By George K. Francis
Praise for George Francis's A Topological Picturebook:
Bravo to Springer for reissuing this precise and lovely e-book! It not just reminds the older new release of the pleasures of doing arithmetic through hand, but additionally exhibits the hot new release 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 truth: The Fourth measurement in Relativity, Cubism, and sleek Thought
The vintage reference for a way to provide topological details visually, jam-packed with awesome hand-drawn photographs of advanced 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 banquet for somebody eager about mathematical photos. Francis offers beautiful examples to construct one's "visualization muscles". while, he explains the underlying rules and layout innovations for readers to create their very own lucid drawings.
- George W. Hart, Stony Brook University
In this selection of narrative gemstones and exciting hand-drawn photos, George Francis demonstrates the chicken-and-egg dating, in arithmetic, of photo and textual content. because the e-book used to be first released, the case for images in arithmetic has been received, and now it's time to examine their which means. A Topological Picturebook continues to be indispensable.
- Marjorie Senechal, Smith collage and co-editor of the Mathematical Intelligencer
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Extra resources for A Topological Picturebook
In analogy to the projective plane, whose points correspond to antipodal pairs of points on a sphere under central projection, projective space has a Euclidean model in 4-space, consisting of antipodally identified objects on the 3-sphere. That two parallel lines "meet at infinity" and that two parallel planes have a common "infinite line" has the following perspective interpretation. 46 A TOPOLOGICAL PrCTUREBOOK As the object point at the end of the sightline moves away from the observer along a straight line in space, its trace on the picture plane moves along a line segment until it stops at the vanishing point of the object line, which is now parallel to the sight line.
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. They contain an acid but can be erased with a suitable fluid, at least for a while. This is usually neater than xerography, but more time-consuming. Since the solvent of many inks will smear adjacent pigments already applied, I sometimes color on alternating sides of the sheet.
Moreover, no two vertices of a northern triangle should fall between two vertices of a southern triangle. For this I first had the machine draw a lot of such triangles, far too many for a good picture. Then, in successive tracings I found the few that appeared to look good. The computer was little help for the surface spanning the knot beneath. The challenge of getting this object to look right led to a lengthy preoccupation with surfaces spanning knots which matured into the final picture story of this book.
A Topological Picturebook by George K. Francis