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By George K. Francis

Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this specific and lovely booklet! It not just reminds the older new release of the pleasures of doing arithmetic via hand, but additionally exhibits the recent new release what ``hands on'' rather means.

- John Stillwell, college of San Francisco

The Topological Picturebook has taught a complete iteration 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 smooth Thought

The vintage reference for the way to offer topological details visually, choked with remarkable hand-drawn photos of complex 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 an individual enthusiastic about mathematical pictures. Francis offers beautiful examples to construct one's "visualization muscles". even as, he explains the underlying rules and layout innovations for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this selection of narrative gemstones and fascinating hand-drawn images, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of snapshot and textual content. because the ebook used to be first released, the case for photos in arithmetic has been received, and now it's time to think about their that means. A Topological Picturebook continues to be indispensable.

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

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Example text

First, isolate a detail of this corner, 4(13), and bend the (new) borders. 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).

I have, however, left the interior of the shell unshaded to heighten the contrast. The wire, that wends its way through the surface as seen through a window, is also meant to enhance the sense of spatial extension. A 2-dimensional approach is shown on the right. First reduce the number of layers by sending a point on the surface to infinity. Think of a stereographic projection from the south pole of 7(12) to the paper plane. More directly, consider a plane minus a disc and connect opposite sides of this disc with a half twisted strip, 7(13).

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.

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