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100 Great Problems of Elementary Mathematics [Paperback]

Heinrich Dörrie

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Book Description

June 1 1965 0486613488 978-0486613482 1
Problems that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and other greats, ready to challenge today's would-be problem solvers. Among them: How is a sundial constructed? How can you calculate the logarithm of a given number without the use of logarithm table? No advanced math is required. Includes 100 problems with proofs.

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Amazon.com: 4.6 out of 5 stars  8 reviews
119 of 120 people found the following review helpful
4.0 out of 5 stars The Problems Are Better Than The Solutions March 19 1998
By A Customer - Published on Amazon.com
Format:Paperback
This is a translation of a book originally published in 1932 under the title Triumph der Mathematik. The original title was better. Most of the problems here are far from elementary. For example, there is a nine-page proof of the Hermite-Lindemann theorem on the transcendence of pi and e, and a 12-page proof of Abel's theorem on the insolvability in closed form of equations higher than fourth degree. These are not what you normally call elementary problems. To understand them, and to understand their solutions, one might do better to consult more specialized texts in the areas under discussion.
On the other hand, the book is a gold mine of fascinating mathematics: How much must a sailboat tack with a north wind in order to get north as quickly as possible? From the altitude of two known stars determine your time and position. Construct the five regular solids. Prove that of all solids of equal surface the sphere possesses the maximum volume. Determine pi experimentally by throwing a needle across parallel lines.
The selection of problems is outstanding and lives up to the book's original title. The proofs are concise, clever, elegant, often extremely difficult and not particularly enlightening. To say that this book requires a background in college math is like saying that playing chess requires a background in how to move the pieces; it also requires a lot of thought and, preferably, a lot of experience.
I would recommend this book to practicing mathematicians, both amature and professional. For the rest of us, the author has surveyed more than 2,000 years of mathematical problems and picked out some real beauties.
20 of 21 people found the following review helpful
5.0 out of 5 stars 100 Mathematical Triumphs of Genius Feb. 9 2002
By JON STRICKLAND - Published on Amazon.com
Format:Paperback
100 Great Problems of Elementary Mathematics is such a goldmine of ingenuity that it is hard to comprehend how it could be sold for so low a price. Ten dollars is practically a steal.
This publication, which was translated into English back in 1965, is a concise summary of some of the greatest works of mathematics throughout mankind's history. The problems contained are quite challenging. Many are such that if you understood any one of them, then you would probably know something that even the best math professor nearest you would not. This may sound like an overstatement, but in a day and age where some PhD's in math have either forgotten or never really learned how to determine so little as the square root of a number by just pencil and paper, it is probably not.
It is from analyzing the book's passages of Bernoulli's Power Sum Problem that I was able to achieve a great mathematical triumph after discovering the following challenge found in William Dunham's The Mathematical Universe: determining a precise mathematical formula to figure out how Jakob Bernoulli could take all the positive integers from 1 to 1000, raise each of them to the tenth power, and then add them up to where the sum came up to over 30 digits! I tried to develop algorithms that would work but failed each time, until I, once again, read this volume.
The situations presented are quite difficult to grasp, but once you get to where you know how to apply any one of them in solving mathematical puzzles, you feel elated. I know I did.
For the individual who enjoys looking at mathematics in a historical context and who wants to approach problems that are perhaps not entirely solvable with the use of the calculator and/or the computer, I recommend this book.
8 of 8 people found the following review helpful
5.0 out of 5 stars best summary of classic problem solutions by masters Nov. 2 2001
By A Customer - Published on Amazon.com
Format:Paperback
Elementary algebra and ingenius ideas are combined to solve some of the most difficult problems in the history of math.This book helped me solve several difficult technical problems .
The concise treatment and cross reference to other solutions is outstanding . This is the finest treatment of advanced mathematical treatments I have ever seen. First published in 1932, it represents the best from the masters and can be used to discover tricks which were helpful to me in algorithm development . The treatment of astronomical problems alone is worth the price .
6 of 6 people found the following review helpful
5.0 out of 5 stars Wonderful book, and a clarification on the term "Elementary" June 8 2008
By Amazon Customer - Published on Amazon.com
Format:Paperback
I love this book, and recommend it very highly, if you're the type who would like to understand, say, why the Fundamental Theorem of Algebra (every polynomial equation as a (possibly complex) root, is true. Yes, it takes intellectual effort to follow the proofs, but that can be incredibly rewarding, once you finally understand.

But this review is mostly to clarify the term "Elementary" in the title. This is used in a technical sense. Many (most?) of the theorems have multiple proofs. And sometimes the clearest proofs involve calculus, and often the calculus of complex variables. But if a proof doesn't involve calculus, then mathematicians refer to these as "elementary". It is in this sense that the title uses the term.
8 of 9 people found the following review helpful
5.0 out of 5 stars The best book about elementary problems I have read till now Aug. 17 2001
By Massimiliano Celaschi - Published on Amazon.com
Format:Paperback
Perhaps the stress given to geometry gives evidence to the age of the book, but it still represents an example of how a collection of problems should be written. It is too entangled with mathematics to be defined an issue about mathematical games, but also fans of games can find out some enjoying items. Because, if much room has been given to proofs and resolutions, the boundary of elementary curiosity never goes out of sight, even if it can sometimes look like a far horizon. It is surely the best book about elementary problems, mathematical games and jokes I have ever read till now, and I have found its language as clear and straight as a non-English reader (like me) usually finds a non-English writer.

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