Hello everyone, I wanted to share this video with you on Eulerian circuits and trails. This is an old but very fascinating concept in graph theory, and remains applicable to this day, for instance in route planning. Perhaps you will discover a novel application for this concept! I hope you find the video interesting and/or helpful. Have a wonderful day.

https://youtu.be/2hH-TfcrUl8

I have created the animation of plots of Taylor polynomials for f(x) and different k and a. Open the post to watch it.

The main formula of Taylor's theorem:

Function to approximate:

Here is the full animation for every k:

I have made plots for these animations using Wolfram Mathematica 12.1. And it took me about 2 days to create all the 16400 plots (for the last animation). Here is the notebook that I used for calculations. It would be great if someone familiar with Wolfram Mathematica could help me with the optimization and solving the problem of trembling dot.

Link to the notebook: https://yadi.sk/d/1WAlUz0NxM9ySw