Proabilistic Determination of the Value of e by Shuffling

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This application is designed and developed by Saumitra Chakravarty under GNU General Public License. May be used or distributed for non-commercial educational purposes only.


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What is this thing?

If you give an identiacl set of random ‘objects’ to each of the ‘participants’ in a group to shuffle and order as randomly as they can, then counting and matching all those arrangements may provide a good approximation of the base of natural logarithm (denoted ‘e’). You have to randomly choose a particular sequence of those objects as ‘standard’ and then match all other randomly generated sequence to see how many of those sequences match your standard sequence in at least one position. After discarding those sequences which match, even at a single position with the standard (including the standard itself), the remaining sequences are called ‘derangements’. Dividing the total number of arrangements (including the standard) with the number of derangements give an approximate value of e. The above application shows what happens to the approximation if we keep increasing the number of participants (that is, number of arrangements) for different numbers of objects.

This flash web application is cited in the following work(s) by Saumitra Chakravarty:

  1. Sombhoboto (BOOK) > Section 2.12
  2. Goniter Sather Bosobas (BOOK) > Chapter 4