@henryseg@mathstodon.xyz
@henryseg@mathstodon.xyz avatar

henryseg

@henryseg@mathstodon.xyz

Mathematician working mostly in three-dimensional geometry and topology, and mathematical maker/artist working mostly in 3D printing and virtual reality.
#Math #Maths #Art #3DPrinting #Geometry

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henryseg, to random
@henryseg@mathstodon.xyz avatar

Apologies in advance to the mathematicians who follow this link: https://cims.nyu.edu/~tjl8195/survey/results.html

GerardWestendorp, to random
@GerardWestendorp@mathstodon.xyz avatar

I was at the G4G (maths, puzzles, gadgets etc) conference this week. This was one of the “exchange gifts”. I don’t know the creator, if someone knows, please let me know.
It is a torus tiled by 5 squares. I was surprised this is possible, so I figured out a fundamental polygon. This also turns out to be a square, which is possible because ( 5 = 2^2 + 1^2) .

henryseg,
@henryseg@mathstodon.xyz avatar

@oschene @GerardWestendorp Yes, that is her gift exchange.

ProfKinyon, to random
@ProfKinyon@mathstodon.xyz avatar

Student: I get what lemmas and corollaries are, but what's the difference between a theorem and a proposition?

Me: That's a great question. Throughout this term, I've been trying to create a welcoming and supportive atmosphere in the class where everybody can feel comfortable asking questions like that. Your question makes me feel like I've at least partially succeeded.

Student: So you don't know either?

Me (to class): Are there any other questions?

henryseg,
@henryseg@mathstodon.xyz avatar

@ProfKinyon Theorems are fancier than propositions.

henryseg, to random
@henryseg@mathstodon.xyz avatar

"Six axis racks" is a symmetric arrangement of gears and racks. Full video at https://youtu.be/zZdSNUoifV4

Twelve 3D printed sticks, each with two racks, moves around a core with twelve gears.

DoctorChunder, to random

Hi @henryseg I made a mastodon account just to ask this question: For this cohomology fractal, is there a way to calculate the distance traveled if one were to take an infinitely zigzagging path from A to B to C?

henryseg,
@henryseg@mathstodon.xyz avatar

@DoctorChunder I'm not sure if I understand your question... if you are travelling along the space-filling Cannon-Thurston map to get from A to B to C then I can't think of a way to interpret the question that doesn't give the answer "infinitely far". @saulsch

MotivicKyle, to random
@MotivicKyle@mathstodon.xyz avatar

OEIS may be the only nonempty encyclopedia containing 0% of the subject matter it purports to cover.

henryseg,
@henryseg@mathstodon.xyz avatar

@MotivicKyle At first I thought you were pointing out that it contains no integer sequences at all, because it doesn’t actually list the infinitely many elements of any integer sequence. (Spot the numerous problems with this interpretation!)

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

One reason we can't have Trump as president: he operates as a gangster. Today's bomb threat to the judge in his bank fraud trial is just the latest example. Two weeks ago, after the Colorado Supreme Court ruled him ineligible to run for office because of the insurrection he led, they got hit with death threats. And many in the Republican party have fallen in line because of such threats - see below!

People not following the news may not realize how big a problem this is.

It works like this: Trump threatens that judgements against him will cause havoc... and his more unhinged supporters fill in the details. It's called 'stochastic terrorism' - and it's not just chatter. Republican attacks against the Speaker of the House eventually led a guy to break into her house: not finding her, he broke her husband's skull with a hammer. Earlier, right-wingers plotted to kidnap the governor of Michigan, but were stopped by the FBI.

It's horrific. If we don't stop Trump by making him lose this election, we're going to have a mob boss in charge of the USA.

For more details, read on!

(1/n)

https://www.vox.com/23899688/2024-election-republican-primary-death-threats-trump

henryseg,
@henryseg@mathstodon.xyz avatar

@tomruen @johncarlosbaez

“Trump is a menace but I’ll blame Biden and Trump voters if Trump wins.”

That’s not how the function from votes to the outcome of the election works... If we end up with Trump and Biden on the ballot then (third party miracles aside), one of them will win, and only votes for one of them matter. I don’t like it either, but that’s the way the system works at the moment.

henryseg, to random
@henryseg@mathstodon.xyz avatar

Surprised to find out that our Cannon-Thurston carving won a prize in the Mathematical Art Exhibition at the Joint Mathematics Meetings! With @saulsch and Will Segerman.

henryseg,
@henryseg@mathstodon.xyz avatar

Here’s the video we made about these curves if you want to know more:
https://youtu.be/FpeeFcK3lTk

henryseg, to random
@henryseg@mathstodon.xyz avatar

At the Serious recreational mathematics session at the joint mathematics meeting. Persi Diaconis’ train is stuck on the way to San Francisco so Erik Demaine is “improvising”, talking about curved origami.

henryseg,
@henryseg@mathstodon.xyz avatar

Persi made it! His talk is about strategies for playing card solitaire.

aeva, to random
@aeva@mastodon.gamedev.place avatar

"hey aeva what do you do for fun?"

oh, you know, normal things,

henryseg,
@henryseg@mathstodon.xyz avatar

@Atridas @aeva Many of my calculus students still do this - I guess they learned it in high school. Nobody at university level cares about clearing radicals out of the denominator.

