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 exact and lovely ebook! It not just reminds the older iteration of the pleasures of doing arithmetic through hand, but in addition exhibits the recent iteration what ``hands on'' quite means.

- John Stillwell, collage of San Francisco

The Topological Picturebook has taught an entire iteration 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 smooth Thought

The vintage reference for the way to offer topological details visually, jam-packed with notable 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 desirous about mathematical photos. Francis offers beautiful examples to construct one's "visualization muscles". even as, 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 choice of narrative gemstones and interesting hand-drawn images, 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 photographs 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 university and co-editor of the Mathematical Intelligencer

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In preparing a transparency, you have some choices to make. Despite technical advances, xerographic copies of your ink or pencil drawings on the plastic sheets usually require some touching up. Drawing ink works fine, and the picture can be enhanced further with the judicious use of colored inks. These come in two kinds, the water soluble, and thus eraseable, and the permanent ink markers. A combination of the two is useful if the transparency is to be reused. Ordinary india ink can also be erased by just rubbing.

Or, what comes to the same thing, the cross-ratio CR(D';Z,D,B) = - 1. Since it is the "perspectivist's ruler", a brief digression on the cross-ratio function is appropriate. For three points, O-U- V, on a line directed towards V, the function . _(X-O)(U-V) CR(X,O,U, V) - (X - V) (U - 0) assigns numbers to all points X on the line, once you give terms like (X - Q) the value of the signed distance from Q to X. Note that the function has values 0,1,00 when X = O,U,v. The mnemonic for the cross-ratio is: 0 for "origin", U for "unit" and V for "vanishing point".

Use razor blades to cut out, not scratch out, hopeless mistakes. An overlay will patch the hole nicely. I find it convenient to put the most complicated parts of a figure on the transparency before the lecture, CHAPTER 2 METHODS AND MEDIA 29 and add some details to it, or on an overlay, during the talk. Remember, you can work on both sides of the plastic. A figure can be drawn directly on the acetate, using a line pattern or complete picture as an underlay. Ordinary drawing ink works; inks more specifically intended for drawing on film are more permanent.

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