Book:Ian Stewart/Taming the Infinite

From ProofWiki
Jump to navigation Jump to search

Ian Stewart: Taming the Infinite: The Story of Mathematics from the First Numbers to Chaos Theory

Published $2008$, Quercus

ISBN 978-1-84724-768-1.


1. Tokens, Tallies and Tablets
2. The Logic of Shape
3. Notations and Numbers
4. Lure of the Unknown
5. Eternal Triangles
6. Curves and Coordinates
7. Patterns in Numbers
8. The System of the World
9. Patterns in Nature
10. Impossible Quantities
11. Firm Foundations
12. Impossible Triangles
13. The Rise of Symmetry
14. Algebra Comes of Age
15. Rubber Sheet Geometry
16. The Fourth Dimension
17. The Shape of Logic
18. How Likely is That?
19. Number Crunching
Further Reading



Historical Note on Arabic Numerals

Chapter $2$: Notations and Numbers: Indian number symbols

The earliest Indian numerals were more like the Egyptian system. For example, Khasrosthi numerals, used from $400$ bc to ad $100$, represented the numbers $1$ to $8$ as ...

Historical Note on Spherical Law of Sines

Chapter $5$: Eternal Triangles: Early trigonometry

Georg Joachim Rhaeticus calculated sines for a circle of radius $10^{15}$ -- effectively, tables accurate to $15$ decimal places, but multiplying all numbers by $10^{15}$ to get integers -- for all multiples of one second of arc. He stated the law of sines for spherical triangles
$\dfrac {\sin a} {\sin A} = \dfrac {\sin b} {\sin B} = \dfrac {\sin c} {\sin C}$
and the law of cosines
$\cos a = \cos b \cos c + \sin b \sin c \cos A$
in his De Triangulis, written in $1462$-$3$ but not published until $1533$.

Mersenne Numbers

Chapter $7$: Patterns in Numbers: Euclid

Numbers of the form $2^p - 1$, with $p$ prime, are called Mersenne primes, ...