It All Adds Up: The Story of People and Mathematics
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Stephen Wilson S.. It All Adds Up: The Story of People and Mathematics
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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
Отрывок из книги
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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