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Pi - Unleashed Paperback – January 25, 2001

by Jörg Arndt (Author), Christoph Haenel (Author), C. Lischka (Translator),

4 customer reviews

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In the 4,000-year history of research into Pi, results have never been as prolific as present. This book describes, in easy-to-understand language, the latest and most fascinating findings of mathematicians and computer scientists in the field of Pi. Attention is focused on new methods of high-speed computation.

Pi - Unleashed

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Product Details

Paperback: 270 pages
Publisher: Springer; Softcover reprint of the original 1st ed. 2001 edition (January 25, 2001)
Language: English
ISBN-10: 3540665722
ISBN-13: 978-3540665724
Product Dimensions: 6.1 x 0.6 x 9.2 inches
Shipping Weight: 1.1 pounds
Average Customer Review: 4.5 out of 5 stars See all reviews (4 customer reviews)
Amazon Best Sellers Rank: #3,663,313 in Books (See Top 100 in Books)
- #1286 in Books > Science & Math > Mathematics > Pure Mathematics > Number Theory
- #1631 in Books > Computers & Technology > Programming > Algorithms
- #2198 in Books > Computers & Technology > Databases & Big Data > Data Processing

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20 of 23 people found the following review helpful

Have your pi and eat it too

By Pi eater on December 9, 2001

Format: Paperback

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.

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4 of 4 people found the following review helpful

Indispensable for the Pursuits on Contemporary Pi Calculation

By Man Kam Tam on November 30, 2008

Format: Paperback

"PI Unleashed" of Jorg Arndt and Christoph Haenel's has seventeen chapters, one appendix, and one CDROM. The first chapter presents a brief history on pi calculation. Generally speaking, we are in the 3rd era of pi calculation, which began around 1980. This era has three major developments. They are the development of high speed: (1) multiplications of large numbers, (2) algorithms on calculating pi, and (3) computers. Since 1980, the number of known pi digits grows twice (200%) per year. The new goal now is to calculate individual digits at the far end of pi. By BBP algorithm, one is able to calculate any digits of pi without calculating any prior digits. The 2nd era began around 1650. Since then the arc tan method dominated the pi calculation until 1980. The method of the 1st era (250BC-1650) is to calculate the circumferences of the two regular polygons placed inside and outside of a circle.

The methods on high speed multiplication for large numbers are introduced on chapter 11. They are the Fast Fourier Transform and Karatsuba multiplication. Chapter 6 through 10 introduces the algorithms. They are the spigot algorithm, Gauss AGM algorithm (a popular algorithm), Ramanujan's algorithm (50 correct decimal places per term), Borweins' algorithms (every iteration generates four to five times more digits than the previous iteration), and the BBP algorithm. Other than supercomputer, the Internet is a valuable computing resource. The binsplit algorithm enables pi to be distribute computed by the computers on the Internet.

The CDROM comes with a few extreme precision library packages. One of them is hfloat. The author of hfloat is Jorg Arndt, which is also one of the authors of the book. The appendix of the book documents the hfloat library.Read more ›

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13 of 17 people found the following review helpful

One of many recent pieces on pi

By Marvin J. Greenberg on November 4, 2004

Format: Paperback

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.

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1 of 1 people found the following review helpful

Good introduction to pi

By Junn on February 9, 2009

Format: Paperback

This book, together with the accompanying CD, is directed towards the decimal expansion of the number pi. The authors' account of the history of the development of this topic is illuminating. They discuss the recent results of Kanada's and Borweins', and Ramanujan's. Their exhaustive list of mathematical formulas of pi is helpful. However, if the reader is mathematically oriented, be warned that very few proofs are provided for these formulas.

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