The Spirit of Mathematics 1st edition by David Acheson 0192659682 9780192659682

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ISBN-10 ‏ : ‎0192659682 

ISBN-13 ‏ : ‎9780192659682

Author:   David Acheson 

What makes mathematics so special? Whether you have anxious memories of the subject from school, or solve quadratic equations for fun, David Acheson’s book will make you look at mathematics afresh. Following on from his previous bestsellers, The Calculus Story and The Wonder Book of Geometry, here Acheson highlights the power of algebra, combining it with arithmetic and geometry to capture the spirit of mathematics. This short book encompasses an astonishing array of ideas and concepts, from number tricks and magic squares to infinite series and imaginary numbers. Acheson’s enthusiasm is infectious, and, as ever, a sense of quirkiness and fun pervades the book. But it also seeks to crystallize what is special about mathematics: the delight of discovery; the importance of proof; and the joy of contemplating an elegant solution. Using only the simplest of materials, it conjures up the depth and the magic of the subject.

The Spirit of Mathematics 1st Table of contents:

1. Introduction
2. Whatever Happened to A, B, and C?
The human element in mathematics?
Stylish bath-filling?
3. The 1089 Trick
Why does it work?
Who invented it?
Another explanation
4. Another Kind of Magic
A magic square
The magic constant
What goes in the central box?
5. Just Imagine…
Euclid’s Elements
Proof of Thales’ theorem
6. A Most Unusual Lecture
Prime time
Infinitely many primes
7. Why Are Mathematicians Obsessed by Proof?
‘Try to prove theorem’
A tempting proposition
8. Puzzling Mathematics
A chocolate bar problem
The roll of the dice
C ‘wins’ again!
The mutilated chessboard
A four-card puzzle
9. Why Does (−1) × (−1) = +1?
Addition
Multiplication
Area
The distributive rule
Negative numbers
So…why does (−1) × (−1) = +1?
10. It’s a Square World
The importance of being square
Square roots
11. Algebra in Action
A ‘picture proof’
Proof by algebra
Pythagoras’ theorem
12. ‘Compleating the Square’
Another view
Completing the square
But what’s it all for?
13. Slices of Pi
Measuring π
The area of a circle
Infinity enters the picture
14. The Golden Ratio
A quadratic equation
15. Proof by Chocolate
In search of an infinite series
In search of 1/3
16. The Puzzled Farmer
An imaginative solution
17. Mathematics and Snooker
18. The Wicked Schoolteacher
Another general result
The puzzled farmer (again!)
19. Trains, Boats, and Planes
Passing trains
After the event
A windy flight
The missing hat
20. I’ve Seen that Before, Somewhere…
A crossed-ladders problem
Motion pictures
21. An Apple Falls…
Circular motion
22. Rollercoaster Mathematics
The apple revisited
Rollercoaster dynamics
23. The Electric Guitar Revisited
The method of dimensions
Circular motion
The simple pendulum
The guitar revisited
24. The Domino Effect
Proof by induction
A two-colour theorem
25. Real or Imaginary?
The spinning top
26. The Square Root of Minus One
The cubic equation
Real or imaginary?
27. Inspector Riemann Investigates…
28. Infinite Danger
Infinity again
What robbery?
29. 1 + 1 = 2 to the Rescue!
The AM-GM inequality
An unexpected twist
30. And Finally…
Notes
3. The 1089 trick
6. A most unusual lecture
8. Puzzling mathematics
15. Proof by chocolate
16. The puzzled farmer
17. Mathematics and snooker
18. The wicked schoolteacher
19. Trains, boats, and planes
24. The Domino Effect
25. real or imaginary?
26. The square root of minus one
29. 1 + 1 = 2 to the rescue!
30. And finally . . .
Further Reading
Acknowledgments
Picture Credits
Index
1089 AND ALL THAT

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