Two mathematical notes – new homogenised Simpson's rules and a riffle shuffle conjecture
Abstract
Purpose
Seeks to derive a class of “homogeneous” rules for numerical integration from earlier results and empirical findings to treat the apparently magical reordering of a pack of cards after successive shuffles, previously discussed by Zeeberg, from a new angle and to form a mathematical conjecture.
Design/methodology/approach
The studies were made using computer programs for which the language JavaScript proved adequate.
Findings
The rules for numerical integration are more precise than earlier versions. The conjecture associated with card shuffling appears to be novel.
Practical implications
Improved methods of numerical integration have practical value in many areas. The conjecture is in the field of number theory, with no obvious immediate applications.
Originality/value
The findings and methods are original. The demonstration of a plausible mathematical conjecture may provoke further studies aimed at its proof as a theorem, or its refutation.
Keywords
Citation
Andrew, A.M. (2006), "Two mathematical notes – new homogenised Simpson's rules and a riffle shuffle conjecture", Kybernetes, Vol. 35 No. 5, pp. 748-752. https://doi.org/10.1108/03684920610662502
Publisher
:Emerald Group Publishing Limited
Copyright © 2006, Emerald Group Publishing Limited