100 great problems of elementary mathematics: their history by Heinrich Dorrie

By Heinrich Dorrie

"The assortment, drawn from mathematics, algebra, natural and algebraic geometry and astronomy, is awfully fascinating and attractive." — Mathematical Gazette

This uncommonly attention-grabbing quantity covers a hundred of the main well-known old difficulties of trouble-free arithmetic. not just does the ebook endure witness to the intense ingenuity of a few of the best mathematical minds of background — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and so on — however it offers infrequent perception and notion to any reader, from highschool math scholar to expert mathematician. this can be certainly an strange and uniquely necessary book.
The 100 difficulties are offered in six different types: 26 arithmetical difficulties, 15 planimetric difficulties, 25 vintage difficulties relating conic sections and cycloids, 10 stereometric difficulties, 12 nautical and astronomical difficulties, and 12 maxima and minima difficulties. as well as defining the issues and giving complete strategies and proofs, the writer recounts their origins and background and discusses personalities linked to them. usually he offers no longer the unique resolution, yet one or less complicated or extra fascinating demonstrations. in just or 3 situations does the answer imagine something greater than a data of theorems of user-friendly arithmetic; for this reason, this can be a booklet with an exceptionally huge appeal.
Some of the main celebrated and exciting goods are: Archimedes' "Problema Bovinum," Euler's challenge of polygon department, Omar Khayyam's binomial growth, the Euler quantity, Newton's exponential sequence, the sine and cosine sequence, Mercator's logarithmic sequence, the Fermat-Euler major quantity theorem, the Feuerbach circle, the tangency challenge of Apollonius, Archimedes' decision of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 typical solids, the Mercator projection, the Kepler equation, selection of the location of a boat at sea, Lambert's comet challenge, and Steiner's ellipse, circle, and sphere problems.
This translation, ready in particular for Dover by means of David Antin, brings Dörrie's "Triumph der Mathematik" to the English-language viewers for the 1st time.

Reprint of Triumph der Mathematik, 5th variation.

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It also follows from R = 1 and S = 0 that M = m + 1, thus m 8, and the product 7 of the sixth line cannot be higher than 87nopq. II. Consequently, the only possible values for the second divisor numeral β are 0, 1, and 2. ) β = 0 is eliminated because even when multiplied by nine 109979 does not give a seven-figure number, which, for example, is required by the eighth line. Let us then consider the case of β = 1. This requires γ to be equal to only 0 or 1. ) γ = 0, however, is impossible as a result of the seven figures of line 8, since not even 9 · 110979 yields a seven-figure product.

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Two men sit next to their own wives (when Mμ = Mv or Mμ = Mv + 1 and at the same time Xn = M1 that is, when in our arrangement the order M1F1 occurs). Thus, we must consider other seating arrangements in addition to the one prescribed in the problem. In the following we will distinguish between three types of arrangements: arrangements A, B, and C. An A-arrangement will be one in which no man sits next to his wife. A B-arrangement will be one in which a certain man sits on a certain side of his wife.

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