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Download A Mathematical Tapestry: Demonstrating the Beautiful Unity by Peter Hilton, Jean Pedersen, Sylvie Donmoyer PDF

By Peter Hilton, Jean Pedersen, Sylvie Donmoyer

ISBN-10:

ISBN-13: 1397805217641

ISBN-10: 0521764106

ISBN-13: 9780521764100

This easy-to-read e-book demonstrates how an easy geometric inspiration finds interesting connections and ends up in quantity idea, the math of polyhedra, combinatorial geometry, and team idea. utilizing a scientific paper-folding technique it truly is attainable to build a customary polygon with any variety of aspects. This striking set of rules has resulted in fascinating proofs of convinced ends up in quantity idea, has been used to reply to combinatorial questions related to walls of house, and has enabled the authors to acquire the formulation for the amount of a typical tetrahedron in round 3 steps, utilizing not anything extra advanced than simple mathematics and the main basic airplane geometry. All of those principles, and extra, demonstrate the great thing about arithmetic and the interconnectedness of its numerous branches. designated directions, together with transparent illustrations, permit the reader to realize hands-on adventure developing those versions and to find for themselves the styles and relationships they unearth.

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Extra resources for A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics

Sample text

4 Showing the result of a move. square; whereas in (b) the orientation of the symbol tells you to flip the square over a vertical axis along the right-hand side of the square. 4 the heavy right-pointing arrow indicates that by performing the move on the left-hand figure (rotating the entire figure 90◦ in a clockwise direction about the right angle), we obtain the right-hand figure. C. the Greeks were fascinated with the idea of constructing regular N -gons with Euclidean tools (straightedge and compass).

We’ll wait. Look at your flexagon. Observe that there are subtle differences between the 2 visible faces. 9. Surprisingly, this flexagon can change its shape. 10. Of course, after you have gone from left to right you will need to reverse the moves to get the flexagon back into its original shape. You may wish to practice these procedures until you have a feel for them. Take your time. Then come back and we’ll tell you how to flex your 8-flexagon in ways similar to your procedures with the 6-flexagon.

In the next paragraph we describe two aspects of our paper-folding, and building, instructions where we do advise rather rigid adherence to our specifications. However, we are very far from recommending that you fold all your regular polygons and construct all your polyhedra exactly as described. What we have done is to give you algorithms for the relevant constructions. Machines follow algorithms with relentless fervor, while human beings look for special ways of doing particular, convenient things.

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A Mathematical Tapestry: Demonstrating the Beautiful Unity of Mathematics by Peter Hilton, Jean Pedersen, Sylvie Donmoyer


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