The Exact Sciences in Antiquity

exactSciencesMarch’s Book of the Month is: The Exact Sciences in Antiquity by Otto Neugebauer. Second edition published in 1957 by Brown University Press, now republished by Dover in 1969.

Commentary adapted from the Amazon website, see this link for further information: Based on a series of lectures to non-experts 1949, this is the standard non-technical coverage of Egyptian and Babylonian mathematics and astronomy. It reveals that the Babylonian strength in algebraic and numerical work is comparable to the mathematics of the early Renaissance in Europe. In the realm of astronomy, it describes a sophistication which is interpreted less as the result of millennia of observations (as used to be the interpretation) than as a competent mathematical system. An Appendix discusses certain aspects of Greek astronomy and the indebtedness of the Copernican system to Ptolemaic and Islamic methods.

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CultureMATH

culturMATHMarch’s Site of the Month is: CultureMATH

CultureMATH is a French language website dedicated to secondary mathematics teacher education. Published articles present mathematical ideas at several levels. The topics are often related to the curriculum, to present them more deeply. Other resources are also available: some pedagogical experiences, examples of problem solving (in order to present the diversity of procedures), and a series of puzzles.

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Mathematical Etudes

01_301_2February’s Site of the Month: Mathematical Etudes

This is a Russian site, but has an English and a French version, use “en” or “fr” at the end of the URL.

The site contains several 3D animated films that illustrate theorems or ideas in mathematics, and much more. For example, in the Apps for iPhones there are 90 cryptarithms which are available in English, French, German, Italian, Russian, and Spanish.

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The Story of a Number

storyofanumberFebruary’s Book of the Month is: The Story of a Number by Eli Manor. First published in 1993 and available in paperback in the Princeton Science Library.

From the “Goodreads” website. See here for more details.
“…. Geared to the reader with only a modest background in mathematics, the book describes the story of e from a human as well as a mathematical perspective. In a sense, it is the story of an entire period in the history of mathematics, from the early seventeenth to the late nineteenth century, with the invention of calculus at its center. Many of the players who took part in this story are here brought to life. …. The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics …. The book ends with an account of the discovery of transcendental numbers ….”

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The Largest Known Primes

BigPrimeBigJanuary’s Site of the Month: The Largest Known Primes – A Summary

In January a new largest prime was found – with over 22 million digits. Cooper, Woltman, Kurowski and Blosser used GIMPS (Great Internet Mersenne Prime Search) which is software that, since 1996, has generated many new primes.
This web page describes these, and other, types of large primes, links to further information, and discusses Euclid’s proof of the infinitude of primes

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Mathematics for the Million

Lancelot HogbenJanuary’s Book of the Month is Mathematics for the Million: How to Master the Magic of Numbers by Lancelot Hogben. First published in 1936 and reprinted many times.

From the Prologue: “The customary way of writing a book about mathematics is show how each step follows logically from the one before without telling you what use there will be in taking it. This book is written to show you how each step follows historically from the step before and what use it will be to you or someone else if it is taken. The first method repels many people who are intelligent and socially alive, because intelligent people are suspicious of mere logic, and people who are socially alive regard the human brain as an instrument for social activity”

Chapters:
Mathematics in Remote Antiquity
The Grammar of Size, Order, and Shape
Euclid as a Springboard
Number Lore in Antiquity
The Rise and Decline of the Alexandrian Culture
The Dawn of Nothing
Mathematics for the Mariner
The Geometry of Motion
Logarithms and the Search for Series
The Calculus of Newton and Leibnitz
The Algebra of the Chessboard
The Algebra of Choice and Chance

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Historical Topics for the Mathematics Classroom

MathClassroomDecember’s Book of the Month is Historical Topics for the Mathematics Classroom by J.K. Baumgart, D.E. Deal, B.R. Vogeli, A.E. Hallerberg, eds., published by the National Council of Teachers of Mathematics.

This book has a summary of the history of each major branch of mathematics (Number, Computation, Algebra, Geometry, Trigonometry and Calculus) followed by brief essays on specific topics of significance within each branch. The last two chapters of the book give a brief, integrated view of the direction of mathematics development over the last century.
Originally published in 1969, and updated in 1989, the book continues to offer high school and university teachers an excellent tool for their own development.
(Adapted from a review by Tim Keenan).

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Imaginary

OberwolfachDecember’s Site of the Month: IMAGINARY

Imaginary is a site containing “vignette-like” short articles on modern mathematics for a general audience. It emanates from the Mathematics Research Centre at Oberwolfach, where groups of mathematicians meet to work on particular areas or projects. The articles are written by experts in the field and then edited for a general readership.

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Geometry and the Imagination

GeoAndImagNovember’s Book of the Month is Geometry and the Imagination by Hilbert and Cohn-Vossen. First published in 1952.

The AMS website says: “This remarkable book has endured as a true masterpiece of mathematical exposition. … The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians.
[It] is full of interesting facts, many of which you wish you had known before. … The book begins with examples of the simplest curves and surfaces, including thread constructions of certain quadrics and other surfaces. The chapter on regular systems of points leads to the crystallographic groups and the regular polyhedra in \mathbb{R}^3. …
One of the most remarkable chapters is “Projective Configurations”. … Hilbert and Cohn-Vossen give perhaps the most concise and lucid description of why a general geometer would care about projective geometry and why such an ostensibly plain setup is truly rich in structure and ideas. …
A particularly intriguing section … is Eleven Properties of the Sphere. Which eleven properties of such a ubiquitous mathematical object caught their discerning eye and why? … The book includes pictures of some of the models that are found in the Göttingen collection. Furthermore, the mysterious lines that mark these surfaces are finally explained! …”

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Accromath

AccromathNovember’s site of the month: Accromath

This is the site of a French-Canadian journal aimed at a mathematics teacher audience.

Now in its 10th volume, the journal has articles in French that can be read online or download as pdf.

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