Steve Trettel

Steve Trettel

Hello! I'm a mathematician and artist at the University of San Francisco, who works in geometry and mathematical visualization. This site collects my illustration, code, and writing. Sometimes I also take photographs and cook.

Art

Mathematical art that has been displayed in art shows, galleries, or museums.

Cubic Lines
Cubic Lines — Framed Print
Julia
Julia — Framed Print
Lightfall
Lightfall — Print on Metal
Space(time)
Space(time) — Prints on Metal
Geodesic Boards
Geodesic Boards — Wood
Singularity
Singularity — Print on Metal
Showing 6 of 13 artworks View full gallery →

Blog

Mostly notes to myself about things I'm trying to learn, or calculations from larger projects that may be interesting in their own right.

Showing 10 of 71 posts All posts →

Demos

Small web programs illustrating various mathematical objects, from both teaching and research.

Cubic Lines Live hopf torus list hyerbolic embedding flows weierstrass hex weierstrass square hex curve hex curve elliptic 11 4
Showing 8 of 372 demos Browse all →

Graphics

An archive of mathematical illustrations I've made over the years.

First Light Hyperbolic Disk in Euclidean Space The Hex Torus in S³ Airplug Hyperbolic Cube Analog Gravity Gravitational Portrait Negroni at the Event Horizon
Showing 8 of 290 graphics Browse all →

Software

Larger systems and one-off tools, built mostly for research and teaching.

Systems

Projects

10 software projects Details & documentation →

Books & Course Notes

Long-form expositions, mostly notes from courses I've taught.

Course Notes

Modern Geometry

Notes / textbook for a 1 semester undergraduate course in geometry, taking calculus as the foundations. Covers Euclidean, Spherical and a bit of Hyperbolic geometry.

Course Notes

Multivariable Calculus

Supplementary Course Notes for the multivariable calculus course I teach at USF, with live animations.

Textbook

Reaching for Infinity

A year-long advanced undergraduate real analysis textbook, with an emphasis on historically important problems.

Course Notes

Shaders

Course notes for GPU shader programming as a tool for mathematical visualization, covering fractals, implicit surfaces, tilings, and physical simulations in GLSL.

4 works All books & course notes →

Websites

Project sites built for collaborations and research groups.

algebraicstarscapes.com

Algebraic Starscapes

with Edmund Harriss, Kate Stange
elliptic-curves.art

Visualizing Elliptic Curves over Finite Fields

with Nadir Hajouji
stevejtrettel.site

Geodesic Boards

with Edmund Harriss
3-dimensional.space

Raymarching Thurston Geometries

with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Academic

This semester I am on sabbatical in Europe, and not teaching. (previous semesters)

When not at USF, I'm occasionally on the road for math — upcoming trips below, and where I've recently been. I particularly enjoy giving undergraduate colloquia and public lectures — if you'd like to have me visit, please get in touch.

Recent Papers

All papers →

Recent Talks

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