By Eli Maor, Eugen Jost

ISBN-10: 0691150990

ISBN-13: 9780691150994

If you've ever concept that arithmetic and artwork don't combine, this attractive visible background of geometry will switch your brain. As a lot a piece of paintings as a ebook approximately arithmetic, attractive Geometry offers greater than sixty beautiful colour plates illustrating a variety of geometric styles and theorems, followed by way of short bills of the interesting historical past and other people in the back of each one. With art through Swiss artist Eugen Jost and textual content by means of acclaimed math historian Eli Maor, this distinct social gathering of geometry covers a number of topics, from straightedge-and-compass structures to exciting configurations related to infinity. the result's a pleasant and informative illustrated travel in the course of the 2,500-year-old background of 1 of an important and gorgeous branches of arithmetic.

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From C drop the altitude CD = h to the hypotenuse, dividing it into segments AD = m and DB = n . The first proof—the one found in most geometry textbooks—relies on the similarity of triangles ADC and CDB, since they share a right angle at D and equal angles ∠DAC and ∠DCB. Thus, AD / DC = CD / DB , or m/h = h/n, or h2 = mn (as before, all line segments are nondirectional, so that CD = DC ). The second proof is a direct consequence of Thales’s theorem (or rather its converse; see chapter 1, note 1) and Euclid III 35 (chapter 11).

Do we see here an optical illusion? Not really: the illustration is, after all, an artistic rendition of the Pythagorean theorem, not the theorem itself; as such it is not bound by the laws of mathematics. 1. Joseph Needham, Science and Civilisation in China, courtesy of Cambridge University Press, Cambridge, UK. 2 6 The Pythagorean Theorem II T he Pythagorean theorem is listed as Proposition 47 in the first book of Euclid’s Elements. But you will not find Pythagoras’s name heading it: true to his terse, matter-of-fact style, Euclid avoided any reference to persons in his work, instead letting the geometry speak for itself.

Html, 2013. 15 Two Prime Mysteries A mong the many unsettled questions about the primes, two stand out for their deceptive simplicity.  . , 101 and 103, and so on. One can find these twin primes even among very large numbers: 29,879 and 29,881, 140,737,488,353,699 and 140,737,488,353,701. 1 How many twin primes are there? Mathematicians are nearly unanimous in their belief that there exist infinitely many of them, just like the primes themselves. But belief counts for very little in mathematics; what counts is proof, and thus far no one has been able to prove this twin prime conjecture.

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Beautiful Geometry by Eli Maor, Eugen Jost


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