W1292 Useful Randomness

Within these castle walls be forged Mavens of Computer Science ...

— Merlin, The Coder

Random Bitmap

Research

• Random Number Generation
• How Random is Your Randomness?
• The Search for π

Background

The value of π can be calculated by:

1. Randomly throwing "darts" at a unit circle
2. Counting the total number of "darts", N
3. Counting the number of "darts" that fall within the unit circle, C
4. The ratio of the area inside the circle to the total area is C/N
5. The value of π is four times this value (because the area of the total square is 2 units x 2 units)

Exercises

1. Estimate the value of π by performing the above experiment
   1. Throw 100 darts. What result do you obtain?
   2. Throw 1000 darts. What result do you obtain? How is this different from your previous result?
2. How many digits are you able to accurately estimate π by varying N?
3. How important is it that the dart be "thrown" randomly?