By Alex Bellos

From triangles, rotations and gear legislation, to fractals, cones and curves, top promoting writer Alex Bellos takes you on a trip of mathematical discovery together with his signature wit, attractive tales and unlimited enthusiasm. As he narrates a sequence of eye-opening encounters with vigorous personalities around the world, Alex demonstrates how numbers have end up our neighbors, are interesting and intensely available, and the way they've got replaced our world.

He turns even the feared calculus into an easy-to-grasp mathematical exposition, and sifts via over 30,000 survey submissions to bare the world's favorite quantity. In Germany, he meets the engineer who designed the 1st roller-coaster loop, while in India he joins the world's hugely numerate neighborhood on the overseas Congress of Mathematicians. He explores the wonders at the back of the sport of lifestyles software, and explains mathematical common sense, progress and damaging numbers. Stateside, he hangs out with a personal detective in Oregon and meets the mathematician who seems to be for universes from his storage in Illinois.

Read this beautiful booklet, and also you won't understand that you're studying approximately advanced techniques. Alex gets you addicted to maths as he delves deep into humankind's turbulent dating with numbers, and proves simply how a lot enjoyable we will be able to have with them.

**Read Online or Download Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life PDF**

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**Extra resources for Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life**

**Example text**

If H is empty, the lemma is trivial. If H has no vertices, we can create two vertices by a 0 → 2 move. Encircle each vertex of H by a closed curve: this set of n curves intersects H at most 4n times and decomposes S into n blocks of the ﬁrst type and a surface S whose Euler characteristic is χ(S) − n. If H = H ∩ S contains parallel edges, we apply O(n) 0 → 2-moves in order to replace each set of parallel edges by a single edge branching only in the neighborhood of ∂S . Then we add one curve per component of ∂S in order to enclose all these trivalent vertices in annular regions.

GT/0411016. 16. S. King, ‘Polytopality of triangulations’, PhD Thesis, Universit´e Louis Pasteur, Strasbourg, June 2001. 17. R. Kirby and P. Melvin, ‘Evaluations of the 3-manifold invariants of Witten and Reshetikhin–Turaev for sl(2, C)’, Geometry of low-dimensional manifolds, 2, Durham, 1990 (ed. S. K. Donaldson and C. B. Thomas), London Mathematical Society Lecture Notes Series 151 (Cambridge University Press, Cambridge, 1990) 101–114. 18. R. Kirby and P. Melvin, ‘Local surgery formulas for quantum invariants and the Arf invariant’, Proceedings of the Casson Fest (ed.

References 1. J. F. Brock, ‘The Weil–Petersson metric and volumes of 3-dimensional hyperbolic convex cores’, J. Amer. Math. Soc. 16 (2003) 495–535. 744 FRANCESCO COSTANTINO AND DYLAN THURSTON 2. J. F. Brock, ‘Weil–Petersson translation distance and volumes of mapping tori’, Comm. Anal. Geom. 11 (2003) 987–999. 3. O. Burlet and G. de Rham, ‘Sur certaines applications g´en´eriques d’une vari´et´e close `a 3 dimensions dans le plan’, Enseign. Math. (2) 20 (1974) 275–292. 4. F. Costantino, ‘Shadows and branched shadows of 3 and 4-manifolds’, PhD Thesis, Scuola Normale Superiore, Pisa, Italy, May 2004.