Book:Ian Stewart/Taming the Infinite

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

Next

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

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