To run in “forever” mode where data is continuously generated

1. Download and open the PiMonteCarlo2 file.

2. Hit “setup” and wait for the picture to be drawn

3. Hit “go” and observe for a while.

4. Jot down a few observations. Some things to write about are:

a. Describe what is happening in the picture display.

b. Explain what the graph shows about the simulation.

c. The pi value generated by the simulation is updated for each step and printed in the text box. What happens to the pi value as you let the simulation run?

5. Switch the “random-walk” button to “on” (this can be done while the program is running). Write down some observations. Consider:

a. Does this look like a random walk?

b. Explain how you know whether or not this is a random walk.

To run slowly

1. Set up a new run. Watch the simulation in slow motion. This can be done two ways: use the “single-step” button to move the turtle or use the slider above the picture display and press “go” to run the turtle slowly but continuously.

2. Watch the program run. Write down what happens to the value for pi after

a. 10 steps

b. 100 steps

c. 1000 steps

d. 10 000 steps?

3. How do you think the program calculates a value for pi? Can you explain the mathematical steps that are needed?

Going farther-Breaking the Model

All models have simplifications which limit the accuracy of the model. Systematically explore the limits of this simulation.

1. How many steps on average does it take to get and keep the first digit “3”?

2. How many steps does it take to consistently produce “3.1”? How about “3.14”?

3. Come up with an estimate of how many steps you would need to come up with a value of pi equal to 3.1415. Explain how you made this estimate.