By George K. Francis

Goals to motivate mathematicians to demonstrate their paintings and to assist artists comprehend the information expressed via such drawings. This e-book explains the photo layout of illustrations from Thurston's global 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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**Example text**

It collapses first to the cone, 5(23). This, in tum, collapses to its vertex, starting from the free edge along the rim, 5(24). Though the entire biography of the dunce hat does not fit into this chapter, a few of its properties are worth mentioning. It is a contractible but not collapsible spine of the 3-ball. It is, however, I-collapsible, which means that its Cartesian product with a "I-ball" is collapsible. You should think of this product as a thickening of the surface into the fourth dimension.

Photography is the only way to preserve such fragile works. To make sure that you have some record use a Polaroid camera. But 35mm slides are more satisfactory and can also be shown to a larger audience. 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.

Use drafting tape instead of thumbtacks to hold the paper to the board. For small circles, 26 A TOPOLOGICAL PICTUREBOOK a template is more convenient than an inking compass. Though tricky to use, splines (french curves) are a blessing for unsteady hands. To insure continuous curvature, it is a good idea to fit a french curve to three points, two of which match those of adjacent triplets. Beyond this, the sky is the limit and art supply stores are a good source of liberal advice on advanced tools such as lettering guides, pencil sharpeners, electric erasers and the like.