### Assignment #9

**Due: 15 March, 1999**

### Squarez

Suppose we take a unit square, *i.e.* one with sides of length 1. To the middle of each side attach a square with sides 1/3 the length. To the middle of each side of the resulting object attach a square with sides 1/3 the length. To the middle of each side of the resulting object attach a square with sides 1/3 the length, and so on.

Consider the object that you would have at the end of this (infinite!) process.

**1.** What is the length of the border of the limit object? *[4]*

**2.** What is the area of the limit object? *[5]*

**3.** What is the limit object very close to being? *[1]*

Department of Mathematics
Trent University

Maintained by Stefan Bilaniuk. Last updated 1999.12.03.