An Exploration of Triangular-Square Numbers

Start: 04/11/2018 - 4:15pm
End  : 04/11/2018 - 5:15pm


Berit N. Givens (Cal State Polytechnic University, Pomona)


A triangular-square number is both a perfect square of the form m2 and the sum of all integers from 1 to some value n.  In my first year teaching, I assigned a homework problem about triangular-square numbers that turned out to be much harder than I had realized.  The known solutions required material from later in the curriculum.  Years later, a colleague and I became convinced that "morally" there should be a way for students to solve the problem using only the techniques they had been taught so far. That started us on a path of mathematical discovery, learning about Pell's Equation and continued fractions, while also drawing lots and lots of pictures of triangles and squares as we searched for a visual solution to the original problem.  In this talk, I will give an overview of the Pell’s Equation and continued fractions material involved, then show our visual solutions.  The talk will be accessible to students at any level.

Freeberg Forum, LC 62, Kravis Center, CMC

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