W1292 Useful Randomness

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

— Merlin, The Coder

Random Bitmap

Kuntze-Konicz Fortune

Prerequisites

• W1151 Conditional and Flow Chart
• W1152 While Loop
• W1153 Repeat-While Loop
• W1154 For Loop

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)

Prepare

Create a new directory in your ~/Experiences directory named "project-1292". Use emacs to edit a file named "main.swift":

zay-vin@codermerlin:~$  cd ~/Experiences

zay-vin@codermerlin:~/Experiences$  mkdir project-1292

zay-vin@codermerlin:~/Experiences$  cd project-1292

zay-vin@codermerlin:~/Experiences/project-1292$  touch main.swift

zay-vin@codermerlin:~/Experiences/project-1292$  makeSwiftMake

zay-vin@codermerlin:~/Experiences/project-1292$  emacs main.swift

Observe

Observe, Ponder, and Journal: Section 1

Complete your program, then answers these questions.

1. Estimate the value of π using your program
   1. Throw 100 darts (N = 100). What result do you obtain?
   2. Throw 1000 darts (N = 1000). What result do you obtain?
2. How is the second result different from your previous result?
3. How large should N be to accurately estimate π to five digits?
4. How important is it that the dart be "thrown" randomly?

Key Concepts

Key Concepts

• Random numbers meet the following two criteria:
  • Even distribution over a defined interval
  • Impossible to predict subsequent values based upon previous values
• Random numbers can be very useful in certain circumstances