- John Stillwell, college of San Francisco

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

- Tony Robbin, artist and writer of Shadows of truth: The Fourth measurement in Relativity, Cubism, and smooth Thought

The vintage reference for the way to give topological details visually, jam-packed with notable hand-drawn photographs of advanced surfaces.

- John Sullivan, Technische Universitat Berlin

A Topological Picturebook we could 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 somebody taken with mathematical photos. Francis presents beautiful examples to construct one's "visualization muscles". whilst, he explains the underlying ideas and layout recommendations for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this choice of narrative gemstones and interesting hand-drawn images, George Francis demonstrates the chicken-and-egg dating, in arithmetic, of picture and textual content. because the publication was once first released, the case for photographs in arithmetic has been received, and now it's time to consider their which means. A Topological Picturebook is still indispensable.

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

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Extra resources for A Topological Picturebook

Sample text

The composition of G followed by R contracts D to V. To imagine the route on D a point X of D takes, just retract the radial line XV onto D and contract the two curves in synchrony. DUNS EGG. Figure 6. A contour line drawing, 5(42) or 5(43), for the snail shaped dunce hat is too complicated to remember. Here is a more systematic way of designing a dunce hat with better symmetry as well as a simpler contour, 6(31). Moreover, it illustrates, in dimension two, a particular way of cutting and pasting topological objects which is even more useful in three dimensions.

At the bottom, the surface is immersed. It is curious that small inaccuracies in my tracing are more disturbing, when viewed stereoptically, than the wiggliness of the lines in the screen print of the wire frame. 34 A TOPOLOGICAL PICTUREBOOK ............. CANCELLING PINCH POINTS: ELABORATIONS ~ . Figure 11 These pictures explore the various possibilities for achieving a sense of space without the danger of eyestrain. Detail 11 (11) is a line drawing. The dotted part of the double curve is called the whisker.

A figure can be drawn directly on the acetate, using a line pattern or complete picture as an underlay. Ordinary drawing ink works; inks more specifically intended for drawing on film are more permanent. They contain an acid but can be erased with a suitable fluid, at least for a while. This is usually neater than xerography, but more time-consuming. 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.

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