@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

This profile is from a federated server and may be incomplete. Browse more on the original instance.

henryseg, to random
@henryseg@mathstodon.xyz avatar
bathsheba, to random
@bathsheba@mathstodon.xyz avatar

I have a lot of links embedded prettily in 3-space, and I want to look at Seifert surfaces on them.
I can flatten them into knot diagrams and find the braid word etc and use the standard algos, but then how would I pull the result back onto my original nice embedding?
Or is there any method of building Seifert surfaces on links in 3D without relaxing and flattening them into canonical posture?

henryseg,
@henryseg@mathstodon.xyz avatar

@bathsheba @nervous_jesse

@Danpiker has some animations of Seifert surfaces in situ on fibered 3D knots. I think the idea is, for every point in space you send a sphere of rays out, and you see how much each ray “winds” around the knot. Then average that fractional winding number over all rays at that point. You get a function from R^3 to [0, 2pi). The level sets of that function are the Seifert surfaces in the animation.

henryseg,
@henryseg@mathstodon.xyz avatar

@bathsheba @nervous_jesse @Danpiker Here’s an example: https://mathstodon.xyz/@Danpiker/110233669569515853

henryseg, to random
@henryseg@mathstodon.xyz avatar

New video about wild knots:
https://youtu.be/o7U3yvMF8Sw

henryseg,
@henryseg@mathstodon.xyz avatar

@christianp 1) Thanks! 2) I had no idea...but it’s not so surprising I guess!

henryseg,
@henryseg@mathstodon.xyz avatar

@optozorax Yes, both are wild topological objects.

henryseg,
@henryseg@mathstodon.xyz avatar

Hsin-Po Wang (https://www.instagram.com/symbolone1) came up with this awesome animation of undoing the wild slipknot (which is of course impossible):

https://www.desmos.com/3d/ng4mkltbi3

henryseg, to random
@henryseg@mathstodon.xyz avatar

What parking space number is under the backpack?

henryseg, to random
@henryseg@mathstodon.xyz avatar

Lots of flat foldable structures with arbitrary cross-sections. @csk @Chaimgoodmanstrauss

henryseg, to random
@henryseg@mathstodon.xyz avatar

Lots of flat foldable structures with arbitrary cross-sections. @csk @Chaimgoodmanstrauss

image/jpeg
image/jpeg
image/jpeg

henryseg, to random
@henryseg@mathstodon.xyz avatar

The next talk at this workshop (Structures - Polyhedra, Meshes, Platforms, at RICAM in Linz) is “Exploring T-hedral Origami across varied topologies”, by Kiumars Sharifmoghaddam.

henryseg, to random
@henryseg@mathstodon.xyz avatar

Rational six-bar linkage by Daniel Huczala and collaborators. Here's the paper: https://arxiv.org/pdf/2403.00558

A linkage of six bars joined by revolute joints, rotating around a loop of configurations.

henryseg,
@henryseg@mathstodon.xyz avatar

Here's an application in robotics of these kinds of linkages.

A simple robot made out of a four-bar linkage moves a marble up to the top of a marble run.

henryseg, to random
@henryseg@mathstodon.xyz avatar

Nathan Toups interviewed me on his podcast, “Functionally Imperative”. Among other things, we talked about 3D printing, VR, making stuff, the internet, and aphantasia. https://youtu.be/dcS8FjGaOws?si=HmCQr7YQuInP9tVQ

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
#Mechanism #KineticArt

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.

  • All
  • Subscribed
  • Moderated
  • Favorites
  • •
  • megavids
  • thenastyranch
  • rosin
  • GTA5RPClips
  • osvaldo12
  • love
  • Youngstown
  • slotface
  • khanakhh
  • everett
  • kavyap
  • mdbf
  • DreamBathrooms
  • ngwrru68w68
  • provamag3
  • magazineikmin
  • InstantRegret
  • normalnudes
  • tacticalgear
  • cubers
  • ethstaker
  • modclub
  • cisconetworking
  • Durango
  • anitta
  • Leos
  • tester
  • JUstTest
  • All magazines
    •