It All Adds Up

It All Adds Up
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‘Fascinating … so enlightening that suddenly maths doesn’t seem so fearsome as it once did’ SIMON WINCHESTERFrom Aristotle to Ada Lovelace: a brief history of the mathematical ideas that have forever changed the world and the everyday people and pioneers behind them. The story of our best invention yet.From our ability to calculate the passing of time to the algorithms that control computers and much else in our lives, numbers are everywhere. They are so indispensable that we forget how fundamental they are to our way of life.In this international bestseller, Mickaël Launay mixes history and anecdotes from around the world to reveal how mathematics became pivotal to the story of humankind. It is a journey into numbers with Launay as a guide. In museums, monuments or train stations, he uses the objects around us to explain what art can reveal about geometry, how Babylonian scholars developed one of the first complex written languages, and how ‘Arabic’ numbers were adopted from India. It All Adds Up also tells the story of how mapping the trajectory of an eclipse has helped to trace the precise day of one of the oldest battles in history, how the course of the modern-day Greenwich Meridian was established, and why negative numbers were accepted just last century.This book is a vital compendium of the great men and women of mathematics from Aristotle to Ada Lovelace, which demonstrates how mathematics shaped the written word and the world. With clarity, passion and wisdom, the author unveils the unexpected and at times serendipitous ways in which big mathematical ideas were created. Supporting the belief that – just like music or literature – maths should be accessible to everyone, Launay will inspire a new fondness for the numbers that surround us and the rich stories they contain.

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Mickael Launay. It All Adds Up

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FOREWORD

1. MATHEMATICIANS WITHOUT KNOWING IT

HOW TO RECOGNIZE THE SEVEN CATEGORIES OF FRIEZES

2. AND THEN THERE WERE NUMBERS

3. LET NO ONE IGNORANT OF GEOMETRY ENTER

SOME PROBLEMS OF THE PERIOD

4. THE AGE OF THEOREMS

5. A LITTLE METHOD

6. Π IN THE SKY

ARCHIMEDES’ METHOD

7. NOTHING AND LESS THAN NOTHING

WHY DOES MINUS TIMES MINUS EQUAL PLUS?

8. THE POWER OF TRIANGLES

THE TILINGS OF THE ALHAMBRA

9. INTO THE UNKNOWN

THE CLASSIFICATION OF EQUATIONS

10. IN SEQUENCE

THE GOLDEN RATIO

11. IMAGINARY WORLDS

INVENTING YOUR OWN MATHEMATICAL THEORY

12. A LANGUAGE FOR MATHEMATICS

CARTESIAN COORDINATES

13. THE WORLD’S ALPHABET

CRYSTALLOGRAPHY

14. THE INFINITELY SMALL

15. MEASURING THE FUTURE

PASCAL’S TRIANGLE

16. THE COMING OF MACHINES

THE FOUR-COLOUR THEOREM

17. MATHS TO COME

GÖDEL’S EXQUISITE CATASTROPHE

EPILOGUE

TO GO FURTHER

MUSEUMS AND EVENTS

BOOKS

ONLINE

FOOTNOTES. 3. LET NO ONE IGNORANT OF GEOMETRY ENTER

5. A LITTLE METHOD

6. Π IN THE SKY

8. THE POWER OF TRIANGLES

10. IN SEQUENCE

11. IMAGINARY WORLDS

13. THE WORLD’S ALPHABET

14. THE INFINITELY SMALL

15. MEASURING THE FUTURE

16. THE COMING OF MACHINES

17. MATHS TO COME

BIBLIOGRAPHY

INDEX

About the Author

About the Publisher

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Cover

Title Page

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The fourth category is that of friezes that are invariant under a rotation by a half-turn. Whether you look at these friezes from above or below you will always see the same thing.

The fifth category is that of glide symmetries. This notable category was the last one I discovered while passing through Mesopotamia. If you reflect such a frieze about a horizontal axis of symmetry (as per the second category) the frieze obtained is similar, but translated by half a pattern length.

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