# Illustration

## Algebraic Numbers in motion

Various animations of what happens to the roots of polynomials with integer coefficients when changing each coefficient. The results are pretty.

## Complex points of Weierstrass elliptic curves

with Silviana Amethyst

An elliptic curve is usually depicted as a donut or as the real points of its Weierstrass equation. These don't look related. Silviana and I explored representations of the complex points of the Weierstrass equation using computer renderings, virtual reality, and 3D prints.

## Complex points of curve singularities

in progress...

## Projective space in VR

A program for exploring real algebraic projective surfaces in RP^3 in room-scale virtual reality.

## Projective curve viewer

A program for exploring algebraic curves in the real projective plane. Available under the terms of the GPL.

## Numberscope

A project headed by Kate Stange with the goal of creating a suite of visualization tools for the study of integer sequences. I participated in Fall 2018-Spring 2019 and Spring 2020.

# u-substitution

We can think of u-substitution visually as consisting of a horizontal stretch, which screws up areas, then a vertical stretch to compensate. This is a tool to see that.