Pi: A Biography of the World's Most Mysterious Number
Alfred S. Posamentier,Ingmar Lehmann | 2004-08-31 00:00:00 | Prometheus Books | 324 | Mathematics
In this delightful layperson's introduction to one of math's most interesting phenomena, Drs Posamentier and Lehmann review p's history from pre-biblical times to the 21st century, the many amusing and mind-boggling ways of estimating p over the centuries, quirky examples of obsessing about p (including an attempt to legislate its exact value), and useful applications of p in everyday life, including statistics.
Reviews
I think 'fascinating' is a good word for this book, but it is probably not for everyone. I liked it, but my wife's eyes glaze over when I tell her about it. It is written in an understandable fashion and does not try to snow the average person or go into too much detail. If it did, I would have put it down. The authors are excited about the subject and want to communicate that excitement to the readers. I think they did a good job of it, but the fact is that you really have to be a math fan to like this book.
Let me give you a flavor of the book. For example, by how much would the addition of a single meter to an imaginary band about the earth raise that band above the earth? If you would say something like a micrometer, that would be a good intuitive answer (at least what I would have said) but incorrect. The surprising answer (which I will let the book reveal) has nothing to do with how big the original circle is, but relates instead to only how much the circumference is changed and the constant of pi.
The book gives a history of how pi is calculated, all the way back to Archimedes and, later, Euler who might have been the most brilliant mind in the history of math. His famous formula the natural log e raised to the power of pi times i = -1 was mentioned in the book and well it should have. How does an irrational number raised to an irrational, imaginary power result in a real, rational number? In passing, the book explored how an imaginary number of i raised to the power of i can come out to a real number. (This involves natural log e being raised to a power of pi). Where did these amazing formulas and continued fractions for pi come from? Some of the formulas are astounding! It is also shown that pi is related to integers in certain formulas that have nothing to do with circles!
This information is amazing, at least to me; and I'm more amazed by the brilliant minds that thought this stuff up!
Reviews
A previous reviewer has already given a synopsis of this book. The book belongs in the libraries of high schools and junior colleges, and would be a worthy addition there. It is relatively non-technical, and perhaps inevitably so, as the authors are not professional mathematicians, but rather "mathematics educators."
A faster, more technical, and more complete work is, "Pi Unleashed", by Arndt and Haenel, and published by Springer (ISBN 3540665722).
Reviews
+++++
This book, by Professors Alfred Posamentier and Igmar Lehmann, reveals the mystery behind the constant number Pi. It is designated by the symbol of the sixteenth lower-case letter of the Greek alphabet and is formally calculated by dividing the circumference of any circle by its diameter. Its value is (3.14...) or approximately (22/7).
This book convinced me that Pi is special and comes up in the most unexpected places. The mathematics needed to fully understand this easy-to-read, informative, engaging, and fun book is "no more...than that of high school mathematics." Large, helpful diagrams accompany all mathematical explanations.
This book consists of nine chapters:
(1) Tells the reader what Pi is and how it achieved its current prominence.
(2) Takes the reader through a brief history of the evolution of Pi. This history goes back four thousand years.
(3) Provides various methods for arriving at Pi's value. A wide variety of methods have been chosen, "some precise, some experimental, and some just good
guessing."
(4) Centers on activities and findings by mathematicians and math hobbyists who have explored the value of Pi and related fields in ways that the ancient mathematicians would never have dreamed of.
(5) Explores some of the curious phenomena that focus on the value and concept of Pi. Primarily here is how Pi relates to other famous numbers and to seemingly unrelated concepts.
(6) Is dedicated to some applications of Pi. The lesson from this chapter is that Pi is ubiquitous -- it always comes up!
(7) Presents some fascinating relationships involving Pi and circles.
(8) This is the book's epilogue. Here, we are presented with Pi to 100,000 decimal places (which uses up almost thirty pages).
(9) This is an afterword by Dr. Herbert Hauptman who won the Nobel Prize in Chemistry in 1985. He is known "as the first mathematician to win a Nobel Prize."
This book also presents little unknown things about Pi. For example, did you know that there is a Pi song? How many decimal places has Pi been calculated (as of 2002)? There is even a Pi day, a specific month and day in which this number is celebrated! (From the information presented above, a reader of this review should be able to figure out the exact month and day.)
After reading this book, the reader should definitely and confidently be able to say what Pi is.
Finally, this book does tell you everything (and I mean everything) about Pi but I was surprised (especially since the afterword is by a Nobel Laureate in chemistry) that there is no mention of the chemical bond called the "pi bond." It is called this because of its shape. In physics, there are elementary particles called "pi-mesons" or "pions."
In conclusion, this book takes the mystery out of the mysterious number Pi. If you're like me and like exploring mysteries, then this is the book for you!!
(first published 2004; acknowledgments; preface; 7 chapters; epilogue; main narrative 245 pages; afterword; four appendices; references; index)
+++++
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