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100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) Paperback – June 1, 1965
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This uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others — but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book.
The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems, and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstrations. In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal.
Some of the most celebrated and intriguing items are: Archimedes' "Problema Bovinum," Euler's problem of polygon division, Omar Khayyam's binomial expansion, the Euler number, Newton's exponential series, the sine and cosine series, Mercator's logarithmic series, the Fermat-Euler prime number theorem, the Feuerbach circle, the tangency problem of Apollonius, Archimedes' determination of pi, Pascal's hexagon theorem, Desargues' involution theorem, the five regular solids, the Mercator projection, the Kepler equation, determination of the position of a ship at sea, Lambert's comet problem, and Steiner's ellipse, circle, and sphere problems.
This translation, prepared especially for Dover by David Antin, brings Dörrie's "Triumph der Mathematik" to the English-language audience for the first time.
- Print length416 pages
- LanguageEnglish
- PublisherDover Publications
- Publication dateJune 1, 1965
- Dimensions5.44 x 0.78 x 8.5 inches
- ISBN-100486613488
- ISBN-13978-0486613482
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Product details
- Publisher : Dover Publications (June 1, 1965)
- Language : English
- Paperback : 416 pages
- ISBN-10 : 0486613488
- ISBN-13 : 978-0486613482
- Item Weight : 15.1 ounces
- Dimensions : 5.44 x 0.78 x 8.5 inches
- Best Sellers Rank: #387,774 in Books (See Top 100 in Books)
- #182 in Popular & Elementary Arithmetic (Books)
- #236 in Mathematics History
- #238 in Math Games
- Customer Reviews:
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The rest has already been well said by the other reviewers.
I will mention there is another book with a very similar title by Hugo Steinhaus (with an intro by Martin Gardener). "One Hundred Problems in Elementary Mathematics". The two books are NOT the same. If you enjoy Dorrie's book, you should check out Steinhaus' book as well. Similar subject matter, but the problems aren't the same 100 problems. Although some are duplicated, most are different, and some of the duplicates are done with a different approach.
Although no fault of the author or the translator, I do think that some of the notation and also the labeling in its diagrams should be more “au courant:” Some of its diagrams actually use Roman numerals! One annoying thing I found was that in three related sections — 68. (Euler’s Tetrahedron Problem), 69. (The Shortest Distance Between Skew Lines), and 70. (The Sphere Circumscribing a Tetrahedron) — the translator seemed not to know the difference between “area” and “volume.” I also found typos elsewhere in the book. (In other settings a typo might not be serious; in a mathematics book, well …)
Despite these slight deficiencies, I consider the book quite worthwhile. In fact, I have worn out five copies in my decades-long acquaintance with it.
Reviewed in the United States on October 28, 2015
Although no fault of the author or the translator, I do think that some of the notation and also the labeling in its diagrams should be more “au courant:” Some of its diagrams actually use Roman numerals! One annoying thing I found was that in three related sections — 68. (Euler’s Tetrahedron Problem), 69. (The Shortest Distance Between Skew Lines), and 70. (The Sphere Circumscribing a Tetrahedron) — the translator seemed not to know the difference between “area” and “volume.” I also found typos elsewhere in the book. (In other settings a typo might not be serious; in a mathematics book, well …)
Despite these slight deficiencies, I consider the book quite worthwhile. In fact, I have worn out five copies in my decades-long acquaintance with it.
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.
Top reviews from other countries
Il n'y a pas de structuration. Le livre est un peu brouillon.
Dommage car le sujet est intéressant et le livre aurait peu être bon.
when ordering this book, I initially wanted to read some topics on conic curves, but I got more interesting subjects now.
I hope the author would have added more figures to it, as the average number of figures per problem is probably less than one.









