Topology

Read e-book online A Topological Picturebook PDF

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 means of such drawings. This publication explains the picture layout of illustrations from Thurston's international of low-dimensional geometry and topology. It provides the rules of linear and aerial standpoint from the point of view of projective geometry.

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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. This idea goes back to Poincare, and in Chapter 6 we shall look at a simple example of this, where the geometry on the building block is our familiar Euclidean one.

My version resulted from a study of the monograph on perspective drawing by Jay Doblin [1956] and the detection of geometrical errors made for aesthetic reasons. I am grateful to Ben Halpern for convincing me of their presence. 3. Given a square and its perpendicular in a picture, discover and use its perspective information to draw other common figures, such as circular wheels with perpendicular axles. To solve the first problem, analyze the situation from a third-party view, 2( 11). A right triangle has been placed between picture and observer.

Figure 4. An example involving nontrivial contours is this graphical transformation of a piecewise flat saddle, top center, to a smooth surface spanning the same border frame, bottom center. The square, horizontal face of 4(22) has two face edges (left) and two contour edges (right). The right column shows how the confluence of these two contour edges becomes a cusp. First, isolate a detail of this corner, 4(13), and bend the (new) borders. This initiates two contours, 4(23), which, in this case, cannot merge smoothly into a border or into each other.

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A Topological Picturebook by George K. Francis


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