An Introduction to the Seminar and to Polygonal Numbers
September 17, 2012
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 at 4:45
I plan to spend a few minutes at the beginning of the hour talking about the seminar and what you should expect this year. After those introductory remarks, I'll talk about polygonal numbers.
Intuitively, a positive integer $n$ is a polygonal number if $n$ dots can be arranged in the shape of a polygon. To give what might be a familiar example, the number 10 is triangular because 10 dots can be arranged in the shape of a triangle like the 10 pins at a bowling alley. Similarly, 9 dots can be arranged in the shape of a square grid, so 9 is a square number. We'll prove a number of elementary results about triangular and square numbers and then move on to pentagonal numbers ... and beyond. The only pre-requisites for this talk are addition and multiplication and an ability to recognize patterns in sequences of numbers and shapes.
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