W1292 Useful Randomness

Random Bitmap

Kuntze-Konicz Fortune

Prerequisites[edit]

	Coming Soon
	Background summary on how random numbers are generated

	Coming Soon
	Add section on throwing dart at ¼ of square

The value of π can be calculated by:

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

Create a new directory in your ~/Experiences directory named "W1292". Use emacs to edit a file named "main.swift":

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

zay-vin@codermerlin:~/Experiences$  mkdir W1292

zay-vin@codermerlin:~/Experiences$  cd W1292

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

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

	Helpful Hint
	You can run your program from within emacs with F5-r

Helpful Hint

You can find the square root of a number using the squareRoot function. This function is included in the Foundation library, so it must be imported.

For example:

import Foundation

let d = 12.0
print(d.squareRoot())

Observe, Ponder, and Journal Section 1

Complete your program, then answers these questions.

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?
How is the second result different from your previous result?
How large should N be to accurately estimate π to five digits?
How important is it that the dart be "thrown" randomly?

Exercises

Write a program that randomly throws a series of N darts at a virtual dartboard as described above. At the conclusion of throwing N darts, the program should print an estimate for the value of π. Be sure to complete this part of the exercise in your ~/Experiences/W1292 directory.
J1292 Create a journal and answer all questions in this experience. Be sure to include all sections of the journal, properly formatted.

	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