Preface 

vii  
History in the Mathematics Classroom 

1  (4) 
The History of Mathematics in a Large Nutshell 

5  (60) 


6  (8) 


14  (10) 


24  (4) 


28  (4) 


32  (3) 

The 15th and 16th Centuries 


35  (2) 


37  (5) 

Calculus and Applied Mathematics 


42  (5) 

Rigor and Professionalism 


47  (6) 

Abstraction, Computers, and New Applications 


53  (6) 


59  (6) 
Sketches 


1. Keeping Count Writing Whole Numbers 


65  (8) 

2. Reading and Writing Arithmetic Where the Symbols Came From 


73  (6) 

3. Nothing Becomes a Number The Story of Zero 


79  (6) 

4. Broken Numbers Writing Fractions 


85  (8) 

5. Something Less Than Nothing? Negative Numbers 


93  (8) 

6. By Tens and Tenths Metric Measurement 


101  (6) 

7. Measuring the Circle The Story of π 


107  (6) 

8. The Cossic Art Writing Algebra with Symbols 


113  (8) 

9. Linear Thinking Solving First Degree Equations 


121  (6) 

10. A Square and Things Quadratic Equations 


127  (6) 

11. Intrigue in Renaissance Italy Solving Cubic Equations 


133  (6) 

12. A Cheerful Fact The Pythagorean Theorem 


139  (8) 

13. A Marvelous Proof Fermat's Last Theorem 


147  (8) 

14. On Beauty Bare Euclid's Plane Geometry 


155  (8) 

15. In Perfect Shape The Platonic Solids 


163  (6) 

16. Shapes by the Numbers Coordinate Geometry 


169  (8) 

17. Impossible, Imaginary, Useful Complex Numbers 


177  (8) 

18. Half Is Better Sine and Cosine 


185  (8) 

19. Strange New Worlds The NonEuclidean Geometries 


193  (8) 

20. In the Eye of the Beholder Projective Geometry 


201  (6) 

21. What's in a Game? The Start of Probability Theory 


207  (8) 

22. Making Sense of Data Statistics Becomes a Science 


215  (8) 

23. Machines that Think? Electronic Computers 


223  (8) 

24. The Arithmetic of Reasoning Logic and Boolean Algebra 


231  (6) 

25. Beyond Counting Infinity and the Theory of Sets 


237  (8) 
What to Read Next 

245  (8) 


245  (3) 

Fifteen Historical Books You Ought to Read 


248  (2) 

The Internet and Other Media 


250  (3) 
Bibliography 

253  (10) 
Index 

263  