Pi - Unleashed

Rating:
Summary: Have your pi and eat it too
Review: A must have for the pi gourmet. Ever since reading Beckman's "History of Pi" years ago, I have had a love for pi. Finding Blatner's "The Joy of Pi" only added to it. With "Pi-Unleashed", Arndt and Haenel help to sate the appetite for more pi left by the first two books. While Beckman weaves the tale of pi as only he can in his book, and Blatner does indeed bring joy to the pi lover in the way he pulls together so many aspects of pi, Arndt and Haenel help to satisfy the number junkie who likes to experience pi, not just read about it. This book was so good that after giving it a good sniffing, I just had to roll all over in it to get its scent all over me. The book covers the many roads to pi, from the oldest arctangent series and product series to the latest series used for calculating hundreds of billions of digits. For the algorithm junkie, it has 17 whole pages of nothing but pi formulas, followed by thousands of digits of pi in decimal and hexadecimal as well as continued fraction format. The mathematics is deeper than Beckman or Blatner, but nothing beyond college level. The CD that comes with the book contains 400 million digits of pi along with a whole slew of programs on pi or high precision numbers that I just had to dig into. I know I will be spending many weeks chewing on all the wonderful new bones offered in this book.

Rating:
Summary: Have your pi and eat it too
Review: A must have for the pi gourmet. Ever since reading Beckman's "History of Pi" years ago, I have had a love for pi. Finding Blatner's "The Joy of Pi" only added to it. With "Pi-Unleashed", Arndt and Haenel help to sate the appetite for more pi left by the first two books. While Beckman weaves the tale of pi as only he can in his book, and Blatner does indeed bring joy to the pi lover in the way he pulls together so many aspects of pi, Arndt and Haenel help to satisfy the number junkie who likes to experience pi, not just read about it. This book was so good that after giving it a good sniffing, I just had to roll all over in it to get its scent all over me. The book covers the many roads to pi, from the oldest arctangent series and product series to the latest series used for calculating hundreds of billions of digits. For the algorithm junkie, it has 17 whole pages of nothing but pi formulas, followed by thousands of digits of pi in decimal and hexadecimal as well as continued fraction format. The mathematics is deeper than Beckman or Blatner, but nothing beyond college level. The CD that comes with the book contains 400 million digits of pi along with a whole slew of programs on pi or high precision numbers that I just had to dig into. I know I will be spending many weeks chewing on all the wonderful new bones offered in this book.

Rating:
Summary: One of many recent pieces on pi
Review: Why the flood of books on pi (do a search, you'll see)? And why calculate its decimal expansion to enormous numbers of places? Is number mysticism having a revival?

Certainly there are many fascinating theorems involving pi, which is one of the two most important transcendental numbers (the other being e) and which shows up unexpectedly in many different branches of mathematics. These books are well worth reading to learn those theorems, those lovely, unexpected formulas, and the interesting history.

If you are a trained mathematician, the best of these books by far is the recent one by Eymard and Lafon, but it is very difficult.

My complaint about all these books is that not one of them proves that pi exists! I mean pi is defined as the ratio of the circumference to the diameter of any circle; in order for that definition to make sense, one must prove that ratio to be constant. But that ratio is only constant in Euclidean geometry, not hyperbolic or elliptic geometries, so the proof depends on the Euclidean parallel postulate and is not at all obvious.

There is a proof in the book by Moise "Elementary Geometry from an Advanced Viewpoint."

This book is a good one, its main competition being the good one by Posamentier and Lehmann.