Due Date: Thursday of week 02

The following guidelines are expected for all homework submissions:

• I don't care too much about what font you use or how large your margins are; however, you might want to check out a monospaced font for typing code, as it will be easy to see the indentations.
• Speaking of indenting, PLEASE DON'T USE TABS TO INDENT YOUR CODE. Tabs can often get interpreted differently by different computers, peripherals, and applications, and could make code that is nicely formatted on *your* computer look all over the map on *my* computer or in my editor. USE SPACES INSTEAD. You can set up almost every modern text editor to insert spaces whenever you press the TAB key, or you can simply pound the spacebar.
• On assignments 1, 2, and 3, WORK BY YOURSELF. On assignments 4 and 5, YOU MAY WORK IN A GROUP if you would like to do so. However, I can't stress this enough; part of this policy is don't split up the work – YOU MUST WORK TOGETHER on the assignment if you work together!. This activity mimics an industry code development model called pair programming which is part of the Extreme Programming software development method. Feel free to collaborate within your group as much as you want, doing the entire assignment together.
• DO NOT share your work between individuals or groups. Doing so will count as plagiarism. If you wish to discuss solutions with another group over coffee in the Lair, that's fine as long as it is kept at the conceptual level and you don't share your code between groups or individuals. Each person or group needs to turn in its own version of the solutions.
• Submit your assignment in GitHub, in your repository, to which I must be invited to be a collaborator. I cannot evaluate what I cannot see!
• If you are working in a group you only need to turn in ONE COPY per group.
• MAKE SURE YOUR GITHUB REPO IS PRIVATE [for reasons explained on the syllabus page and in class].
• MAKE SURE TO INCLUDE ME IN YOUR REPO AS A CONTRIBUTOR so that I can upload your evaluations.

Problems for Assignment #1

Learning Outcomes: 1) make sure your Python Development Environment is working; 2) make sure your GitHub repository is set up and accessible; 3) make sure you can check code into your repository; 4) learn the basics of python on a simple simulation

This assignment is actually really easy. All you need to do is:

1. Get your GitHub account set up; use the naming convention CMSI-3630_<your_name> so I can easily tell which one is which
2. Create your repository with all the required folders; use the empty file README.md to start the folders [GitHub won't let you create just an empty folder ~ you need something in it]
3. Make sure that the folder structure is set up the same as on the week one page under the Assignment Submissions section
4. Make sure that the repository is PRIVATE for reasons explained in class
5. Invite your professor to participate in your repository; my GitHub name is bjohnson05 and my squirrel drinking coffee logo should be visible
6. Be sure to check that your code runs from the command line, the REAL one, not one that is part of an editor or IDE like Eclipse or VScode
7. Commit one copy of your week one in-class exercise to your homework01 directory; if you are in a group

Part Two: As Shown In Class ~ piSolver.py

OUR FIRST SIMULATION ALGORITHM! WOOHOO!

One easy way to determine the approximate value of PI is to use what's known as the Monte Carlo simulation. To do this, implement the following steps:

1. Imagine a unit circle which is a circle with a radius of one unit
2. Inscribe that circle inside a square, so that the four sides of the square are tangent to the circle on all four sides; this means you have a square that is 2 units by two units with the circle inside it
3. The center of the circle will be at the intersection of the diagonals of the square
4. Now imagine throwing a large bunch of darts that RANDOMLY land inside the square; some will land in the circle, some will land in the square OUTSIDE the circle
5. Given the area of the square is Area_square = 2 * 2 = 4 units
6. Given the area of the circle is Area_circle = PI * r * r and since r = 1, then Area_circle = PI units
7. Taking the ratio of Area_square to Area_circle give the equation Area_square / Area_circle = 4 / PI
8. Rearranging that equation gives PI = (Area_circle * 4) / Area_square
9. OK, now we can create a program for this! See if you can write a program in Python that will give an approximate value of PI using Monte Carlo Simulation. The steps are as follows:
   1. Generate a large number of random X and Y paired values to simulate points where darts hit
   2. Count how many total points there are to simulate the area of the square — you know this because it's the number of darts thrown
   3. Calculate the distance of each point from the center [origin] of the circle; if it is less than or equal to one, that dart is INSIDE the circle so count it using a counter variable
   4. When all darts are thrown, use the total number thrown as Area_square and the total count INSIDE the circle as Area_circle
   5. Calculate and output the approximate value of PI using the equation developed above
10. Note there are some special considerations here. For example you are counting integers, but when you divide you will need a real number for the result. You will need real numbers for the X and Y values, and for the distance from the origin. The distance of each point from the origin will be the hypoteneus of a right triangle.