New PDF release: A Topological Picturebook

By George K. Francis

ISBN-10: 0387681205

ISBN-13: 9780387681207

Goals to motivate mathematicians to demonstrate their paintings and to aid artists comprehend the tips expressed via such drawings. This e-book explains the image layout of illustrations from Thurston's international of low-dimensional geometry and topology. It offers the foundations of linear and aerial point of view from the point of view of projective geometry.

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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. This medium tolerates a great deal of expository ingenuity and individual freedom. 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.

Figure 3. 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.

Windows or cross sections would have detracted from the continuity. I had no choice but to try my hand at a transparent outer knot, just as Thurston had suggested in the manuscript. CHAPTER Figure 13 2 METHODS AND MEDIA LAMINATION AND EIGHT KNOT 37 38 A Figure 14 CABLE KNOT AND COMPANION TOPOLOGICAL PICTUREBOOK CHAPTER 2 METHODS AND MEDIA 39 CxC coordinates: (<2tt,t<2ir,2<2it/f) t= 0 .. =0 .. 360/f; 1/32, f =3/2, CABLING TEMPLATE Figure 15 A standard way to produce 3-dimensional manifolds is to identify the faces of a solid polyhedron in a particular way.

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A Topological Picturebook by George K. Francis

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