Euclid's Window: The Story of Geometry from Parallel Lines by Leonard Mlodinow PDF

By Leonard Mlodinow

ISBN-10: 0684865238

ISBN-13: 9780684865232

Flatbed test: 2 ebook pages = 1 dossier web page, no OCR

via Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a trip via 5 revolutions in geometry, from the Greek proposal of parallel traces to the most recent notions of hyperspace. here's an altogether new, fresh, substitute background of math revealing how uncomplicated questions someone may perhaps ask approximately area -- within the lounge or in another galaxy -- were the hidden engine of the top achievements in technological know-how and expertise.
Mlodinow finds how geometry's first revolution all started with a "little" scheme hatched through Pythagoras: the discovery of a procedure of summary ideas that can version the universe. That modest notion was once the foundation of clinical civilization. yet additional develop used to be halted whilst the Western brain nodded off into the darkish a while. ultimately within the fourteenth century an imprecise bishop in France invented the graph and heralded the subsequent revolution: the wedding of geometry and quantity. Then, whereas intrepid mariners have been crusing backward and forward around the Atlantic to the recent global, a fifteen-year-old genius learned that, just like the earth's floor, house may be curved. may parallel traces particularly meet? may possibly the angles of a triangle particularly upload as much as extra -- or much less -- than one hundred eighty levels? The curved-space revolution reinvented either arithmetic and physics; it additionally set the degree for a patent workplace clerk named Einstein so as to add time to the size of house. His nice geometric revolution ushered within the smooth period of physics.
this present day we're in the middle of a brand new revolution. At Caltech, Princeton, and universities worldwide, scientists are spotting that every one the numerous and wondrous forces of nature will be understood via geometry -- a unusual new geometry. it's a exciting math of additional, twisted dimensions, within which area and time, subject and effort, are all intertwined and published as outcomes of a deep, underlying constitution of the universe.
in response to Mlodinow's huge ancient study; his stories along colleagues comparable to Richard Feynman and Kip Thorne; and interviews with major physicists and mathematicians akin to Murray Gell-Mann, Edward Witten, and Brian Greene, Euclid's Window is a unprecedented combination of rigorous, authoritative research and available, good-humored storytelling that makes a stunningly unique argument announcing the primacy of geometry. should you have appeared via Euclid's Window, no house, no factor, and no time will ever be relatively an analogous.

Show description

Read Online or Download Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace PDF

Best geometry books

Get Guide to Computational Geometry Processing: Foundations, PDF

This publication experiences the algorithms for processing geometric info, with a realistic specialise in very important strategies now not coated through conventional classes on computing device imaginative and prescient and special effects. gains: provides an outline of the underlying mathematical idea, overlaying vector areas, metric house, affine areas, differential geometry, and finite distinction equipment for derivatives and differential equations; reports geometry representations, together with polygonal meshes, splines, and subdivision surfaces; examines suggestions for computing curvature from polygonal meshes; describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification; discusses element situation databases and convex hulls of element units; investigates the reconstruction of triangle meshes from element clouds, together with equipment for registration of aspect clouds and floor reconstruction; offers extra fabric at a supplementary site; contains self-study routines during the textual content.

Lectures on Algebraic Geometry I, 2nd Edition: Sheaves, by Günter Harder PDF

This booklet and the subsequent moment quantity is an advent into glossy algebraic geometry. within the first quantity the tools of homological algebra, concept of sheaves, and sheaf cohomology are built. those equipment are essential for contemporary algebraic geometry, yet also they are basic for different branches of arithmetic and of serious curiosity of their personal.

New PDF release: Geometry and analysis on complex manifolds : festschrift for

This article examines the true variable idea of HP areas, focusing on its functions to numerous points of research fields

Geometry of Numbers by C. G. Lekkerkerker, N. G. De Bruijn, J. De Groot, A. C. PDF

This quantity features a relatively whole photograph of the geometry of numbers, together with family to different branches of arithmetic comparable to analytic quantity thought, diophantine approximation, coding and numerical research. It bargains with convex or non-convex our bodies and lattices in euclidean house, and so on. This moment variation used to be ready together via P.

Extra info for Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

Sample text

The n o t i o n line element~ circa superficies first to later, der of w a s made curves". isolate after intrinsic clear (See page and understand B. I". } of notion revolutionary iiegen", one of In say deduced "Ubcr that from he was the A quarter die of a century ~typothesen, Riemannian a generales particular curvature. address can as "l)iseuisitiones welche geometry was founded. On t h e ingredients fel wax t h e the metric ordinary other first were to the absolute diff~rentiel his student completed m ake a v a i l a b l e ly clear in ]900 to exposition modern this played by text the cover]ant derivation the of theory, one of a connection.

Let A(G),A(H),A(K) be the corresponding Lie algebras, and choose some ad(H)-invariant complement P of A(H) in A(G), some ad(K)-invariant complement Q of A(K) in A(H). Then any ad(H)-invariant scalar product on P gives rise to a G-invariant metric h on G/H; similarly any ad(K)-invariant scalar product on Q gives rise to a H-invariant metric on H/K. Now if g is the G-invariant metric on G/K corresponding to the scalar product on P @ Q given by the two preceding scalar products on P and Q and the condition that P and Q are orthogonal, then~rg is a Riemannian submersion from (G/K,g) onto (G/H,h) with totally geodesic fibres isometric to (H/K,k).

I-oj) i 0 Green's Assume theorem. (A) and let I max M Proof: (i) an Einstein (ai_oj)2 + nR . space, n > 3 , = fll g r a d Use do i__ n-1 Theorem. p > 0 be . f. let (M,g) be [6]. an E i n s t e i n space, n ~ 3 , R > 0 , equality . Then max ~ ~ DR . {p 6 M I f(P) M (ii) If in (i) sphere holds of iff = 0} (M,g) curvature is n o w h e r e is R and dense isometrically H ~ nR .

Download PDF sample

Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow

by David

Rated 4.29 of 5 – based on 3 votes