Hello there!

I'm Steve Trettel, a mathematician who is also interested in computers, physics, and language.

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I'm currently an assistant professor at the University of San Francisco. This is both my personal and academic website, so you’ll find math I like explaining, updates on my computer graphics hobby, physics I'm learning, and some favorite meals, among other things.

Note: This website is a new redesign (as of summer 2022) for me, and my first attempt at learning hugo for site building: it’s definitely still under construction so apologies in advance for broken links or non-existent pages!

My blogging comes in two broad types, which I’ll call posts, notes. Posts are planned content that I think will be of interest to others, usually of a math/physics/computer science nature. Notes are just pages in my personal notebook: containing enlightening computations and worked examples of various things, short personal writings, and interesting things I don’t want to forget. I will try hard to ensure posts are relatively free of errors, but cannot promise the same for notes - its easy to make mistakes when learning new things, and I hope risk of public embarassment is worth whatever use others may find in them.


Coming Soon!


Rigidity in Curved Space:
Working out the definitions relevant for modeling physical objects in curved space.

Deriving the ODE for a spring which is pushed in hyperbolic geometry (it oscillates!)

Convolution and Differentiation of Distributions:
If F is a distribution and g is a function, why is (DF)*g equal to F*Dg?

Topologizing The Space Of Distributions:
Why do we need to require convergence of the derivatives when defining a topology on the set of distributions?

Deep Time:
Some thoughts on the importance of appreciating the immensity of earth's history.

Life in Hyperbolic Space:
The dangers of life in a negatively curved space

Saying goodbye to my favorite space craft, on the eve of its entry into Saturn's atmosphere.

Cubics and Braids:
The bridge between the 3-strand braid group and the trefoil knot complement

An old note, from my early graduate school days, explaining the hopf fibration.

Lattices in the Plane and the Trefoil Knot

All Notes


All Art


A closed timelike curve in the Godel universe
Riemann Sum
Secant Line
Three Body
Spring Cube
This program simulates a 3 dimensional network of coupled harmonic oscillators, to model a deformable solid such as jello.
A cloth simulation built from a 2D grid of coupled harmonic oscillators.
Integral Curves
Curvature & Torsion
Space curves are determined uniquely up to rigid motion by their curvature and torsion. This program computes a representative curve from these invariants.
Knot Complements
Visualizing the complement the regular neighborhood of knots in the 3-sphere.

All Code



All Talks


All Courses


All Papers


All Recipes