100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) [Paperback]

Heinrich Dorrie (Author)

Book Description

ISBN-10: 0486613488 | ISBN-13: 978-0486613482 | Publication Date: June 1, 1965

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.

Product Details

• Paperback: 393 pages
• Publisher: Dover Publications (June 1, 1965)
• Language: English
• ISBN-10: 0486613488
• ISBN-13: 978-0486613482
• Product Dimensions: 8.5 x 5.4 x 0.8 inches
• Shipping Weight: 1 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #311,649 in Books (See Top 100 in Books)
  • #90 in Books > Humor & Entertainment > Puzzles & Games > Math Games

Customer Reviews

Most Helpful Customer Reviews

114 of 115 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

This review is from: 100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) (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.

19 of 20 people found the following review helpful:

5.0 out of 5 stars 100 Mathematical Triumphs of Genius, February 9, 2002

By 

JON STRICKLAND "Jon Strickland" (Smithfield, NC United States) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: 100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) (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, November 2, 2001

By A Customer

This review is from: 100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) (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 .