In 1981, during the waning days of the best of the “calculator wars” between Hewlett-Packard, Texas Instruments, and other manufacturers, I was forced to learn the “standard” algorithm for calculating square roots by hand. Never mind the reality that the rise of inexpensive scientific calculators was fast making this algorithm obsolete,;my 11th-grade math teacher was quite insistent that this was a skill we all needed to master.
I still know that algorithm, and use it about once a year to dazzle and confuse students. Thus, I am pleased to see it making a comeback — at a sensible level — in Inside Your Calculator , where alternate algorithms for many common calculator functions (cosine, square root, and logarithms among them) are presented and discussed. Rising makes it clear that the algorithms he presents are not the ones used by the TI-84 plus calculator, but simple programs that compute the necessary values while illustrating important calculation issues. To find the cosine of an angle entered in degrees takes only a 7-line program, for example. (There is a chapter that discusses CORDIC calculation of the cosine function, as is used in many calculators.) In that sense, he lives up to his title and provides simple programs that lead to significant insights.
This is a book for “active reading”, in the same vein as the “active learning” trend that runs through classrooms around the country. Not only because reading calculator program code is a bit on the dry side, but because the concepts that Rising is describing are only really appreciated when you see a calculator producing results — accurate results from easily-understood programs. For readers unfamiliar with programming a calculator, several appendices provide a simple introduction to this powerful tool. Everyone — from novice math students to experienced calculator users — will find something useful and interesting in this book.
Mark Bollman (firstname.lastname@example.org) is an associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock. Mark shares his office at Albion with 818 new and old calculators, which were certainly an inspiration for this review, and a regulation 3-reel slot machine, which was merely a distraction.
PART I: THE SETTING.
Chapter 1. Introduction.
PART II: ALGORITHMS AND PROGRAMS.
Chapter 2. Numbers, Algorithms and Programs.
Chapter 3. Integer Powers.
Chapter 4. Square Root.
Chapter 5. Rational Powers and Roots.
Chapter 6. Logarithms.
Chapter 7. Archimedes' Calculation of π.
Chapter 8. Trigonometry.
Chapter 9. CORDIC.
PART III: DISPLAYING INFORMATION.