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از ساعت 7 صبح تا 10 شب
ویرایش: [1 ed.]
نویسندگان: Béla Bollobás
سری:
ISBN (شابک) : 1108833276, 9781108833271
ناشر: Cambridge University Press
سال نشر: 2022
تعداد صفحات: 348
[349]
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 13 Mb
در صورت تبدیل فایل کتاب The Art of Mathematics – Take Two: Tea Time in Cambridge به فرمت های PDF، EPUB، AZW3، MOBI و یا DJVU می توانید به پشتیبان اطلاع دهید تا فایل مورد نظر را تبدیل نمایند.
توجه داشته باشید کتاب هنر ریاضیات - دو تا: وقت چای در کمبریج نسخه زبان اصلی می باشد و کتاب ترجمه شده به فارسی نمی باشد. وبسایت اینترنشنال لایبرری ارائه دهنده کتاب های زبان اصلی می باشد و هیچ گونه کتاب ترجمه شده یا نوشته شده به فارسی را ارائه نمی دهد.
مسائل سرگرم کننده، غافلگیرکننده و چالش برانگیز ریاضی از این دست که نسل ها در طول چای بعد از ظهر به آن فکر می کنند.
Entertaining, surprising and challenging mathematics problems of the sort pondered by generations during afternoon tea.
Contents Preface The Problems The Hints The Solutions 1. Real Sequences – An Interview Question 2. Vulgar Fractions – Sylvester’s Theorem 3. Rational and Irrational Sums 4. Ships in Fog 5. A Family of Intersections 6. The Basel Problem – Euler’s Solution 7. Reciprocals of Primes – Euler and Erdős 8. Reciprocals of Integers 9. Completing Matrices 10. Convex Polyhedra – Take One 11. Convex Polyhedra – Take Two 12. A Very Old Tripos Problem 13. Angle Bisectors – the Lehmus–Steiner Theorem 14. Langley’s Adventitious Angles 15. The Tantalus Problem – from The Washington Post 16. Pythagorean Triples 17. Fermat’s Theorem for Fourth Powers 18. Congruent Numbers – Fermat 19. A Rational Sum 20. A Quartic Equation 21. Regular Polygons 22. Flexible Polygons 23. Polygons of Maximal Area 24. Constructing √2 – Philon of Byzantium 25. Circumscribed Quadrilaterals – Newton 26. Partitions of Integers 27. Parts Divisible by m and 2m 28. Unequal vs Odd Partitions 29. Sparse Bases 30. Small Intersections – Sárközy and Szemerédi 31. The Diagonals of Zero–One Matrices 32. Tromino and Tetronimo Tilings 33. Tromino Tilings of Rectangles 34. Number of Matrices 35. Halving Circles 36. The Number of Halving Circles 37. A Basic Identity of Binomial Coefficients 38. Tepper’s Identity 39. Dixon’s Identity – Take One 40. Dixon’s Identity – Take Two 41. An Unusual Inequality 42. Hilbert’s Inequality 43. The Central Binomial Coefficient 44. Properties of the Central Binomial Coefficient 45. Products of Primes 46. The Erdős Proof of Bertrand’s Postulate 47. Powers of 2 and 3 48. Powers of 2 Just Less Than a Perfect Power 49. Powers of 2 Just Greater Than a Perfect Power 50. Powers of Primes Just Less Than a Perfect Power 51. Banach’s Matchbox Problem 52. Cayley’s Problem 53. Min vs Max 54. Sums of Squares 55. The Monkey and the Coconuts 56. Complex Polynomials 57. Gambler’s Ruin 58. Bertrand’s Box Paradox 59. The Monty Hall Problem 60. Divisibility in a Sequence of Integers 61. Moving Sofa Problem 62. Minimum Least Common Multiple 63. Vieta Jumping 64. Infinite Primitive Sequences 65. Primitive Sequences with a Small Term 66. Hypertrees 67. Subtrees 68. All in a Row 69. An American Story 70. Six Equal Parts 71. Products of Real Polynomials 72. Sums of Squares 73. Diagrams of Partitions 74. Euler’s Pentagonal Number Theorem 75. Partitions – Maximum and Parity 76. Periodic Cellular Automata 77. Meeting Set Systems 78. Dense Sets of Reals – An Application of the Baire Category Theorem 79. Partitions of Boxes 80. Distinct Representatives 81. Decomposing a Complete Graph: The Graham–Pollak Theorem – Take One 82. Matrices and Decompositions: The Graham–Pollak Theorem – Take Two 83. Patterns and Decompositions: The Graham–Pollak Theorem – Take Three 84. Six Concurrent Lines 85. Short Words – First Cases 86. Short Words – The General Case 87. The Number of Divisors 88. Common Neighbours 89. Squares in Sums 90. Extension of Bessel’s Inequality – Bombieri and Selberg 91. Equitable Colourings 92. Scattered Discs 93. East Model 94. Perfect Triangles 95. A Triangle Inequality 96. An Inequality for Two Triangles 97. Random Intersections 98. Disjoint Squares 99. Increasing Subsequences – Erdős and Szekeres 100. A Permutation Game 101. Ants on a Rod 102. Two Cyclists and a Swallow 103. Almost Disjoint Subsets of Natural Numbers 104. Primitive Sequences 105. The Time of Infection on a Grid 106. Areas of Triangles: Routh’s Theorem 107. Lines and Vectors – Euler and Sylvester 108. Feuerbach’s Remarkable Circle 109. Euler’s Ratio–Product–Sum Theorem 110. Bachet’s Weight Problem 111. Perfect Partitions 112. Countably Many Players 113. One Hundred Players 114. River Crossings: Alcuin of York – Take One 115. River Crossings: Alcuin of York – Take Two 116. Fibonacci and a Medieval Mathematics Tournament 117. Triangles and Quadrilaterals – Regiomontanus 118. The Cross-Ratios of Points and Lines 119. Hexagons in Circles: Pascal’s Hexagon Theorem – Take One 120. Hexagons in Circles: Pascal’s Theorem – Take Two 121. A Sequence in Zp 122. Elements of Prime Order 123. Flat Triangulations 124. Triangular Billiard Tables 125. Chords of an Ellipse: The Butterfly Theorem 126. Recurrence Relations for the Partition Function 127. The Growth of the Partition Function 128. Dense Orbits