- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Can one prove that 1 + 1 = 2? How long is the coastline of Britain? Which US president proved Pythagoras' theorem on right-angled triangles? Who originated the quadratic equation we learned at school? In how many ways can you tile your bathroom? Is there a formula for prime numbers? How often are two winning lottery numbers consecutive? Who was the witch of Agnesi? What is 'the most important theorem in mathematics'? Who scratched mathematical equations on a Dublin bridge? What is a 'space-filling curve'? Must all infinities be the same size?
These and many other questions are answered in this book which presents eighteen 'Stories' featuring famous mathematical equations and their historical development. The equations arise from geometry, arithmetic, algebra, calculus, combinatorics, number theory, and mathematical logic, and range over 4,000 years from early counting and circle measurement via Renaissance algebra to fractal geometry, and from the geometry of the ancient Greeks via the development of calculus to Boolean algebra and computing. The Stories are well illustrated with historical artefacts and explanatory diagrams.
Presented in a straightforward, intelligible, and entertaining manner, Sum Stories is written for general readers of all ages with an interest in mathematics and its historical development.
Contents
Preface
1: 1 + 1 = 2
2: α + β + γ = 180o
3: a² + b² = c²
4: C = 2πr and A = πr²
5: ax² + bx + c = 0
6: φ² = φ + 1
7: x² = x
8: Mₙ = 2ⁿ - 1 and Fₙ = 2²ˆⁿ + 1
9: C(n, r) = C(n - 1, r) + C(n - 1, r - 1)
10: V - E + F = 2
11: y = mx + c
12: ∫ f'(x) dx = f (x)
13: log (a x b) = log a + log b
14: i² = -1
15: eⁱˣ = cos x + i sin x
16: 1 + 1/4 + 1/9 + 1/16 + 1/25 + . . . = π²/6
17: zₙ₊₁ = zₙ² + c
18: ℵ₀ + ℵ₀ = ℵ₀
