This is your brain on hyperbolic geometry.

If you find yourself in terminal 2 of SFO airport between now and May 2022, you can see two of my sculptures at an exhibit co-curated by Cliff Stoll!

More photos from the exhibition at SFO international airport.

I'm writing code with Saul Schleimer to (re)implement the 2-3 Pachner move on triangulations of three-manifolds. I had to break out my old ASCII art skills for the comments.

Approximation to a fundamental domain for the Cannon-Thurston map for the figure eight knot complement, joint work with Saul Schleimer.

The European Women in Maths released a poster featuring Notable Women of Mathematics and short biographies.

It is free to download and print in Dutch and English (for now, more translations are ongoing as far as I know), it would be great to display it on the walls our mathematics departments: ewmnetherlands.nl/projects/wom

Two mathematicians messing around on Discord. With @saulsch.

Today, I dragged @StuartBeveridge to Chorley to see a fantastic bridge.

Because the railway and canal are at such a sharp angle, a normal arch wouldn't stay up. Instead, the stones are hand-carved in curves so that the joins between them are perpendicular to the bridge's weight.

A brief article on a brief proof. I'll be interested to see how well mathematicians that aren't topologists can grok the concepts described here.

quantamagazine.org/how-complex

A version of a figure from almost exactly four years ago (version 7 apparently), and the hopefully near finished version (version 31) from earlier today, with @saulsch.

Related discussions online include:

I sort of disagree with. I think that being a mathematician helps a lot (because I already think in terms of definitions, lemmas, and so on).

suggests that the checker just computes to high precision, or perhaps computes "the function" at several test points (every construction can be recast as a function).

I've gotten a bit obsessed with "euclidea" - this is a euclidean geometry game You are given a goal (build something) and allowed certain constructions (draw a line, a circle, and so on). When you succeed, the goal (point, line, circle, triangle, or other) turns a lovely shade of yellowy-orange. My question: given that there are infinitely many different constructions, how does the game "know" when you have won?

Stages of debugging: (1) That can't happen. (2) That doesn't happen on my machine. (3) That shouldn't happen. (4) Why does that happen? (5) Oh, I see. (6) How did that ever work? -- M.W.Cremer

RE @KangarooPhysics @robinhouston: Also, looks like you don't even need that restriction on the dimensions 2022-05-03 12:46:59 UTC

@ColinTheMathmo @nilesjohnson I invited @saulsch using an invite link a couple of days ago and it seemed to go through quickly.

@neilbickford Hmm. Actually this is a concern: if two parts are identical (like the ball bearings here), then the puzzle cannot mechanically tell them apart. This introduces symmetries in the configuration space, and so reduces its size (?).

Oskar van Deventer has a new mechanical puzzle that requires 4^55 moves to solve: twistypuzzles.com/forum/viewto

So, he's got a system that produces a puzzle whose solution length grows exponentially in the number of parts.

Question: Is it possible to come up with a system whose solution lengths are super-exponential in the number of parts?

Nobody quite knows how it works, but occasionally people will wake up to find they have been given a Gift, a special ability like Healer, or Invulnerable, or Prophetic. And somehow everyone knows about their new Gift.
You woke this morning knowing you are a Bestower of Gifts.
#MicroFiction #SmallStories

Katie Steckles and I have a podcast called Mathematical Objects, which releases a short chat on a mathematical topic fortnightly in seasons of 8 episodes.

Today's episode is "A joke" with special guest Bec Hill. We talk about similarities and differences between maths and jokes.

Hopefully you can find it where you normally find podcasts (let me know if not!) or listen/subscribe/etc. via aperiodical.com/2022/05/mathem

Hello all. I am a mathematician interested in geometric topology and group theory, and computational aspects of those areas. I also very much like pretty pictures. :)

Show older

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!