Math 459, Senior Seminar
11/14/11
Name: Tim Joyce
Title: Pythagorean Triples Recursively
Source: Peter W. Wade and William R. Wade, Recursions That Produce Pythagorean Triples,
The College Math Journal, Vol. 31, No.2 (Mar., 2000), pp. 98-101
Senior Project Ideas
1. The authors give a recursive formula that they prove generates Pythagorean triples
that have a height that is neither a perfect square nor a double square and that none of
its devisors are perfect squares or double squares. My first senior project idea would
be to investigate what happens with Pythagorean triples that have a height that is
neither a perfect square nor a double square but is a multiple of a perfect square.
i.e.H=12 Does the recursive formula not work or could they just not prove it worked?
2. The first formula given in the article is non-recursive but it can be proven that it only
generates Pythagorean triples that are reduced. Another senior project idea would be
to investigate other types of non-recursive formulas that give you Pythagorean triples.
This could be done class wise like finding a formula that gives all unreduced
Pythagorean triples or it could be attempted to find a formula that generates all
Pythagorean triples generally.
3. The authors present a recursive formula that gives a specific group of Pythagorean
triples. My last senior project idea would be to investigate into a recursive formula
that generates all Pythagorean triples.
(1) a = m2 – n2 , b = 2mn , c = m2 + n2
(2) ak+1 = ak + D , bk+1 = βak + bk + βD/2 , ck+1 = βak + ck + βD/2