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Pascal's Prism

Published online by Cambridge University Press:  23 January 2015

Harlan J. Brothers
Harlan J. Brothers*
Affiliation:
Brothers Technology, LLC, PO Box 1016, Branford, CT 06405-8016, USA, e-mail: harlan@brotherstechnology.com
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Extract

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.

2. From Pascal to Leibniz

In Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.

Specifically, we define the sequence sn; as follows [6]:

Type
Articles
Information
The Mathematical Gazette , Volume 96 , Issue 536 , July 2012 , pp. 213 - 220
Copyright
Copyright © The Mathematical Association 2012

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