Home Elementary • Download PDF by Heinrich Dorrie: 100 great problems of elementary mathematics: their history

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

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 awfully fascinating and attractive." — Mathematical Gazette

This uncommonly fascinating quantity covers a hundred of the main recognized old difficulties of undemanding arithmetic. not just does the e-book undergo 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 concept to any reader, from highschool math pupil to expert mathematician. this is often certainly an strange and uniquely priceless 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 suggestions and proofs, the writer recounts their origins and background and discusses personalities linked to them. usually he supplies no longer the unique answer, yet one or less complicated or extra attention-grabbing demonstrations. in just or 3 cases does the answer suppose whatever greater than an information of theorems of common arithmetic; consequently, it is a ebook with an incredibly large appeal.
Some of the main celebrated and interesting 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 best quantity theorem, the Feuerbach circle, the tangency challenge of Apollonius, Archimedes' selection of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 normal 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 specially 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 version.

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

Sample text

Respectively, in agreement with the formula. The individual possibilities of forming the product P can also be represented geometrically. We can, for example, represent the first possibility considered above in the following way: We mark off a horizontal distance of α1 successive segments a, and from the end of this distance extend a vertical distance of β1 successive segments b, from the end of this vertical line a third horizontal distance of α2 successive segments a, etc. In a similar manner we represent the other possibilities of forming the product P; however, we begin all C zigzag traces, which represent the C possibilities, from the same point.

Can then be derived from (7). The difficult point in the calculation of A can therefore be considered as eliminated. The problem is solved. , in which An can be calculated from Laisant’s recurrence formula. 9 Omar Khayyam’s Binomial Expansion To obtain the nth power of the binomial a + b in powers of a and b when n is any positive whole number. SOLUTION. In order to determine the binomial expansion we write where the right side consists of a product of n identical parentheses (a + b). As is known, the multiplication of parentheses consists of choosing one term from each parenthesis and obtaining the product of the terms chosen, and continuing this process until all the possible choices are exhausted.

The Astroid 53. Steiner’s Three-pointed Hypocycloid 54. The Most Nearly Circular Ellipse Circumscribing a Quadrilateral 55. The Curvature of Conic Sections 56. Archimedes’ Squaring of a Parabola 57. Squaring a Hyperbola 58. Rectification of a Parabola 59. Desargues’ Homology Theorem (Theorem of Homologous Triangles) 60. Steiner’s Double Element Construction 61. 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.

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

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