By Heinrich Dorrie
"The assortment, drawn from mathematics, algebra, natural and algebraic geometry and astronomy, is awfully attention-grabbing and attractive." — Mathematical Gazette
This uncommonly attention-grabbing quantity covers a hundred of the main well-known historic difficulties of effortless arithmetic. not just does the ebook endure witness to the extreme 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 forth — however it offers infrequent perception and concept to any reader, from highschool math pupil to specialist mathematician. this is often certainly an strange and uniquely necessary book.
The 100 difficulties are provided 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 ideas and proofs, the writer recounts their origins and heritage and discusses personalities linked to them. frequently he provides now not the unique resolution, yet one or less complicated or extra attention-grabbing demonstrations. in just or 3 circumstances does the answer imagine something greater than a data of theorems of undemanding arithmetic; as a result, this can be a ebook with an incredibly broad 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 major quantity theorem, the Feuerbach circle, the tangency challenge of Apollonius, Archimedes' decision of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 average solids, the Mercator projection, the Kepler equation, selection of the placement of a boat at sea, Lambert's comet challenge, and Steiner's ellipse, circle, and sphere problems.
This translation, ready particularly for Dover via 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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This vintage best-seller by means of a well known writer introduces arithmetic heritage to math and math schooling majors. steered essay subject matters and challenge reports problem scholars. CULTURAL CONNECTIONS sections clarify the time and tradition during which arithmetic constructed and developed. pics of mathematicians and fabric on girls in arithmetic are of distinctive curiosity.
The booklet bargains with bilinear varieties in genuine random vectors and their generalizations in addition to zonal polynomials and their functions in dealing with generalized quadratic and bilinear kinds. The booklet is generally self-contained. It begins from uncomplicated ideas and brings the readers to the present learn point in those parts.
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Extra info for 100 great problems of elementary mathematics: their history and solution
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.
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.
Moreover, we also obtain from P the two (n + l)-membered paired products f · P and P · f. The described arrangement of the factors f thus yields from only one (P) of the Rn n-membered products (4n – 2) (n + 1)-membered products. From all Rn n-membered paired products we therefore obtain Rn · (4n – 2) (n + l)-membered paired products. , and finally The second question can also be answered by returning to a recurrence formula. Let the n factors fv in the prescribed order be φl, φ2, …, φn. We will take from the Cn paired w-membered products belonging to this series those having the form where the parenthesis on the left includes the r members φl, φ2, …, φn and the one on the right the s = n – r members φr + l + φr + 2, … + φr + s = φn.
100 great problems of elementary mathematics: their history and solution by Heinrich Dorrie