Book:Heinrich Dörrie/100 Great Problems of Elementary Mathematics

Heinrich Dörrie: 100 Great Problems of Elementary Mathematics

Published $\text {1965}$ (translated by David Antin)

Subject Matter

• General Mathematics

Contents

Preface

Preface to the Second Edition

Arithmetical Problems

1. Archimedes' Problema Bovinum

2. The Weight Problem of Bachet de Méziriac

3. Newton's Problem of the Fields and Cows

4. Berwicks 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. 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. 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 $\pi$

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 Quadrilerateral

55. The Curvature of Conic Sections

56. Archimedes' Squaring of a Parabola

57. Squaring a Hyperbola

58. Rectification of a Parabola

59. Desargues' Homology Theorem (Theorem of Homologous Triangles)

60. Steiner's Double Element Construction

61. Pascal's Hexagon Theorem

62. Brianchon's Hexagram Theorem

63. Desargues' Involution Theorem

64. A Conic Section from Five Elements

65. A Conic Section and a Straight Line

66. A Conic Section and a Point

Stereometric Problems

67. Steiner's Division of Space by Planes

68. Euler's Tetrahedron Problem

69. The Shortest Distance Between Skew Lines

70. The Sphere Circumscribing a Tetrahedron

71. The Five Regular Solids

72. The Square as an Image of a Quadrilateral

73. The Pohlke-Schwarz Theorem

74. Gauss' Fundamental Theorem of Axonometry

75. Hipparchus' Stereographic Projection

76. The Mercator Projection

Nautical and Astronomical Problems

77. The Problem of the Loxodrome

78. Determining the Position of a Ship at Sea

79. Gauss' Two-Altitude Problem

80. Gauss' Three-Altitude Problem

81. The Kepler Equation

82. Star Setting

83. The Problem of the Sundial

84. The Shadow Curve

85. Solar and Lunar Eclipses

86. Sidereal and Synodic Revolution Periods

87. Progressive and Retrograde Motion of the Planets

88. Lambert's Comet Problem

89. Steiner's Problem Concerning the Euler Number

90. Fagnano's Altitude Base Point Problem

91. Fermat's Problem for Torricelli

92. Tacking Under a Headwind

93. The Honeybee Cell (Problem by Réaumur)

94. Regiomontanus' Maximum Problem

95. The Maximum Brightness of Problem

96. A Comet Inside the Earth's Orbit

97. The Problem of the Shortest Twilight

98. Steiner's Ellipse Problem

99. Steiner's Circle Problem

100. Steiner's Sphere Problem

Index of Names

Cited by

• 1992: David Wells: Curious and Interesting Puzzles