The Journal of Online Mathematics and Its Applications, Volume 8 (2008)
Modeling Spiral Growth in a GSP Environment, Dogan-Dunlap and Jordan

## Sample Worksheet

#### Note

In this sample worksheet, we have omitted the white space in which students would ordinarily copy and paste the resuts from the GSP Program.

#### Directions

Use the file Spirals.gsp to enter the numbers.

### Questions

1. Define rational numbers.
2. Define irrational numbers.
3. Enter the following rational numbers (1/4, 1/5, 1/8, 2/10) :
1. 1st Rational: 1/4. Copy and Paste the GSP result in the space provided below:
2. 2nd Rational: 1/5. Copy and Paste the GSP result in the space provided below:
3. 3rd Rational: 1/8. Copy and Paste the GSP result in the space provided below:
4. 4th Rational: 2/10. Copy and Paste the GSP result in the space provided below:
4. Enter the following irrational numbers (π, e, √2 ).
1. 1st Irrational: π. Copy and Paste the GSP result in the space provided below:
2. 2nd Irrational: e. Copy and Paste the GSP result in the space provided below:
3. 3rd Irrational: √2. Copy and Paste the GSP result in the space provided below:
5. Compare the sketches from questions 3 and 4, and describe the similarities and differences of each sketch focusing on rational and irrational number behaviors.
6. What number (s) can you input to create a sketch that would produce ten rays?
7. What number (s) would you use to create the sunflower seed placement appearance?
8. Try the following number (1 + √5) / 2. This number is called the golden ratio.

Based upon your observations, make a conjecture as to why rational numbers spike out and eventually create rays while some irrational number approximations make more spirals.