Tom de Jong
@de_Jong_Tom@mathstodon.xyz  ·  activity timestamp last week

My paper "Continuous and algebraic domains in univalent foundations" with @MartinEscardo was accepted for publication by the Journal of Pure and Applied Algebra! 🎉
https://martinescardo.github.io/papers/continuous-algebraic-domains-in-uf.pdf

This paper has its origin in my very first paper with Martín (and my second paper overall) "Domain Theory in Constructive and Predicative Univalent Foundations" which appeared at Computer Science Logic (CSL) back in 2021.

Since then I wrote my PhD thesis on this topic (and worked on other things in type theory after) and the present paper is a revision of both the CLS'21 paper and my PhD thesis (which I completed in 2022).

Everything in the paper has been formalized and an HTML rendering of the Agda file that directly links the code to the paper can be found here: https://martinescardo.github.io/TypeTopology/DomainTheory.Continuous-and-algebraic-domains.html

#typetheory #agda #logic #math #computerscience
Tom de Jong
@de_Jong_Tom@mathstodon.xyz  ·  activity timestamp last week

My paper "Continuous and algebraic domains in univalent foundations" with @MartinEscardo was accepted for publication by the Journal of Pure and Applied Algebra! 🎉
https://martinescardo.github.io/papers/continuous-algebraic-domains-in-uf.pdf

This paper has its origin in my very first paper with Martín (and my second paper overall) "Domain Theory in Constructive and Predicative Univalent Foundations" which appeared at Computer Science Logic (CSL) back in 2021.

Since then I wrote my PhD thesis on this topic (and worked on other things in type theory after) and the present paper is a revision of both the CLS'21 paper and my PhD thesis (which I completed in 2022).

Everything in the paper has been formalized and an HTML rendering of the Agda file that directly links the code to the paper can be found here: https://martinescardo.github.io/TypeTopology/DomainTheory.Continuous-and-algebraic-domains.html

#typetheory #agda #logic #math #computerscience
Oscar Cunningham
@OscarCunningham@mathstodon.xyz  ·  activity timestamp last week

Hilbert curve snake

#Math#Maths#Mathematics#MathArt

A square divided into a black half and a white half. The two halves flow into each other following the Hilbert curve like the snake in the game 'Snake'.
A square divided into a black half and a white half. The two halves flow into each other following the Hilbert curve like the snake in the game 'Snake'.
Mark Wyner Won’t Comply :vm:
@markwyner@mas.to  ·  activity timestamp 4 weeks ago

This had me captivated for a good five minutes. I just kept watching how the patterns matched up, trying to parse out the connections in my brain.

Who knew an animation of a Rubik’s Cube and some corresponding concentric circles could be so stimulating?

I have absolutely no idea who created it. Tried to find out to no avail. (Happy to edit with a citation if someone knows.)

#RubiksCube#Math#Animation#Geometry#Patterns#BrainGames

A Rubik’s Cube, depicted on the right as a three-dimensional rendering, is modeled on the left as a series of overlapping concentric circles. Each sub-face of the cube is a colored dot, and each rotation of the cube corresponds to a rotation of the dots along one of the circles. The dots always fall at the overlaps of two circles, representing that they can always be moved in two different directions.
A Rubik’s Cube, depicted on the right as a three-dimensional rendering, is modeled on the left as a series of overlapping concentric circles. Each sub-face of the cube is a colored dot, and each rotation of the cube corresponds to a rotation of the dots along one of the circles. The dots always fall at the overlaps of two circles, representing that they can always be moved in two different directions.
Mark Wyner Won’t Comply :vm:
@markwyner@mas.to  ·  activity timestamp 4 weeks ago

This had me captivated for a good five minutes. I just kept watching how the patterns matched up, trying to parse out the connections in my brain.

Who knew an animation of a Rubik’s Cube and some corresponding concentric circles could be so stimulating?

I have absolutely no idea who created it. Tried to find out to no avail. (Happy to edit with a citation if someone knows.)

#RubiksCube#Math#Animation#Geometry#Patterns#BrainGames

A Rubik’s Cube, depicted on the right as a three-dimensional rendering, is modeled on the left as a series of overlapping concentric circles. Each sub-face of the cube is a colored dot, and each rotation of the cube corresponds to a rotation of the dots along one of the circles. The dots always fall at the overlaps of two circles, representing that they can always be moved in two different directions.
A Rubik’s Cube, depicted on the right as a three-dimensional rendering, is modeled on the left as a series of overlapping concentric circles. Each sub-face of the cube is a colored dot, and each rotation of the cube corresponds to a rotation of the dots along one of the circles. The dots always fall at the overlaps of two circles, representing that they can always be moved in two different directions.
Rasmus
@rasjor@mathstodon.xyz  ·  activity timestamp last month

Monohedral triangle tiling of the gyroid, which is the dual tessellation of a partial Cayley surface complex of the group:

<br/>G = ⟨ f₁,t₁ | f₁², t₁⁶, (f₁t₁)⁴, (f₁t₁f₁t₁⁻¹f₁t₁²)² ⟩<br/>

Ball of radius 21. (1/2)

#TilingTuesday #tiling #geometry #math #3d

priryo@linernotes.club
OliverUv
priryo@linernotes.club and 1 other boosted
Mark Wyner Won’t Comply :vm:
@markwyner@mas.to  ·  activity timestamp 2 months ago

In my journey to continue to find the good things in a world that’s breaking my heart on the daily, I found some beautifully-serene art.

Kinetic artist, Reuben Margolin uses skills in design, engineering, physics, electronics, and more. He creates motorized pieces that seem impossible. The one is called “Interlaced.”

More:
https://www.reubenmargolin.com/

#Art#Engineering#Physics#Math#KineticArt#Sculpture#Artist#ReubenMargolin#Mechanical

A horizontal set of tall polished wooden planks that are arranged tightly together. Vertical wires pull them up and down in a pattern that makes them look like two sets of waves, gracefully dancing together. Then the shot zooms out to show the complicated array of gears and pulleys above them.
A horizontal set of tall polished wooden planks that are arranged tightly together. Vertical wires pull them up and down in a pattern that makes them look like two sets of waves, gracefully dancing together. Then the shot zooms out to show the complicated array of gears and pulleys above them.
Mark Wyner Won’t Comply :vm:
@markwyner@mas.to  ·  activity timestamp 2 months ago

In my journey to continue to find the good things in a world that’s breaking my heart on the daily, I found some beautifully-serene art.

Kinetic artist, Reuben Margolin uses skills in design, engineering, physics, electronics, and more. He creates motorized pieces that seem impossible. The one is called “Interlaced.”

More:
https://www.reubenmargolin.com/

#Art#Engineering#Physics#Math#KineticArt#Sculpture#Artist#ReubenMargolin#Mechanical

A horizontal set of tall polished wooden planks that are arranged tightly together. Vertical wires pull them up and down in a pattern that makes them look like two sets of waves, gracefully dancing together. Then the shot zooms out to show the complicated array of gears and pulleys above them.
A horizontal set of tall polished wooden planks that are arranged tightly together. Vertical wires pull them up and down in a pattern that makes them look like two sets of waves, gracefully dancing together. Then the shot zooms out to show the complicated array of gears and pulleys above them.