Download e-book for iPad: 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 particular and gorgeous publication! It not just reminds the older new release of the pleasures of doing arithmetic via hand, but in addition exhibits the hot iteration what ``hands on'' quite means.

- John Stillwell, college 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 fact: The Fourth size in Relativity, Cubism, and sleek Thought

The vintage reference for the way to provide topological info visually, filled with extraordinary 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 banquet for an individual eager about mathematical photos. Francis presents beautiful examples to construct one's "visualization muscles". whilst, he explains the underlying ideas and layout concepts for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this choice of narrative gemstones and exciting hand-drawn photographs, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of photo and textual content. because the ebook was once first released, the case for photos in arithmetic has been gained, and now it's time to contemplate their that means. A Topological Picturebook is still indispensable.

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

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Example text

Let R:B3~D denote the retraction that collapses the ball to its spine. Let Gt(X) = (1 - t)X + t V denote the radial contraction of the ball. The composition of G followed by R contracts D to V. To imagine the route on D a point X of D takes, just retract the radial line XV onto D and contract the two curves in synchrony. DUNS EGG. Figure 6. A contour line drawing, 5(42) or 5(43), for the snail shaped dunce hat is too complicated to remember. Here is a more systematic way of designing a dunce hat with better symmetry as well as a simpler contour, 6(31).

PLATE III. Cross Cap and Limar;on. Donna Cox and Ray Idaszak, Electronic Imaging Laboratory and National Center for Supercomputing Applications, University of Illinois. PLATE IV. Etruscan Venus. Donna Cox, George Francis and Ray Idaszak, National Center for Supercomputing Applications, University of Illinois. CHAPTER 2 Figure 2 METHODS AND MEDIA 17 BASIC SURFACE PATTERNS elegant torus 2(21) with just two additional lines. In a line pattern, 2(12), the contour for the hole in the torus is a closed curve with two swallowtails.

In designing a line pattern for a surface one is sometimes able to place the border curves with confidence, only to wonder where the contours should go. To obtain a plausible answer I smoothe a piecewise flat and cornered version of the surface. Each line on such a polyhedral swface is an edge bordering one face, or separating two or more faces. Because it is flat, each 18 Figure 3 A TOPOLOGICAL PICTUREBOOK TRIPRONG face of the polyhedron is either wholly visible or wholly invisible. A simple edge separates only two faces, one of which might be hidden.

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