Download e-book for kindle: A Topological Picturebook by George K. Francis

By George K. Francis

ISBN-10: 0387345426

ISBN-13: 9780387345420

ISBN-10: 0387681205

ISBN-13: 9780387681207

Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this designated and gorgeous ebook! It not just reminds the older new release of the pleasures of doing arithmetic by means of hand, but in addition indicates the recent iteration what ``hands on'' particularly means.

- John Stillwell, collage of San Francisco

The Topological Picturebook has taught an entire new release of mathematicians to attract, to determine, 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 provide topological info visually, packed with outstanding hand-drawn images of advanced 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 banquet for somebody involved in mathematical photos. Francis presents beautiful examples to construct one's "visualization muscles". whilst, he explains the underlying rules and layout thoughts for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this number of narrative gem stones and exciting hand-drawn photos, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of photo and textual content. because the publication was once first released, the case for photos in arithmetic has been gained, and now it's time to examine their that means. A Topological Picturebook continues to be indispensable.

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

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Extra info for A Topological Picturebook

Sample text

The next three pictures are a computer-assisted exploration of how to cancel a pair of pinch points. The program uses Morin's parametrization of the homotopy, (X, Y,Z) = (x,1 + (t - r)y,y). First come three wireframe stereographs corresponding to moving t from negative to positive through zero. You can isolate the parabolic double curve by factoring the equation Y = 0 into y = 0 and y = r - t. In the space coordinates these become Z = 0 and Z = X2 - t. Thus the vertex of the parabola is at (O,O,t).

Move the tip closer or further away until two of the four fuzzy images fuse. The center image will still be fuzzy at first. Don't try to focus on the page. Continue to look at the tip of the pencil, and think about the surface until the middle image becomes sharp. With a little practice, you should be able to visualize reversed stereographs on paper or the computer screen quite easily. If you have a stereoscope or get a headache from crossing your eyes, just xerox, cut and paste the stereograph, reversing the right and left sides.

What the dunce hat might look like is not at all obvious from this prescription, nor that it lives in 3-space at all. Our first visualization uses only common topological ingredients. Suppose you tilt the seam, 5( 13), into the same plane as the rim, thereby drawing out a triangular flap or sail. Wrap this around the cone, 5(14), and finish the gluing, 5(21). The resulting 2-complex, 5(22), is not the dunce hat. It has two extra edges: where the sail meets the cone, and the free edge of the sail.

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A Topological Picturebook by George K. Francis

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