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# An Introduction to the Seminar and to Polygonal Numbers

by

Karl Zimmermann
Union College

September 17, 2012
5:00 pm
Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:45

## Abstract:

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.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
Up: Student Seminars for 2012
Top: Math Department Student Seminars

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