Pi: Algorithmen, Computer, Arithmetik

by Jörg Arndt, Christoph Haenel

Ausgehend von der Programmierung moderner Hochleistungsalgorithmen stellen die Autoren das mathematische und programmtechnische Umfeld der Zahl Pi ausführlich dar. So werden zur Berechnung von Pi sowohl die arithmetischen Algorithmen, etwa die FFT-Multiplikation, die super-linear konvergenten Verfahren von Gauß, Brent, Salamin, Borwein, die Formeln von Ramanujan und Borwein-Bailey-Plouffe bis zum neuen Tröpfel-Algorithmus behandelt. Der Leser findet viel Anregendes wie auch Skurriles, etwa interessante Anmerkungen zur Quadratur des Kreises. Die beigelegte CD-ROM bietet dem User mannigfaltigen Nutzen, z.B. die ausgeführte Langzahlarithmetik hfloat im C++ Source-Code, die FFT- Multiplikation und Algorithmen zur Pi-Berechnung. Die zweite, überarbeitete Auflage nimmt zahlreiche Leseranregungen auf und berichtet über die wichtigsten neuesten Ergebnisse der Pi-Forschung. Zahlreiche Verweise auf Internetquellen, ausführlicher Index und Literaturverzeichnis ergänzen das Buch.

Genres: Mathematics

Hardcover

First published June 30, 1998

About the author

Mathematician

Reviews

[Maurizio Codogno · Rating 5 out of 5]

Oltre le solite informazioni

Si parla di pi greco, magari senza chiamarlo così, da svariati millenni. Ci sono molti libri che raccontano la storia di questo numero. In questo libro, però, l'approccio è diverso: gli autori sono più interessati alla parte algoritmica moderna - ci sono anche programmi da eseguire - e antica, nel senso che è uno dei pochi testi a mia conoscenza dove viene spiegato come si arriva a ricavare alcuni degli sviluppi in serie più famosi. Nella parte iniziale del libro ci sono anche varie presentazioni di numeri "strani" che hanno a che fare con il nostro pi greco, oltre a un piccolo excursus filosofico. Il testo non è sicuramente a livello elementare, ma è imprescindibile per chi è seriamente interessato a studiare il pi greco.

[Ghada · Rating 4 out of 5]

In tribute to Pi Day (3.14.2011) rather than baking pies, this year I decided to read “Pi Unleashed”. Even though the book was originally written in German, I found that no meaning was lost in translation. All the chapters were clear and comprehensible, allowing me to easily go through the derivations and theories with no confusing significant grammatical mistakes*.

The book was almost bursting with π facts, history, derivations and algorithms. It was such a blast going through all the different mathematical methods (utilizing trigonometry, calculus, series analysis... etc) that were all leading up to many representations of the one and only π. In fact, there are over 15 pages at the end solely dedicated to the π formula collection!!! In addition, the book comes with a CD that contains the first 400,000,000 decimal places of π… As well as algorithms and programming codes for high precision calculations of pi (ah if only I could program, it would’ve been so much fun to try out the codes this weekend!!:( )…

Anybody who is even remotely intrigued by π is bound to enjoy reading this book. This is definitely one that I would recommend to the mathematics enthusiasts out there!


*Except for one mistake which was clearly a typo. I did not keep track of which page it was on, but it was on one of the right hand side pages along the end of the second or third line, in the last 1/5th of the book. It was just a missing “s” that should have been used to indicate a plural.

[George · Rating 5 out of 5]

It also has a great CD.