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100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) Paperback – June 1, 1965

4.6 4.6 out of 5 stars 50 ratings

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"The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive." — Mathematical Gazette
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.

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  • 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
  • Customer Reviews:
    4.6 4.6 out of 5 stars 50 ratings

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4.6 out of 5 stars
4.6 out of 5
50 global ratings
Imperfect but well worthwhile: 100 Great Problems of Elementary Mathematics
4 Stars
Imperfect but well worthwhile: 100 Great Problems of Elementary Mathematics
“100 Great Problems of Elementary Mathematics” is translated from “Triumph der Mathematik,” originally published in German. The title describes the book well enough. Its articles describe not only the mathematics behind the solution of each well-known problem, but also the identities of the innovators and the time frame in which each labored.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.
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Reviewed in the United States on April 18, 2010
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4.0 out of 5 stars Imperfect but well worthwhile: 100 Great Problems of Elementary Mathematics
Reviewed in the United States on October 28, 2015
“100 Great Problems of Elementary Mathematics” is translated from “Triumph der Mathematik,” originally published in German. The title describes the book well enough. Its articles describe not only the mathematics behind the solution of each well-known problem, but also the identities of the innovators and the time frame in which each labored.

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.
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J ANTONIO
5.0 out of 5 stars Contenido
Reviewed in Spain on June 5, 2023
Cliente Amazon
5.0 out of 5 stars e' bellissimo
Reviewed in Italy on December 3, 2018
Lecteur
2.0 out of 5 stars Présentation confuse
Reviewed in France on October 21, 2016
Dongxu Li
5.0 out of 5 stars Elementary but not with depth in math
Reviewed in Canada on May 15, 2015
A Customer
5.0 out of 5 stars seductively brilliant arguments
Reviewed in the United Kingdom on September 21, 2014