/sci/ - Science & Math

I have a math degree capstone course this coming spring. I don't know what to do in it. I'm thinking something in numerical algebraic geometry, like homotopy continuation or maybe just visualizations of algebraic sets using MATLAB. I'm at a mid tier university, I'm not quite sure what the capstone course is about to be honest, I'm just assuming its going to be something where I'll pick a topic of interest and write a toy research paper on it.

>Find the center of mass of a lamina in the shape of an isosceles right triangle with equal sides of length if the density at any point is proportional to the square of the distance from the vertex opposite the hypotenuse.