By Heinrich Dorrie

ISBN-10: 0486318478

ISBN-13: 9780486318479

ISBN-10: 0486613488

ISBN-13: 9780486613482

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

This uncommonly fascinating quantity covers a hundred of the main recognized historic difficulties of common arithmetic. not just does the ebook endure witness to the extreme ingenuity of a few of the best mathematical minds of historical past — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and so on — however it presents infrequent perception and suggestion to any reader, from highschool math pupil 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 bearing on 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 ideas and proofs, the writer recounts their origins and historical past and discusses personalities linked to them. frequently he offers no longer the unique resolution, yet one or easier or extra attention-grabbing demonstrations. in just or 3 circumstances does the answer think something greater than an information of theorems of straightforward arithmetic; consequently, it is a publication with a really broad appeal.

Some of the main celebrated and fascinating 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 top quantity theorem, the Feuerbach circle, the tangency challenge of Apollonius, Archimedes' selection of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 average solids, the Mercator projection, the Kepler equation, decision of the location of a boat at sea, Lambert's comet challenge, and Steiner's ellipse, circle, and sphere problems.

This translation, ready specifically for Dover by way 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.

**Read or Download 100 great problems of elementary mathematics: their history and solution PDF**

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**Extra resources for 100 great problems of elementary mathematics: their history and solution**

**Sample text**

Desargues’ Involution Theorem 64. A Conic Section from Five Elements 65. A Conic Section and a Straight Line 66. A Conic Section and a Point STEREOMETRIC PROBLEMS 67. Steiner’s Division of Space by Planes 68. Euler’s Tetrahedron Problem 69. The Shortest Distance Between Skew Lines 70. The Sphere Circumscribing a Tetrahedron 71. The Five Regular Solids 72. The Square as an Image of a Quadrilateral 73. The Pohlke-Schwarz Theorem 74. Gauss’ Fundamental Theorem of Axonometry 75. Hipparchus’ Stereographic Projection 76.

If the n numbers a, b, c, … are not all equal, then at least one, a, for example, must be greater than M, and at least one, let us say b, must be smaller than M. Let us form a new system of n numbers a′, b′, c′ … in such a manner that (1) a′ = M, (2) the pairs a, b and a′ b′ have the same sum, (3) the other numbers c′, d′, e′, … correspond to c, d, e,. … The new numbers then have the same sum K as the old ones, but a greater product P′( = a′b′c′…), since in accordance with the auxiliary theorem a'b′ > ab.

But you will not be reckoned a wise man yet; if you would be, Come and answer me this, using new data I give : When the entire aggregation of white bulls and that of the black bulls Joined together, they all made a formation that was Equally broad and deep; the far-flung Sicilian meadows Now were thoroughly filled, covered by great crowds of bulls. But when the brown and the spotted bulls were assembled together, Then was a triangle formed; one bull stood at the tip ; None of the brown-colored bulls was missing, none of the spotted, Nor was there one to be found different in color from these.

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