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1. Janos Bolyai, Non-Euclidean Geometry,
$62.83
2. Non-Euclidean Geometries: János
 
3. Limit theorems of probability
 
4. Nonparametric Statistical Inference
 
5. Analytic Function Methods in Probability
 
6. Lie groups and their representations:
 
7. Topics in Information Theory (Colloquia
 
8. Number theory (Colloquia mathematica
 
9. Lattice theory (Colloquia mathematica
 
10. Algebra, Combinatorics and Logic
 
11. Limit Theorems in Probability
 
12. Inventory Control and Water Storage
 
13. Qualitative Theory of Differential
 
14. Differential equations (Colloquia
 
15. Fourier Analysis and Approximation
 
16. Topics in topology (Colloquia
 
17. Infinite and Finite Sets: To Paul
 
18. Random Fields: Rigorous Results
 
19. Point Processes and Queuing Problems
 
20. Contributions to universal algebra:

1. Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space
by Jeremy J. Gray
Paperback: 256 Pages (2004-06-01)
list price: US$22.00 -- used & new: US$15.00
(price subject to change: see help)
Asin: 0262571749
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twenty-four-page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry. Bolyai's "Appendix" (published as just that--an appendix to a much longer mathematical work by his father) set up a series of mathematical proposals whose implications would blossom into the new field of non-Euclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp. In this short book, Jeremy Gray explains Bolyai's ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition. Intended for nonspecialists, the book includes facsimiles of Bolyai's original paper and the 1898 English translation by G. B. Halsted, both reproduced from copies in the Burndy Library at MIT. ... Read more

Customer Reviews (1)

4-0 out of 5 stars Readable history, difficult paper
I find Bolyai's paper quite hopeless to read; it's a strange choice for semi-popular publication. Gray's introduction is very pleasant and interesting and full of historical background, but his commentary on Bolyai's actual paper is quite short and not always clear. He does comment extensively on Bolyai's squaring of the circle but this construction is too complicated to be very enjoyable. This result, and Bolyai's entire approach, depends on hyperbolic trigonometric formulae. He saw that such formulae should exist by finding a correspondence between a hyperbolic plane and a surface in hyperbolic space whose geometry is Euclidean (F-surface, horosphere). Today we may interpret this in terms of the half-space model. As our hyperbolic plane we can take a hemisphere centred at the origin and as the horosphere we can take a plane z=c. Lines on the hemisphere are of course intersections with planes perpendicular to the x-y-plane, and lines on the horosphere are Euclidean lines. Under vertical projection of one onto the other lines go to lines and angles are preserved. So a Euclidean right-angle triangle with one vertex at the z-axis correspond to a hyperbolic right-angle triangle with one vertex at the z-axis. And by rotating about the z-axis we see that the ratio of circumferences of the circles generated by the other two vertices is the same on both surfaces. This relates side lengths and thus gives a way of transferring Euclidean trigonometry to the hyperbolic plane. But in hyperbolic geometry the circumference does not grow linearly with the radius (but rather as the hyperbolic sine of the radius, as Bolyai shows later using the angle of parallelism formula), so Euclidean trigonometry does not transfer literally. ... Read more


2. Non-Euclidean Geometries: János Bolyai Memorial Volume (Mathematics and Its Applications)
Hardcover: 506 Pages (2005-11-23)
list price: US$125.00 -- used & new: US$62.83
(price subject to change: see help)
Asin: 0387295542
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Editorial Review

Product Description

"From nothing I have created a new different world," wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture.

The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics.

... Read more

3. Limit theorems of probability theory (Colloquia mathematica Societatis Janos Bolyai ; 11)
 Hardcover: 420 Pages (1975)

Isbn: 0720428343
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4. Nonparametric Statistical Inference (Colloquia mathematica Societatis Janos Bolyai)
 Hardcover: 910 Pages (1982-12)

Isbn: 0444861963
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5. Analytic Function Methods in Probability Theory: Colloquium Proceedings (Colloquia mathematica Societatis Janos Bolyai ; 21)
 Hardcover: 380 Pages (1979-09)

Isbn: 0444853332
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6. Lie groups and their representations: [proceedings of] Summer School of the Bolyai Janos Mathematical Society
 Hardcover: 726 Pages (1975)
list price: US$89.95
Isbn: 0470296003
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7. Topics in Information Theory (Colloquia Mathematica Societatis Janos Bolyai, 16.)
by Hungary, 1975) Colloquium on Information Theory (Keszthely, Imre Csiszar, Peter Elias
 Hardcover: 592 Pages (1976-09)
list price: US$142.00
Isbn: 0720406994
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8. Number theory (Colloquia mathematica societatis Janos Bolyai)
 Hardcover: 244 Pages (1970)

Isbn: 0720420377
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9. Lattice theory (Colloquia mathematica Societatis Janos Bolyai ; 14)
 Hardcover: 462 Pages (1976)

Isbn: 0720404983
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10. Algebra, Combinatorics and Logic in Computer Science (Colloquia Mathematica Societatis Janos Bolyai)
 Hardcover: 890 Pages (1986-05)

Isbn: 0444878696
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11. Limit Theorems in Probability and Statistics (Colloquia Mathematica Societatis Janos Bolyai)
 Hardcover: 561 Pages (1991-02-11)
list price: US$264.50
Isbn: 0444987584
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Editorial Review

Product Description
A broad range of problems are addressed in this volume, the main topics being limit theorems for partial sums of random variables, the dependent and independent case, extreme values, empirical processes, local times and time series. ... Read more


12. Inventory Control and Water Storage (Colloquia mathematica Societatis Janos Bolyai, 7)
by A. Prekopa
 Hardcover: 382 Pages (1973-11)

Isbn: 0720420849
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13. Qualitative Theory of Differential Equations (Colloquia Mathematica Societatis Janos Bolyai)
by Farkas
 Hardcover: 1090 Pages (1981-12)
list price: US$304.00
Isbn: 0444861734
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14. Differential equations (Colloquia mathematica Societatis Janos Bolyai ; 15)
 Hardcover: 418 Pages (1977)

Isbn: 0720404967
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15. Fourier Analysis and Approximation Theory: Colloquium Proceedings (Colloquia mathematica Societatis Janos Bolyai ; 19-)
 Hardcover: 926 Pages (1979-02)

Isbn: 0444851976
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16. Topics in topology (Colloquia mathematica societatis Janos Bolyai ; 8)
 Unknown Binding: 643 Pages (1974)

Isbn: 0444105972
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17. Infinite and Finite Sets: To Paul Erdos on His 60th Birthday (Colloquia mathematica Societatis Janos Bolyai ; v. 10)
by A. Hajnal, etc.
 Hardcover: 1556 Pages (1975-04)

Isbn: 0720428149
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18. Random Fields: Rigorous Results in Statistical Mechanics and Quantum Field Theory (Colloquia Mathematica Societatis Janos Bolyai)
 Hardcover: 1112 Pages (1982-02)

Isbn: 044485441X
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19. Point Processes and Queuing Problems (Colloquia mathematica Societatis Janos Bolyai)
 Hardcover: 426 Pages (1981-03)

Isbn: 0444854320
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20. Contributions to universal algebra: [proceedings] (Colloquia mathematica Societatis Janos Bolyai ; 17)
 Hardcover: 607 Pages (1977)

Isbn: 0720407257
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