## An Introduction to the Seminar and to Polygonal Numbers |

**Karl Zimmermann**

Union College

September 17, 2012

5:00 pm

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.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Fri Apr 20 21:41:11 EDT 2018 |