## Individual Research Projects Section 9.3

### Project 9.5

Prepare a classroom demonstration of topology by drawing geometric figures on a piece of rubber inner tube. Demonstrate to the class various ways in which these figures can be distorted.

### Project 9.6

The problem shown in the News … See the whole entry

Videos:
Introduction to Fractal Geometry (time: 1:41)

If you are fascinated with fractals and would like a complete introduction, this video gives you a complete lecture on this topic. time: 53:45)

This is a video on using geoboards (time: 2:01)… See the whole entry

## Reference Topics 9-3

This site investigates the four-color problem:
http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/The_four_colour_theorem.html

A beautiful gallery of fractal designs are found on these sites:
http://fractals.hauner.cz/1

A site showing some of Escher’s tessellations is interesting:

This site shows the colorful answer to Problems 24 and 25:… See the whole entry

## Homework Hints 9-3

### Note: Homework Hints are given only for the Level 1 and Level 2 problems.

However, as you go through the book be sure you look at all the examples in the text. If you need hints for the Level 3 … See the whole entry

## 9.3 Outline

1. Topology
1. topologically equivalent figures
2. planar curve
3. closed curve
4. interior/exterior
5. simple curve
6. Jordan curve
7. invariant property
8. genus
2. Four-color problem
3. Fractal geometry
4. Tessellations

## 9.3 Essential Ideas

Two geometric figures are said to be topologically equivalent if one figure can … See the whole entry