Lecture 14 - Randomness
As usual, create two directories for today's class. Create a
directory called lecture14 under activities, and
a directory called lab14 under labs.
Randomness
Time to learn a new module! This module lets us generate random numbers, which we can then use within out programs.
In-class Activity 1
How Random(?)
Create a file called how_random.py in your
lecture14 directory. Write a function that uses the
turtle module, and draws a line a random distance (and
location) from the origin. You should do this by generating two
random integers, and going to that location on the screen.
Write another function called euclidean_distance, which
takes 2 integer parameters (x and y), and returns the distance that
the point is from the origin (0,0).
Using these two functions, write a for loop that draws some number of
random lines radiating from the center of the turtle window. Compute
and write (using turtle.write)
the disance from the origin the end point of the line is.
Your for loop should also compute the average distance from the center your set of points are. Print this average to the terminal. Run your program multiple times. Does this average seem random? Does the distribution of points seem random?
More Emacs Commands
- Auto-complete
- Commenting
- Go-to line
- Searching
- Casing words
Lab Assignment 14
Estimating π
If you went to the talk last Friday, you already have a leg up on the rest of the class. Archimedes developed a mechanism that allows one to estimate π based off the radius of a circle and its circumference.
"Wait a minute!" you're probably saying to yourself. "The equation for computing the circumference of a circle relies on π!" And you would be absolutely correct. However, if we can approximate the circumference of a circle, then we could get an approximate value for π, using the following formula:
π = C / (2 × r)Where C is the estimated circumference, and r is the radius of the circle.
In a file called estimate_pi.py in your lab14
directory, write a function that estimates π by computing the
circumference of the polygon that "estimates" a circle. Your
function should take the number of sides the polygon has and the
radius of the circle estimated by the polygon. It should return the
estimate of π based on that polygon.
Recall, from trig, that you can compute the length of a side of the polygon by using the sin of the angle. So:
inner angle of a right triangle = arc_length / 2
Once you have your function written, use a for loop to print the π estimate for all polygons with a number of sides s ≤ 25. Your function should choose a random radius for each. Compare your values with a team close by. Do your values vary greatly?
Testing and Debugging
Your programs are continually growing. Soon, you might get stuck simply because you left off an ")", or even a ":". One way to mitigate this is through the process of incremental design. The first step towards that is through testing your functions. Let's see how that's done.
Submission
When you have finished, create a tar file of your lab14
directory. To create a tar file, execute the following commands:
cd ~/cs120/labs tar czf lab14.tgz lab14/
To submit your activity, go to cseval.roanoke.edu. You should
see an available assignment called Lab Assignment 14. Only
one of your pair should submit your activity. Make sure both partners
are listed in the header of your file.
Do not forget to email your partner todays files!
Last modified: Mon Sep 30 14:06:11 EDT 2013