Inside Your Calculator: From Simple Programs to Significant Insights (Paperback)

Preface xi

PART I THE SETTING

1 Introduction 3

PART II ALGORITHMS AND PROGRAMS

2 Numbers, Algorithms, and Programs 19

3 Integer Powers 40

4 Square Root 51

5 Rational Powers 73

6 Logarithms 84

7 Archimedes’ Calculation of π 106

8 Calculating Trigonometric Functions 117

9 CORDIC Calculation of Cosine 138

PART III DISPLAYING INFORMATION

10 Graphing 163

APPENDIXES 177

A A Primer on Programming 179

B Interpolation 188

C Pre–Electronic Calculation Tools 191

D Fermat’s Last Theorem 204

E An Extension and an Application of Integer Division 206

F Binary Arithmetic 211

G Binary Subtraction 222

H The Rapid Convergence of Newton’s Method 228

I How Newton’s Method Applies to the Square Root Algorithm and the Rth Root of N 230

J The Ancient Greeks Approximate √2 233

K Continued Fraction Approximations 238

L Multiplying Numbers with Many Digits 243

M Finding Equation Roots by Binary Search 249

N Derivation of the Logarithm Change of Base Formula 256

O The Ratio of Decimal to Binary Digits 257

P Constructing a Log Table 260

Q Relations between Sides of Inscribed and Circumscribed Polygons 265

R Change in Form of a Polygon Formula 273

S An Area Approach to Archimedes’ Problem 276

FURTHER READING: A Personal Selection 281

INDEX 285