Book of the Month December: The Pythagorean Theorem

pythagoreantheoremDecember’s Book of the Month is The Pythagorean Theorem: A 4000-year History by Eli Moar, published in 2007 by Princeton Science Library.

This is the third book that celebrates a famous equation, in this case one that is so well known that it needs little introduction. However, its history pre-dates Pythagoras by over 1000 years, and traces through many cultures.

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Book of the Month November: Euler’s Gem

eulersgemNovember’s Book of the Month is Euler’s Gem: The Polyhedron Formula and the Birth of Topology by David Richeson, published in 2008 by Princeton University Press.
(Adapted from the Amazon description)
Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the formula’s far-reaching impact on topology, the study of shapes. David Richeson tells how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope for use with higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula.

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Book of the Month October: E = mc^2

emc2October’s Book of the Month is E = mc^2: A Biography of the World’s Most Famous Equation by David Bodanis. First published in 2003 by Walker and Company, paperback published 2001 by Berkley.
(Adapted from the Amazon description)
Beginning by introducing each of the equation’s letters and symbols, Bodanis brings it to life historically, making clear the astonishing array of discoveries and consequences it made possible. It would prove to be a beacon throughout the twentieth century, coming to inform our daily lives, governing everything from the atomic bomb to the carbon dating of prehistoric paintings.

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Gamma – Exploring Euler’s constant

gammaThe September Book of the Month adds to the collection of books on particular “numbers” from last month:
Gamma: Exploring Euler’s constant by Julian Havil, published in 2003 by Princeton Science Library
and
Brief History of Infinity: The quest to think the unthinkable by Brian Clegg, published in 2003 by Constable and Robinson.

If readers of this blog know of other titles that would fit in this list of “Books about Numbers” please email b.barton@auckland.ac.nz. Please note that the Book of the Month is only used for books that have been in print for at least ten years.

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mathoverflow

appli_grouptheoryAugust Site of the Month is about applications of advanced mathematics: mathoverflow

The site is a thread of MathOverflow, a site for professional mathematicians.
This thread, however, simply collects all the applications of different areas of research mathematics.
Scroll down and enjoy.

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The Story of Phi

theStoryofThe August book of the month is actually a group of books, all “The Story of Phi” particular numbers. These books include a social history as well as the mathematical history.

e: The story of a number by Eli Maor, first published in 1993 and republished in 1998 by Princeton University Press.

An Imaginary Tale: The story of √-1 by Paul Nahin, first published in 1998 and republished in 2007 by Princeton University Press.

A History of π by Petr Beckmann, first published in 1970, republished in 1976 by St Martin’s Griffin.

Zero: The biography of a dangerous idea by Charles Seife, published in paperback in 2000 by Penguin.

The Golden Ratio: The story of phi, the world’s most astonishing number by Mario Livio, first published in 2002, in paperback in 2003 by Random House.

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MathWorld

WolframThe Site of the Month for July is MathWorld from Wolfram. An encyclopedic collection of mathematical items, searchable by topic or alphabetical index. It is “a free resource from Wolfram Research built with Mathematica” and was created (and continues to be nurtured by) Eric Weisstein with help from the global mathematics community.

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4000 Jahre Algebra (4000 Years of Algebra)

4000JahreAlgebraThe July Book of the Month is in German: 4000 Jahre Algebra (4000 Years of Algebra) by Alten, Naini, Eick, Folkerts, Schlosser, Schlote, Wesemüller-Koch, & Wußing. First published in 2003 and republished by Springer-Verlag in 2014 (also available as an e-book), this is one in a series reviewing mathematics from a historical and social standpoint. It traces the development of algebra as part of our culture, linking early ways of calculating up to computer algebra to historical events.

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Fantasia Mathematica

FantasiaMathematicaJune’s Book of the Month is Fantasia Mathematica, a collection of mathematical stories, poems, and humour compiled by Clifton Fadiman, and first published by Simon & Schuster in 1958. Authors include Aldous Huxley, H.G. Wells, and Arthur C. Clarke. It was republished in softback in 1997 by Copernicus (Springer-Verlag). A companion volume called The Mathematical Magpie was published in 1962.

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How do I Solve this Equation? Look at the Symmetries! – The Idea behind Galois Theory

Originating author is Timo Leuders.

Introduction
There are some questions that accompany the development of mathematics through cultures and ages. One of these questions is how to find an unknown quantity x of which one knows some relations such as – in today’s algebraic notation:

    \[x^2 =x+5\]

Finding solutions to such quadratic equations are essentially known since Babylonian
times and are core content school mathematics:

    \[x^2-x-5=0 \, \Rightarrow \, x=\frac{1}{2}+\frac{1}{2} \sqrt{21} \, \vee \, x=\frac{1}{2}-\frac{1}{2} \sqrt{21}\]

But how about x^5 = x + 5 , which looks only slightly different? Are there also straightforward ways to calculate the solutions? Do the solutions also look symmetric in a similar way?

Continue reading

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