Recent knowledge of the number \(\pi \). (Czech) Zbl 0936.11001

Netuka, Ivan; Veselý, Jiří

Pokroky Mat. Fyz. Astron. 43, No. 3, 217-236 (1998).

This is an informative survey of recent achievements in investigation of the number \(\pi \) written for non-specialists. The aim is to show that experimental mathematics is a discipline with a rich history which has developed dramatically with the use of powerful computers and shown useful by finding new valuable results. After a brief introduction to the history the authors present numerous examples of exciting recent results concerning fast algorithms, normality of \(\pi \), probabilistic interpretation, calculation of individual digits etc. on one side, and simply formulated but yet unsolved questions like “Is \(\log \pi \) irrational?” on the other side. The paper is a useful guide which may open e.g. high-school teachers a fascinating view to the world of real numbers.

Reviewer: J.Rákosník (Praha)

MSC:

11-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11Y16	Number-theoretic algorithms; complexity
11Y60	Evaluation of number-theoretic constants

Keywords:

\(\pi \); normality; computational methods; numerical algorithms