# Book:Ian Stewart/Taming the Infinite

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## Ian Stewart:

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

Published $\text {2008}$, **Quercus**

- ISBN 978-1-84724-768-1

### Contents

- Preface

- 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
- Index

## Errata

### 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, ...*

## Source work progress

- 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $9$: Patterns in Nature: Differential equations