Exercise 1 - Python for Data Science

This short exercise is meant to provide a quick guide to various features in the Python programming language and the Scientific Python packages. It is highly recommended that all students attempt this exercise prior to the solutions being posted.

1. Write a Python method using only the standard library - no external packages or methods - to compute the distance between the points (x1, y1) and (x2, y2). Make sure you test it out properly.
2. Do the same thing as (1) but using built-in numpy methods.
3. Write a Python class (please refer to Python documentation to find out what a class is and how to make one) to represent an n-sided regular polygon with vertices at a distance r from the center. Note that n and r should be inputs to your class. E.g., a square with diagonals of length 2 can be instantiated as Polygon(4, 1).
4. Add a method called get_vertices to your Polygon class, which will return a Python list of coordinates (xi, yi) for the vertices. This is not uniquely defined of course, but you can choose any scheme that results in a regular polygon. Hint: think of how to get the angles of polygon and construct the points from there using a for loop.
5. Add a method called get_perimeter to your Polygon class, which will compute the perimeter of the Polygon based on the vertices obtained in (4) and the distance code in qn (1)/(2).
6. Using your class in (4), construct a Pandas DataFrame with n = 3-100 (inclusive) with r = 1 with the following columns: n, r, perimeter.
7. In your DataFrame in (6), add a column for the percentage difference between the perimeter of the n-sided Polygon and a circle of radius 1 (note: it does not matter what the radius is of course, but this makes it a bit more concrete).
8. Using matplotlib, seaborn or any other means, plot the relationship between the percentage difference between the perimeter of the n-side Polygon and a circle of radius 1 against n. Label your x and y axes properly.