On the Normality of Numbers
(Sprache: Englisch)
A number is normal in a base if, in its expansion tothat base, all possible digit strings of any givenlength are equally frequent. While it is generallybelieved that many familiar irrational constants arenormal, normality has only been proven for...
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A number is normal in a base if, in its expansion tothat base, all possible digit strings of any givenlength are equally frequent. While it is generallybelieved that many familiar irrational constants arenormal, normality has only been proven for numbersexpressly invented for the purpose of proving theirnormality.In this study we review some of the main results to date.We then define a new normality criterion, strongnormality, to exclude certain normal but clearlynon-random artificial numbers. We show that stronglynormal numbers are normal but that Champernowne'snumber, the best-known example of a normal number,fails to be strongly normal.We also re-frame the question of normality as aquestion about the frequency of residue classes of anincreasing sequence of integers modulo some fixedinteger. This leads to the beginning of a detailedexamination of the digits of irrational square roots.
Autoren-Porträt von Adrian Belshaw
Adrian Belshaw was born in Canberra, Australia, in 1953. Heearned a BSc in Mathematics at UBC in 1973, and an MA in Biologyat Princeton in 1976. In 2005 he completed an MSC in Mathematicsat SFU, and he is working on his Ph.D. at SFU with Peter Borweinas senior supervisor. Adrian is an instructor at Capilano Collegein Sechelt, Canada.
Bibliographische Angaben
- Autor: Adrian Belshaw
- 52 Seiten, Maße: 22 cm, Kartoniert (TB), Englisch
- Verlag: VDM Verlag Dr. Müller e.K.
- ISBN-10: 3639036247
- ISBN-13: 9783639036244
Sprache:
Englisch
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