Different ways to calculate Cosine Similarity in Python

The last several posts that I have written on have been about cosine similarity, which is an important function relating to natural language processing, or NLP. The reason for this is because I encountered a competition in Kaggle that was based on NLP, but I could not complete it because I am not proficient in programming for this genre of data science. As a result of this I decided that I would study this topic to see if I could improve my skills. What I found out is there are quite a few programs that one can write involving NLP, to include classification problems, recommendation systems, question and answer systems, plagiarism checkers, and even chatbots. With regard to recommendation systems, question and answer systems, and plagiarism checkers, one function that is crucial to the correct implementation of these programs is the cosine similarity function. My most recent post on Cosine Similarity can be found here:- https://medium.com/geekculture/an-easy-way-to-determine-similarity-between-two-strings-of-text-using-python-de9b1b52f022

Any person who is a whiz at math would be interested in knowing the mathematical formula for cosine similarity, which is seen in the diagram below:-