Sebastian Bozlee

Visualizing Elliptic Curves

Most visualizations of elliptic curves neglect either their complex points or their usual algebraic embedding in projective space. See the results of some other visualizations here: Link.

Projective Viewer VR

Displays real algebraic projective surfaces in RP^3 at room scale.

Looking at the Clebsch surface.

GitHub repository

A video


We can think of U-substitution visually as consisting of a horizontal stretch, which screws up areas, then a vertical stretch to compensate. Here's a tool to see that: Link.

Quotient group

This one illustrates a couple of quotient groups of Z/2 x Z/2 x Z/2 x Z/2. Press 1,2,3,4 to add the standard basis elements. Press i,u to move forward and backwards in the process of quotienting by a certain subgroup I, and j,q to do the same for another subgroup J. Link.

Shift similarity of primes mod m

Not sure how to explain this: Link

Projective Curve Viewer

Displays algebraic curves in the real projective plane. Available under the terms of the GPL. I occasionally screw up the dependencies, so if the program fails to run due to missing DLLs, let me know.

Windows Program

GitHub repository

Demo Video: Panning and Zooming in RP2

Demo Video: Animating Pencils of Curves