100 Great Problems of Elementary Mathematics: Their History and Solution

Dover Publications, 1965 - 393 頁
"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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Archimedes Problema Bovinum
The Weight Problem of Bachet de Méziriac
Newtons Problem of the Fields and Cows

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關於作者 (1965)

David Abraham Antin was born in Brooklyn, New York on February 1, 1932. He received a bachelor's degree in English and speech from the City College of New York in 1955 and a master's degree in linguistics at New York University in 1966. After working as an educational curator at the Institute of Contemporary Art in Boston, he taught in the department of visual arts at the University of California, San Diego. From 1968 to 1972, he directed the university's Mandeville Art Gallery. He was also a poet who created a new performance style called talk poems, which was part lecture, part stand-up routine, and part Homeric recitation. After editing his tape-recorded performances, he wrote the poems down. He published several collections of poetry during his lifetime including Talking, Talking at the Boundaries, and What It Means to Be Avant-Garde. A collections of his articles on art, Radical Coherency: Selected Essays on Art and Literature, 1966-2005, were published in 2011. He died from complications of a broken neck that he suffered in a fall on October 11, 2016 at the age of 84.