henryseg, to random
@henryseg@mathstodon.xyz avatar

Red and Green lasers make for a fractal Christmas tree zoom! Full video at
https://youtu.be/uH8w7I1Og1I

video/mp4

henryseg, (edited ) to random
@henryseg@mathstodon.xyz avatar

Zooming into a 3D printed fractal tree. Full video at https://youtu.be/uH8w7I1Og1I

two_star, to random
@two_star@mathstodon.xyz avatar

I got mentioned on this Numberphile video that just came out. The funny bit is that they used a photo of me that was taken 18 years ago when I was interviewed for Jason Scott's documentary on text adventures, Get Lamp. Okay, the funny bit about the funny bit is that Scott barely used the footage from the interview. It's not in the main feature at all; there's just a tiny snippet in a DVD extra. https://www.youtube.com/watch?v=3akBMSJ37Uk
The mention of me is at the 9:15 mark.

henryseg,
@henryseg@mathstodon.xyz avatar

@two_star I have no idea where Brady got the photo!

aeva, (edited ) to random
@aeva@mastodon.gamedev.place avatar

What is the next item in this list:

  1. Translation
  2. Rotation
  3. _
henryseg,
@henryseg@mathstodon.xyz avatar

@aeva Screw motion.

henryseg, to random
@henryseg@mathstodon.xyz avatar

Slide-glide cyclides - a design discovered by Andrew Kepert when investigating ways to “see” why the area of a sphere is four times the area of a disk of the same radius. I added the gears and the base. Full video: https://youtu.be/KD_hRn_97RI

The disk shape.
Midway between the disk and the sphere.
The sphere shape.

henryseg,
@henryseg@mathstodon.xyz avatar

And the files to print out your own version of the mechanism are here: https://www.printables.com/model/651714-slide-glide-cyclides

davidsuculum, to random Spanish
@davidsuculum@mathstodon.xyz avatar

I think I've already asked this before: how do you avoid forgetting new stuff learnt in the areas of physics and mathematics? I'm not talking about things learnt many years ago and practised a lot, so strongly recorded in memory; I'm talking about the new stuff.

Do you revisit the content from time to time? Do you summarize with your own notes and revisit them often? Do you just do nothing and assume that forgetting is part of the game?

henryseg,
@henryseg@mathstodon.xyz avatar

@davidsuculum Hope that my collaborators remember it if I’ve forgotten.

aperiodical, to random
@aperiodical@mathstodon.xyz avatar

Mathematical Drawing Hacks https://aperiodical.com/2023/11/mathematical-drawing-hacks/

henryseg,
@henryseg@mathstodon.xyz avatar

@aperiodical The “smile” in the middle of the usual picture of a torus is very easy to draw once you know it, and instantly makes it look like a torus.

ProfKinyon, to random
@ProfKinyon@mathstodon.xyz avatar

It is surprisingly difficult to convince computer science students not to write things like "elif" in mathematics classes.

henryseg,
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@ProfKinyon If computer scientists aren’t allowed to use “elif”, mathematicians better not use “iff”.

graveolensa, to random
@graveolensa@mathstodon.xyz avatar

https://arxiv.org/abs/2311.06596

/Surfaces in The Tesseract/
Manuel Estévez, Erika Roldan, Henry Segerman (@henryseg)

Abstract: How can we visualize all the surfaces that can be made from the faces of the tesseract? In recent work, Aveni, Govc, and Rold'an showed that the torus and the sphere are the only closed surfaces that can be realized by a subset of two-dimensional faces of the tesseract. They also gave an exhaustive list of all the isomorphic types of embeddings of these two surfaces. Here, we generate 3D models of all these surfaces. We also exhibit, with the help of some hyper-ants, the minimum realization of the M"obius strip on the tesseract.

henryseg,
@henryseg@mathstodon.xyz avatar

@demofox @graveolensa No cutting involved. Just select a bunch of faces of the hypercube and note that they make a torus.

henryseg,
@henryseg@mathstodon.xyz avatar

@narain @demofox @graveolensa Yes, the surface is topologically a torus.

leahwrenn, to random
@leahwrenn@alaskan.social avatar

Which aspect ratio do you prefer, for drawing the Pappus configuration on a torus? L to R: [1,1], [7,4], [3,1].

I'm going to print it next week. Maybe even in color on the super fancy 3D printer my university bought.

Pappus on a torus: a 7 x 4 rectangle folded up
Pappus on a torus: a 3 x 1 rectangle folded up

henryseg,
@henryseg@mathstodon.xyz avatar

@leahwrenn @11011110 This might be relevant for the hex torus: http://m.archive.bridgesmathart.org/2011/bridges2011-593.pdf

gregeganSF, to random
@gregeganSF@mathstodon.xyz avatar

This is a finite piece of Dini’s surface, which has constant negative Gaussian curvature. The same shape, extended indefinitely, can embed an infinitely long strip of the hyperbolic plane, with a geodesic G as one boundary and a hypercycle (a curve a fixed distance from G) as the other. The geodesic is mapped to the central axis of Dini’s surface, while the hypercycle is mapped to the outer helix.

More at https://www.gregegan.net/SCIENCE/PSP/PSP.html

A shape like a trumpet made from helices, with three turns of each helix, tiled with multicoloured triangles.

henryseg,
@henryseg@mathstodon.xyz avatar

@Ianagol @gregeganSF Mass produce? Or just on a small scale? I hear that making new mass-production pasta machines is hard, in part because of the sanitary requirements on food prep machines.

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