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 fascinating quantity covers a hundred of the main recognized historic difficulties of effortless arithmetic. not just does the booklet undergo 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, etc — however it offers infrequent perception and suggestion to any reader, from highschool math scholar to specialist mathematician. this can be certainly an strange and uniquely worthy book.
The 100 difficulties are offered in six different types: 26 arithmetical difficulties, 15 planimetric difficulties, 25 vintage difficulties touching 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. usually he offers now not the unique answer, yet one or easier or extra attention-grabbing demonstrations. in just or 3 cases does the answer suppose something greater than a data of theorems of effortless arithmetic; consequently, it is a e-book with an incredibly extensive 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' choice of pi, Pascal's hexagon theorem, Desargues' involution theorem, the 5 commonplace solids, the Mercator projection, the Kepler equation, selection of the location of a boat at sea, Lambert's comet challenge, and Steiner's ellipse, circle, and sphere problems.
This translation, ready particularly 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 variation.
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Additional info for 100 great problems of elementary mathematics: their history and solution
The solution is, however, extremely difficult because d has the inconveniently large value and even the smallest solution for u and v of this Fermat equation leads to astronomical figures. Even if u is assigned the smallest conceivable value 1, in solving for g the value of ac is 4456749 and the combined number of white and black bulls is over 79 billion. , less than billion m2, it would be quite impossible to place that many bulls on the island, which contradicts the assertion of the seventeenth and eighteenth distichs.
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. André’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. Eulers 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. Steiners Straight-edge Problem 35.
100 great problems of elementary mathematics: their history and solution by Heinrich Dorrie