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Steve Trettel

@stevejtrettel.bsky.social
582 followers 267 following 90 posts

Math Prof: Geometry, Topology and Illustration at University of San Francisco. Minnesotan, from the occupied lands of the Dakota people.

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Steve Trettel @stevejtrettel.bsky.social · 20/05/2025
Summers here - time to catch up sharing some of what I’ve been up to! First up - *gravitational photography* - using (simulated) black holes instead of lenses to focus an image onto a screen. Can you see the ghostly dinosaur? 1/n
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Steve Trettel @stevejtrettel.bsky.social · 29/01/2025
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Steve Trettel @stevejtrettel.bsky.social · 23/01/2025
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Steve Trettel @stevejtrettel.bsky.social · 20/01/2025
The regular hexagon can be rolled up isometrically into a flat torus in 4 dimensional space: here’s a stereographic projection of the result. (Can you see the hexagonal pattern in the spheres covering its surface? 😁)
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Steve Trettel @stevejtrettel.bsky.social · 19/01/2025
Here’s a cute lil donut!
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Steve Trettel @stevejtrettel.bsky.social · 19/01/2025
Fun pic from a new project! Drawing lots of donuts today 😁
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Steve Trettel @stevejtrettel.bsky.social · 07/12/2024
Best of luck to all taking the Putnam today, from our team here at USF! 🤓🤘
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Steve Trettel @stevejtrettel.bsky.social · 06/12/2024
I have a second piece display at O'Hanlon Center for the Arts in Mill Valley CA this month, entitled "Julia". Here it is, and a short math-explainer of what we're looking at
A hexagonal grid in the plane with each cell filled with a small image of a black and white fractal.  Some of the fractals are larger (and darker) than the others, so when looking from a distance another image emerges (as the fractals themselves act like dark/light pixels for the larger image)
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Steve Trettel @stevejtrettel.bsky.social · 06/12/2024
This book is incredibly good
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Steve Trettel @stevejtrettel.bsky.social · 04/12/2024
My artwork "Many Paths to the Beach" is currently on display at O'Hanlon Center for the Arts in Mill Valley CA. here's a math explainer thread: what are we looking at here?
A repeating 3D lattice of blue orbs against a black background.  Looking closely into any one of the orbs reveals a distorted view of sea, sky and sand dunes.  Each orb gives a slightly different perspective on the scene.
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Steve Trettel @stevejtrettel.bsky.social · 04/12/2024
So honored to have some of my pieces on display at O’Hanlon Center for the Arts in their exhibition “Chaos” this month. This one is titled “Many Paths to the Beach” (explanatory thread to follow once I’m to my office)
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Steve Trettel @stevejtrettel.bsky.social · 03/12/2024
Bay Area people: I’m really excited to have two pieces of mathematical art on display at O’Hanlon Center for the Arts in Mill Valley, for their exhibition “Chaos”. The opening reception is today 530-7pm! www.ohanloncenter.org/event/chaos-...
ohanloncenter.org
CHAOS Gallery Show Art Talk and Reception | O'Hanlon Center for the Arts
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Steve Trettel @stevejtrettel.bsky.social · 02/12/2024
The hopf fibers corresponding to the vertices of a regular dodecahedron
Pastel colored circles in space against a white background , linked together in a tangled blob with smaller circles in the center and larger reaching outwards.  Accompanying this to the left is a smaller glass sphere with a dodecahedron inscribed on its surface: pastel vertices (one corresponding to each of the circles) connected by blue edges.
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Steve Trettel @stevejtrettel.bsky.social · 02/12/2024
Some points on the sphere and their preimages under the hopf map
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Steve Trettel @stevejtrettel.bsky.social · 02/12/2024
Some more good fibration - I really like how this one came out 😃
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Steve Trettel @stevejtrettel.bsky.social · 02/12/2024
Some fibers of the Hopf Fibration
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Steve Trettel @stevejtrettel.bsky.social · 26/11/2024
Here's what it would look like to travel in a distant orbit to two extremal charged black holes, which themselves are stationary (grav/electrostatic in balance). As you orbit you see one pass in front of the other and lens it; Ive colored light rays green/red which enter their respective horizons.
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Steve Trettel @stevejtrettel.bsky.social · 25/11/2024
Still having fun with Majumdar Papapetrou black holes over here :) This animation shows six such black holes arranged on the vertices of an octahedron, and traces a null geodesic from a nearby observer. The trajectory, and which BH it enters, depends very sensitively on the initial condition
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Steve Trettel @stevejtrettel.bsky.social · 24/11/2024
@mseri.me introduced me to Majumdar–Papapetrou black holes through his+collaborators paper on the chaotic trajectories of light around 3 or more such black holes. Here's some intrinsic raytraced views of the N=3 case, where light rays falling into each are colored red/green/blue respectively.
Three black holes with event horizons colored red green and blue, from above the plane they lie inThree black holes with event horizons colored red green and blue, from in the plane.  The blue even horizon is distorted by lensing to form a ring.Three black holes with event horizons colored red green and blue, from in the plane.  The red even horizon is especially distorted by lensing.
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Steve Trettel @stevejtrettel.bsky.social · 24/11/2024
Recently learned about Mamjudar-Papapetrou solutions in GR: masses attract but like charges repel, so if you throw enough charge into a collection of black holes they can remain static! Here's such a collection of BHs arranged cubically, and a (numerically found) closed null geodesic.
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Steve Trettel @stevejtrettel.bsky.social · 19/11/2024
One of my fav GR pics for you blueskiers! A bit outside the horizon of a nonrotating black hole lies the photon sphere - a “point of no return” for infalling light. Here’s a light ray that makes a brush with death - skimming the photon sphere, doing a loop, then continuing on its merry way
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Steve Trettel @stevejtrettel.bsky.social · 18/11/2024
Just got into Orange County - beautiful morning for a walk into UC Irvine to talk about mathematical physics!
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Steve Trettel @stevejtrettel.bsky.social · 17/11/2024
Heading down to Southern California today to visit UCI and talk about Newtonian physics in the presence of curvature . So here’s a fun fact: there is no Galilean relativity in curved space ! You can do experiments to determine your precise velocity
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Steve Trettel @stevejtrettel.bsky.social · 15/11/2024
Hello all! I’m bad at keeping up with multiple social medias but as people move here figured I should reintroduce myself 😃 I’m a mathematician at the university of San Francisco who has gotten himself too deep into a computer graphics hobby. Here’s a couple algebraic varieties to cheer up your day ☺️
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Steve Trettel @stevejtrettel.bsky.social · 25/10/2023
I’ll also try to advertise my talks here 😁. Bay Area math lovers - ever wonder why black holes look like this? I’m giving a public talk on curved space and general relativity at the Castro Valley public library tonight (Wed. Oct 25) at 7pm. Register (free!) here: wonderfest.org/curved-space...
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Steve Trettel @stevejtrettel.bsky.social · 25/10/2023
Hello Bluesky! Trying to keep up with the rapidly fragmenting socials landscape over here - so I’m Steve, a mathematician at the U of San Francisco who loves geometry, outreach, and mathematical art! Here’s an algebraic variety in glass to brighten your timelines 😁
Pathtraced image of the Barth Sextic algebraic variety, made of simulated green glass against a primary color background
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