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 very attention-grabbing and attractive." — Mathematical Gazette

This uncommonly attention-grabbing quantity covers a hundred of the main well-known old difficulties of hassle-free arithmetic. not just does the e-book endure witness to the intense ingenuity of a few of the best mathematical minds of heritage — 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 suggestion to any reader, from highschool math scholar to expert mathematician. this can be certainly an strange and uniquely priceless book.
The 100 difficulties are provided 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 suggestions and proofs, the writer recounts their origins and heritage and discusses personalities linked to them. frequently he supplies now not the unique resolution, yet one or less complicated or extra attention-grabbing demonstrations. in just or 3 circumstances does the answer suppose something greater than an information of theorems of undemanding arithmetic; for that reason, it is a e-book with an exceptionally extensive 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 top quantity theorem, the Feuerbach circle, the tangency challenge of Apollonius, Archimedes' decision of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 common solids, the Mercator projection, the Kepler equation, decision of the placement 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 version.

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

Sample text

Pascal’s Hexagon Theorem 62. Brianchon’s Hexagram Theorem 63. 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.

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.

Formation from B-arrangements. The n-pair B-arrangements exhibit the following 2n forms: And there are Bn of each of these forms. Our process of formation is not applicable to the first and the (2n – 1) th of these forms (since the inserted Mn + 1 would have to be exchanged with M1 or Mn, as a result of which, however, M1 would end up on the left side of Fl, or Mn + 1 would be on the left side of Fn + 1). In the second, third, …, (2n – 2)th form, the exchange of the inserted Mn + 1 with M2, M2, M3, M3, …, Mn – 1, Mn – l, Mn transforms the n-pair B-arrangements into (n + l)-pair A-arrangements, as a result of which a total of are obtained.