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 targeted and lovely booklet! It not just reminds the older new release of the pleasures of doing arithmetic through hand, but in addition exhibits the hot new release what ``hands on'' particularly means.

- John Stillwell, collage of San Francisco

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

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

The vintage reference for the way to give topological details visually, packed with extraordinary 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 an individual considering mathematical photographs. Francis presents beautiful examples to construct one's "visualization muscles". even as, he explains the underlying rules 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 photographs, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of picture and textual content. because the publication was once first released, the case for images 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 info for A Topological Picturebook

Sample text

Most pictures drawn by the topologist are of unfamiliar objects. Only rarely do they correspond to any physical reality. While a Mobius band is easily made from a strip of paper, how to sew a disc to its boundary is not a skill taught in the schools. Hand-drawn perspective plays a special role in descriptive topology. Since perspective cubes, cylinders and cones used for framing a drawing can be copied from the computer screen, it is not absolutely essential. However, it does help the topologist to visualize and then design the object in the first place, by whatever means the finished product will be realized.

This picture was now simple enough to remember and reproduce on demand. The green one in the third photo was drawn in "real time" in Benno Artmann's seminar in Darmstadt. With all the practice, it took less time to draw it than to explain the topology, the group theory and the descriptive topology involved. SLIDES AND TRANSPARENCY. For most public mathematical presentations, especially with a time limit and a need for perfect illustrations, there is nothing to replace the trusty overhead projector.

The square, horizontal face of 4(22) has two face edges (left) and two contour edges (right). The right column shows how the confluence of these two contour edges becomes a cusp. 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.

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