MATH 3262 Fall 2005

Homework for Tuesday, Oct. 4

1. Attached is a sheet containing copies of an equilateral triangle, a square, a regular pentagon, a regular hexagon, a regular octagon, and a regular dodecagon. You are asked to cut out these shapes and investigate the number of different ways you can arrange three or more of these polygons around a point (no overlapping and no gaps). Devise a notation to describe each arrangement.

What observations did you make as you did this investigation? Any conclusions?

2. Find as many non-congruent shapes (2-D) made by connecting 5 squares where each square shares at least one whole side with another square. Record your shapes. What method did you use to find the shapes, and how do you know you have found all of them?