By George K. Francis

Praise for George Francis's ** A Topological Picturebook**:

Bravo to Springer for reissuing this particular and gorgeous publication! It not just reminds the older iteration of the pleasures of doing arithmetic by means of hand, but additionally exhibits the recent iteration what ``hands on'' rather means.

- John Stillwell, college of San Francisco

* The Topological Picturebook* has taught a complete new release 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 glossy Thought**

*The vintage reference for the way to give topological details visually, choked with impressive hand-drawn photographs of advanced 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 someone interested in mathematical photos. Francis offers beautiful examples to construct one's "visualization muscles". even as, he explains the underlying ideas and layout concepts for readers to create their very own lucid drawings.

- George W. Hart, Stony Brook University

In this choice of narrative gem stones and exciting hand-drawn photographs, George Francis demonstrates the chicken-and-egg courting, in arithmetic, of photo and textual content. because the publication used to be first released, the case for images in arithmetic has been received, and now it's time to consider their that means. ** A Topological Picturebook** is still indispensable.

- Marjorie Senechal, Smith collage and co-editor of the Mathematical Intelligencer

**Read Online or Download A Topological Picturebook PDF**

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**Additional resources for A Topological Picturebook**

**Example text**

Choose Cartesian coordinates for which the eye, at (0,0, - 0), is located a focal distance 0 behind the xy-picture plane. The perspective image, (X, Y, 0), of the point (x,y,z) is given by X=xZ Y=yZ o where Z = -(- - ) . o+z In this formulation we have compressed the object half space, where z > 0, into the region where < Z < 1. It is a reflected relief. For example, the eye 1(11) at z = - Ph sees the picture 1(12) at z = of the object 1(14) at z = 3 whose relief image 1(13) at z = 0 is sandwiched between the picture plane and its parallel at z = 1.

In the same paper of Thurston, there were other knots to be drawn. The computer furnished remarkable stereographs of the knot twisting about a torus eight times as it goes around the long way thrice. But none of the views worked on its own except this one, which depends on conventional shading for its effect. Only the pen, and perusal of Escher's graphics, helped in designing the knot pair at the bottom. It was essential to depict a knot within a knot. Windows or cross sections would have detracted from the continuity.

Even if accurate execution of these drafting procedures is not always practical, I find the approximation to them useful for sketching a picture freehand. Their demonstration furnishes concrete examples of very beautiful theorems in geometry. They cluster about the following three construction problems: 1. Given a horizon line, find the corresponding zenith point, which is the vanishing point of the lines perpendicular to a plane with that horizon. This is a special case of perspective measurement of angles and distances.