Sine of Theta and Trigonometry

Chapters in this book

1. Frontmatter i
2. Contents v
3. Acknowledgments ix
4. Symbols and Expressions xi
5. Introduction 1
6. I. The Long History of Mathematical Symbols
7. The Birth of Algebra 5
8. How Do We Use Mathematical Symbols? 10
9. The Most Beautiful Mathematical Formulas 14
10. Why Do We Extract Roots? 17
11. II. Numbers and Variables
12. Hindu-Arabic Numerals and Mercantilism 22
13. The Greek Alphabet and Its Predecessors 27
14. Zero 32
15. Symmetry of Symbols 39
16. The Variable x 42
17. Absolute Value and the Father of Analysis 51
18. Powers as Superscripts 55
19. Subscripts 60
20. The Decimal Point 63
21. III. Arithmetic Operators
22. The Greek Cross of Addition 69
23. Subtraction and Negative Numbers 73
24. According to Adam Ries 78
25. The Cross of Multiplication 82
26. The Division Bar 86
27. Homer, the Obelus, and Division 89
28. IV. Relational and Grouping Operators
29. No Two Things Can Be More Equal 94
30. Inequality Symbols 97
31. The Parenthesis versus the Vinculum 100
32. The Comma and the Period 104
33. V. Calculus/Analysis
34. Star Wars: Leibniz versus Newton 107
35. The Partial Derivative 113
36. Nabla, the Harp of Assyria 118
37. John Wallis and Infinity 122
38. Delta 125
39. The Notation f(x) and the Concept of a Function 128
40. Epsilons, Deltas, and the Invention of Real Numbers 134
41. Reaching the Limit 138
42. The Mathematical Dart 143
43. VI. Sets and Functions
44. The Existential Quantifier 149
45. The Universal Quantifier 153
46. ∈ Is for Belonging 157
47. The Set of Rational Numbers 159
48. Mathematics and Nothingness 164
49. Union and Intersection 171
50. The Aleph and the Paradise of Infinities 173
51. VII. Constants
52. The Power of Imagination 180
53. Pi: The Archimedean Constant and the Ludolphian Number 183
54. Euler’s Number and Exponential Growth 189
55. Planck’s Constant: The Quantum of Action 194
56. The Speed of Light c 196
57. VIII. Combinatorics
58. The Factorial 201
59. Sigma: Notation to Sink Your Teeth Into 204
60. A Floor and a Ceiling for Numbers 207
61. The Binomial Symbol 209
62. IX. Various Topics
63. The Invisible Symbol: Einstein’s Convention 213
64. The Halmos Box 215
65. Sine of Theta and Trigonometry 218
66. The Symbol of Congruence and Arithmetic in Miniature 221
67. Matrices: The Mother Structure 224
68. Publish or Perish: The First Scientific Journals 228
69. Epilogue 235
70. Bibliography 237
71. Index 247