Download PDF by George K. Francis: A Topological Picturebook

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 distinct and lovely booklet! It not just reminds the older iteration of the pleasures of doing arithmetic via hand, but additionally exhibits the recent new release what ``hands on'' fairly means.

- John Stillwell, collage of San Francisco

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

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

The vintage reference for a way to provide topological info visually, filled with impressive hand-drawn photographs 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 dinner party for somebody interested in mathematical photos. Francis presents beautiful examples to construct one's "visualization muscles". whilst, he explains the underlying ideas and layout ideas for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this selection of narrative gem stones and interesting hand-drawn photographs, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of picture and textual content. because the booklet used to be first released, the case for photographs in arithmetic has been gained, and now it's time to think about their that means. A Topological Picturebook is still indispensable.

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

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Sample text

The kind of picture to draw on the board depends, of course, on its purpose. In the first instance, the lecturer wants a pictograph to accent the exposition. Here speed and simplicity are essential, while artistry is not. The exposition could proceed quite well without the picture. Simplicity in a pictograph need not mean poverty of imagination. The particular object selected should evoke a rich set of associations in the audience. " The customary rectangle E above a CHAPTER 2 METHODS AND MEDIA 27 segment B with a vertical line F above a point on B illustrates the local product structure but misses the chance to point to global topology.

Later, as my working figure on the main board deteriorates in the heat of the lecture I refresh my audience's attention by referring to the picture off to the side. Once a design is completely worked out in private, a full-color version can be reproduced fairly quickly on demand. For such a picture I go through the usual steps of framing and placing the line pattern into general position. The sheets of the line drawing are colored in solidly with the flat side of the chalk. Lecturer's chalk, though dustier than regular colored chalk, produces richer tones.

The blackboard is an invaluable medium also in the design stage of a picture. The large scale of chalk drawings and ease of correcting them greatly helped me solve the problems in descriptive topology whose solutions you see in this book. Sometimes, the time it takes to draw the picture during the lecture is also useful. The three photos of the Diapered Trefoil Knot have a little 28 A TOPOLOGICAL PICTUREBOOK story worth telling in this regard. It began when Bill Thurston asked me to draw the disc spanning a given curve in the complement of the knot.

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A Topological Picturebook by George K. Francis

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