By George K. Francis
Praise for George Francis's A Topological Picturebook:
Bravo to Springer for reissuing this designated and gorgeous ebook! It not just reminds the older iteration of the pleasures of doing arithmetic by means of hand, but additionally indicates the recent iteration what ``hands on'' fairly means.
- John Stillwell, college of San Francisco
The Topological Picturebook has taught a complete iteration 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 smooth Thought
The vintage reference for a way to provide topological info visually, choked with impressive hand-drawn photos 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 ceremonial dinner for an individual taken with mathematical photos. Francis offers beautiful examples to construct one's "visualization muscles". whilst, he explains the underlying rules and layout options for readers to create their very own lucid drawings.
- George W. Hart, Stony Brook University
In this number of narrative gem stones and exciting hand-drawn photographs, George Francis demonstrates the chicken-and-egg dating, in arithmetic, of picture and textual content. because the e-book was once first released, the case for photographs in arithmetic has been gained, and now it's time to contemplate their which means. A Topological Picturebook is still indispensable.
- Marjorie Senechal, Smith collage and co-editor of the Mathematical Intelligencer
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Extra resources for A Topological Picturebook
A picture of a new object of this kind serves chiefly to "reset the parameters" of an idea already in the imagination. Most pictures drawn by the topologist are of unfamiliar objects. Only rarely do they correspond to any physical reality. While a Mobius band is easily made from a strip of paper, how to sew a disc to its boundary is not a skill taught in the schools. Hand-drawn perspective plays a special role in descriptive topology. Since perspective cubes, cylinders and cones used for framing a drawing can be copied from the computer screen, it is not absolutely essential.
Its anatomy is depicted by 7(32). The two pieces of this figure do not fit together directly. You must first pull the relevant border arcs into a plane perpendicular to the picture plane. " This is a computer graphics film of a Mobius band expressed as a minimal surface in 4-space. INK AND PAPER. This is a good place to say a few words about the drawing equipment which I have found useful. A soft pencil, a pad of blue-lined bond and a kneadable art gum eraser head the list. The blue lines are a handy guide for the horizontal direction and won't reproduce on most copying machines.
A 2-dimensional approach is shown on the right. First reduce the number of layers by sending a point on the surface to infinity. Think of a stereographic projection from the south pole of 7(12) to the paper plane. More directly, consider a plane minus a disc and connect opposite sides of this disc with a half twisted strip, 7(13). To bring the figure eight shaped rim into a plane, you need to untwist one of the two loops, pulling the surface along with it. The result of this deformation is equivalent to sewing in a Cayley cusp, as shown by the arrow.
A Topological Picturebook by George K. Francis