دانلود کتاب Yearning for the impossible : the surprising truths of mathematics

Preface -- 1. The irrational -- 1.1. The Pythagorean dream -- 1.2. The Pythagorean theorem -- 1.3. Irrational triangles -- 1.4. The Pythagorean nightmare -- 1.5. Explaining the irrational -- 1.6. The continued fraction for [square root of] 2 -- 1.7. Equal temperament -- 2. The imaginary -- Negative numbers -- Imaginary numbers -- Solving cubic equations -- 2.4. Real solutions via imaginary numbers -- 2.5. Where were imaginary numbers before 1572? -- 2.6. Geometry of multiplication -- 2. 7. Complex numbers give more than we aked for -- 2.8. Why call them "complex" numbers? -- 3. The horizon -- 3.1. Parallel lines -- 3.2. Coordinates -- 3.3 Parallel lines and vision -- 3.4. Drawing without measurement -- 3.5. The theorems of Pappus and Desargues -- 3.6. The little Desargues theorem -- What are the laws of algebra? -- 3.8. Projective addition and multiplication -- 4. The infinitesimal -- 4.1. Length and area -- 4.2. Volume -- 4.3. Volume of a tetrahedron -- 4.4. The circle -- 4.5. The parabola -- 4.6. The slopes of other curves -- 4.7. Slope and area -- 4.8. The value of [pi] -- 4.9. Ghosts of departed quantities. 5. Curved space -- 5.1. Flat space and medieval space -- 5.2. The 2-sphere and the 3-sphere -- 5.3. Flat surfaces and the parallel axiom -- 5.4. The sphere and the parallel axiom -- 5.5. Non-Euclidean geometry -- 5.6. Negative curvature -- 5.7. The hyperbolic plane -- 5.8. Hyperbolic space -- 5.9. Mathematical space and actual space -- 6. The fourth dimension -- 6.1. Arithmetic of pairs -- 6.2. Searching for an arithmetic of triples -- 6.3. Why n-tuples are unlike numbers when n [is greater than or equal to] 3 -- 6.4. Quaternions -- 6.5. The four-square theorem -- 6.6. Quaternions and space rotations -- 6.7. Symmetry in three dimensions -- 6.8. Tetrahedral symmetry and the 24-cell -- 6.9 The regular polytopes -- 7. The ideal -- 7.1. Discovery and invention -- 7.2. Division with remainder -- 7.3. Unique prime factorization -- 7.4. Gaussian integers -- 7.5. Gaussian primes -- 7.6. Rational slopes and rational angles -- 7.7. Unique prime factorization lost -- 7.8. Ideals, or unique prime factorization regained. 8. Periodic space -- 8.1. The impossible tribar -- 8.2. The cylinder and the plane -- 8.3. Where the wild things are -- 8.4. Periodic worlds -- 8.5. Periodicity and topology -- 8.6. A brief history of periodicity -- 9. The infinite -- 9.1. Finite and infinite -- 9.2. Potential and actual infinity -- 9.3. The uncountable -- 9.4. The diagonal argument -- 9.5. The transcendental -- 9.6. Yearning for completeness -- Epilogue -- Index