Episodes from the Early History of Mathematics (New Mathematical Library) (Paperback)

by Asger Aaboe (Author) "If a schoolboy suddenly finds himself transplanted to a new school in foreign parts, he is naturally puzzled by much of the curriculum..." (more)
Key Phrases: reciprocal table, digit one place, regular heptagon, Euclid's Elements (more...)

Editorial Reviews

Product Description
Among other things, Aaboe shows us how the Babylonians did calculations, how Euclid proved that there are infinitely many primes, how Ptolemy constructed a trigonometric table in his Almagest, and how Archimedes trisected the angle. Some of the topics may be familiar to the reader while the others will seem surprising or be new. By treating episodes, Aaboe is able to give the reader the details of representative pieces of ancient mathematics, bringing clarity and dispelling such myths as the assertion that the greeks allowed only ruler and compass in constructions.

Book Description
Among other things, Aaboe shows us how the Babylonians did calculations, how Euclid proved that there are infinitely many primes, how Ptolemy constructed a trigonometric table in his Almagest, and how Archimedes trisected the angle.

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Product Details

• Paperback: 384 pages
• Publisher: The Mathematical Association of America (August 1997)
• Language: English
• ISBN-10: 0883856131
• ISBN-13: 978-0883856130
• Product Dimensions: 8.8 x 5.9 x 0.4 inches
• Shipping Weight: 8 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars See all reviews (1 customer review)
• Amazon.com Sales Rank: #607,097 in Books (See Bestsellers in Books)

Customer Reviews

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2 of 2 people found the following review helpful:

4.0 out of 5 stars Early and timeless beauty in mathematics, December 29, 2003

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

While mathematics has a long history, in many ways it was not until the publication of Euclid's Elements that it became an abstract science. Babylonian mathematics, the topic of the first chapter, largely dealt with counting and the focus in this book is on the notations the Babylonians used to represent numbers, both integers and fractions. Although their notation had its' limits, we still use it today for time and angle measure.
And then there was Euclid, and all was ordered. There is no reason to believe one way or another that Euclid was the first to prove the theorems in his classic work, but there is no doubt as to his organizational genius. His "rigorous" setting down of the principles of geometric thought was truly a turning point in abstract mathematics, If you are not impressed when reading the material of the second chapter, taken from Euclid, then you have no aesthetic appreciation for what mathematics is. While the mathematics has been cleaned, the beauty has never been topped.
The next chapter is about the greatest genius before Newton, Archimedes. In fact, had he been blessed with better notation, it is possible that he would have invented, or at least pre-invented calculus. If even half of the legends about his mechanical skill are true, they are still amazing. Apparently, entire armies and navies were terrified at the rumor that one of his mechanical devices was about to be used. The crispness of his theorems and the logical progression will be just as instructive thousands of years from now.
The final chapter describes how Ptolemy was able to construct trigonometric tables. Using the chords of circles, he was able to construct tables that can still be used today. Civilization improves and mathematicians continue to expand the mathematical field and refine earlier work. However, the elegance of earlier work still shines through, and in this book you can experience some of the earliest mathematical diamonds, hewn from thought and destined to survive as long as humans do.