You are not currently logged in.
Access JSTOR through your library or other institution:
Pi, the Primes, Periodicities, and Probability
Stephen D. Casey and Brian M. Sadler
The American Mathematical Monthly
Vol. 120, No. 7 (August–September 2013), pp. 594-608
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.07.594
Page Count: 15
You can always find the topics here!Topics: Integers, Algorithms, Mathematical procedures, Datasets, Mathematical functions, Periodicity, Number theory, Mathematical problems, Mathematics, Radio
Were these topics helpful?See somethings inaccurate? Let us know!
Select the topics that are inaccurate.
Preview not available
Abstract The theory of numbers has repeatedly shown itself to be both practical and beautiful. This paper gives an example of this duality. We present a very efficient (and practical) algorithm for extracting the fundamental period from a set of sparse and noisy observations of a periodic process. The procedure is computationally straightforward, stable with respect to noise, and converges quickly. Its use is justified by a theorem, which shows that for a set of randomly chosen positive integers, the probability that they do not all share a common prime factor approaches one quickly as the cardinality of the set increases. The proof of this theorem rests on a (beautiful) probabilistic interpretation of the Riemann zeta function.
Copyright the Mathematical Association of America 2013