Introduction:
I'm a 22 year old currently pursuing a masters in Mathematics at the Faculty of Sciences of the University of Lisbon.
This website may contain anything I find interesting.
Manimations:
I have a small (private) utilitary python library for Manim, an open source Python library originally created by math educator Grant Sanderson. Some of its features include:
- Pascal triangle-like objects whose squares are also objects which can be controlled both individually or as a whole through a behavior function;
- A generalization of continued fractions which support any approximation through iterated compositions, such as repeated exponentiation or radicals;
- Methods for visualizing periodic functions as functions on a circle, and the method of visualization of Fourier series using circles.
By following the construction shown, we can obtain arbitrarily sparse sets of integers with proportionally many solutions to the equation x+y=z in the set. These are called Bohr sets.
By painting only the odd integers in Pascal's triangle we obtain a fractal called Sierpisnki's triangle, shown above.