100 great problems of elementary mathematics 初等数学100题

This uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history: Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others; but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book.
The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems,and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstra-tions, In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal.
Some of the most celebrated and intriguing items are: Archimedes' "Problema Bovinum," Euler's problem of polygon division, Omar Khayyam's binomial ex-pansion, fhe Euler number, Newton's exponential series, the sine and cosine series, Mercator's logarithmic series, the Fermat-Euler prime number theorem, the Feuerbach circle, the tangency problem of Apollonius, Archimedes' deter-ruination of pi, Pascal's hexagon theorem, Desargues'involution theorem, the five regular solids, the Mercator projection, the Kepler equation, determina-tion of the position of a ship at sea, Lambert's comet problem, and Steiner's ellipse, circle, and sphere problems.
This translation, prepared especially for Dover by David Antin, brings D6rrie's "Triumph der Mathematik" to the English-language audience for the first time."The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive," Mathematical Gazette.

ARITHMETICAL PROBLEMS
1.Archimedes' Problema Bovinum
2.The Weight Problem of Bachet de M6ziriac
3.Newton's Problem of the Fields and Cows
4.Berwick's Problem of the Seven Sevens
5.Kirkman's Schoolgirl Problem
6.The Bernoulli-Euler Problem of the Misaddressed Letters
7.Euler's Problem of Polygon Division
8.Lucas' Problem of the Married Couples
9.Omar Khayyam's Binomial Expansion
10.Cauchy's Mean Theorem
11.Bernoulli's Power Sum Problem
12.The Euler Number
13.Newton's Exponential Series
14.Nicolaus Mercator's Logarithmic Series
15.Newton's Sine and Cosine Series
16.Andre's Derivation of the Secant and Tangent Series
17.Gregory's Arc Tangent Series
18.Buffon's Needle Problem
19.The Fermat-Euler Prime Number Theorem
20.The Fermat Equation
21.The Fermat-Gauss Impossibility Theorem
22.The Quadratic Reciprocity Law
23.Gauss' Fundamental Theorem of Algebra
24.Sturm's Problem of the Number of Roots
25.Abel's Impossibility Theorem
26.The Hermite-Lindemann Transcendence Theorem..PLANIMETRIC PROBLEMS
27.Euler's Straight Line
28.The Feuerbach Circle
29.Castillon's Problem
30.Malfatti's Problem
31.Monge's Problem
32.The Tangency Problem of Apollonius
33.Mascheroni's Compass Problem
34.Steiner's Straight-edge Problem
35.The Delian Cube-doubling Problem
36.Trisection of an. Angle
37.The Regular Heptadecagon
38.Archimedes' Determination of the Number
39.Fuss' Problem of the Chord-Tangent Quadrilateral..
40.Annex to a Survey
41.Alhazen's Billiard Problem PROBLEMS CONCERNING CONIC SECTIONS AND CYCLOIDS
42.An Ellipse from Conjugate Radii
43.An Ellipse in a Parallelogram
44.A Parabola from Four Tangents
45.A Parabola from Four Points
46.A Hyperbola from Four Points
47.Van Schooten's Locus Problem
48.Cardan's Spur Wheel Problem
49.Newton's Ellipse Problem
50.The Poncelet-Brianchon Hyperbola Problem
51.A Parabola as Envelope
52.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
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Index of Names