A Topological Picturebook by George K. Francis

By George K. Francis

Praise for George Francis's A Topological Picturebook:

Bravo to Springer for reissuing this precise and lovely booklet! It not just reminds the older new release of the pleasures of doing arithmetic through hand, but in addition indicates the recent iteration 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 glossy Thought

The vintage reference for a way to give topological information visually, packed with outstanding hand-drawn pictures 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 dinner party for a person all in favour of mathematical images.  Francis offers beautiful examples to construct one's "visualization muscles".  while, 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 number of narrative gemstones and fascinating hand-drawn images, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of picture and textual content. because the booklet was once first released, the case for photographs in arithmetic has been gained, and now it's time to examine their which 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

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. Both begin with the Mobius band regarded as a disc with a twisted handle, 7(12), whose border looks like a (nearly) plane figure eight. A deformation of 7(12) to the usual shape of the Mobius band, 7(32) is indicated by the transitional form 7(22). The 3-dimensional approach for modelling a given shape is on the left.

Ou can find out more about knots in the classic text by Crowell and Fox [1963]. Orient the knot projection and label the segments between consecutive under-passes. ) Choose a base point in the complement of the knot and draw an oriented loop from the base point around each of the segments except the superfluous one. Curl your right hand around the knot segment with fingers pointing along the loop. The loop label receives a positive (negative) exponent if your thumb points in the same (opposite) direction as the knot.

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.

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