A Topological Picturebook - download pdf or read online

By George K. Francis

ISBN-10: 0387681205

ISBN-13: 9780387681207

Goals to motivate mathematicians to demonstrate their paintings and to assist artists comprehend the tips expressed by way of such drawings. This booklet explains the image layout of illustrations from Thurston's international of low-dimensional geometry and topology. It offers the foundations of linear and aerial viewpoint from the perspective of projective geometry.

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Example text

Computer-generated visual displays certainly are marvelous aids to the imagination. This spectacular new medium has been used by Tom Banchoff [1977] and Nelson Max [1977] to produce films of great beauty and lucidity in geometry and topology, respectively. Eventually, the graphics computer will be as important a tool in descriptive geometry and topology as india ink and slate blackboards. But not yet. Nelson Max's hidden-line, fully tinted and shaded animation of Morin's sphere eversion is a masterpiece of computer graphics.

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). Moreover, it illustrates, in dimension two, a particular way of cutting and pasting topological objects which is even more useful in three dimensions. Isolate a neighborhood of the vertex by detaching three triangles, 6( 13). Assemble these separately into the cone over the vertex link, 6( 12) of the complex.

Among the color plates in this book are some examples. Three photos, of an early version of the Duns Egg 6(11), show the linedrawing stage, the monochrome version, and a polychrome picture. I used color as a way of labeling matching surface features. For preparing and presenting polychrome pictures, 35mm slides have certain obvious advantages over transparencies. For their preparation I only need a slate blackboard, high-speed film and reasonably quick photo developing services. During the talk I can look at and point to the same image as the audience sees.

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A Topological Picturebook by George K. Francis

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