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
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
"People who want to know how things work will enjoy this book…" (Journal of Recreational Mathematics)
"I recommend this book for anyone who has…an interest in understanding how calculators work or in programming calculators." (Mathematics Teacher, February 2008)
"A book on algorithms for scientific pocket calculators that is written with much dedication." (Zentralblatt MATH, 2008)
- Written by an expert in mathematical education, this well-organized book reflects the author's forty-plus years of teaching and writing experience.
- This book constitutes a complete and multi-faceted exercise in critical thinking.
- The author focuses on explanations that are based on only high school basic algebra and geometry (both of which are reviewed in context) in an effort to appeal to a broad range of readers who are attracted to mathematics and its ideas.
- Well-conceived, illuminating, and entertaining diagrams and other figures are found throughout the book.
- Teachers, at both the high school and college level, will especially enjoy this book since it provides insight to answer student questions such as "Why is this important?"
- The history of mathematics is discussed when appropriate and provides a foundation for further learning.