#spherepacking — Public Fediverse posts

People have looked into circle packings with two kinds of circles. Of course they did. Are they fun to look at? Indeed they are:

https://en.wikipedia.org/wiki/File%3A2-d_dense_packing_r1.svg

Just scroll down to find some more! The article is a bit short, but here it is:

https://en.wikipedia.org/wiki/Circle_packing#Unequal_circles

#spherepacking

Half a year ago, I filled in some sorry's for the massive project [1] to formalize the Fields-medal winning proof that sphere packing in dimension 8 is optimized by the E8-lattice. Last week it was announced that all remaining sorry's were filled by Gauss, an autoformalization agent. Gauss was able to build on the blueprint and other scaffolding built by the community. A few days later, Gauss also formalized the proof in dimension 24, this time working directly from the published paper, without mayor community input [3].
Since Lean verifies the generated proofs, hallucinations are not a problem.
The community now processes the generated proofs to make sure it satisfies the community standards and remains usable in the future [2].

[1] https://thefundamentaltheor3m.github.io/Sphere-Packing-Lean/

[2] https://leanprover.zulipchat.com/#narrow/channel/113486-announce/topic/Sphere.20Packing.20Milestone/with/575354368

[3] https://www.math.inc/sphere-packing

#Lean #spherepacking #gauss #formalization

I derived Planck mass from sphere packing – 0.574 ppm, zero free param

https://zenodo.org/records/18089296

#HackerNews #PlanckMass #SpherePacking #Physics #Research #ScienceInnovation

Spherical Cow
https://lib.rs/crates/spherical-cow
#ycombinator #sphere #obj #geometry #packing #spherepacking

🚀 #Rust #developers unite! The "Spherical Cow" library is here to let you pack spheres like never before—because who doesn’t need high volume sphere packing in arbitrary geometries? 🤔 It’s like trying to solve a Rubik's Cube in the dark while dancing the Macarena. 💃
https://lib.rs/crates/spherical-cow #SphericalCow #SpherePacking #Geometry #Fun #HackerNews #ngated

"In higher dimensions, mathematicians still don’t know the answer [to the sphere packing problem.] [...] Now, in a short manuscript posted online in April, the mathematician Boaz Klartag has bested these previous records by a significant margin. Some researchers even believe his result might be close to optimal."

https://www.quantamagazine.org/new-sphere-packing-record-stems-from-an-unexpected-source-20250707/

#Mathematics #Problems #SpherePacking #Geometry

Lattices and sphere packing - when #Math gets really fun and interesting. A recent development in the #Mathematics world raises the ante in the pursuit of optimal sphere packing in multiple high dimensions. Turns out #lattices and ellipsoids are central to the latest piece of the puzzle. This is for my #MathNerd followers🤓 who enjoy a mind-tweaking read. https://www.quantamagazine.org/new-sphere-packing-record-stems-from-an-unexpected-source-20250707/ New #SpherePacking Record Stems From an Unexpected Source | Quanta Magazine

New Sphere-Packing Record Stems from an Unexpected Source

https://www.quantamagazine.org/new-sphere-packing-record-stems-from-an-unexpected-source-20250707/

#HackerNews #SpherePacking #SpherePackingRecord #Mathematics #UnexpectedSource #QuantumPhysics

Join us now in #L1 in the #oxford #maths #institute for a wonderful talk by Matthew Jenssen on #spherePacking from his new paper!! https://invariants.org.uk

For the Dutch newspaper #NRC I wrote a piece about the new lower bound for #spherepacking, found by Marcelo Campos, Matthew Jenssen, Marcus Michelen, and Julian Sahasrabudhe. With a proof that \( \frac1n \) is a lower bound for the density in dimension \(n\) (it's trivial for mathematicians, but for other people it is interesting, I hope). As a bonus I end with a quote from Terence @tao !

Bollen verpakken in hoge dimensies. Mijn nieuwste artikel voor #nrc. Met formules! En met een bewijs! #spherepacking (paywall) https://www.nrc.nl/nieuws/2023/12/28/de-kerstballen-gaan-terug-in-de-doos-hoe-doe-je-dat-efficient-in-hogerdimensionale-ruimtes-a4185455 https://www.nrc.nl/nieuws/2023/12/28/de-kerstballen-gaan-terug-in-de-doos-hoe-doe-je-dat-efficient-in-hogerdimensionale-ruimtes-a4185455

Apollonial Sphere Packing!

Full-Length full-size Version:
https://youtu.be/BxNMM3IURcA

Soundtrack produced by Capzbeats (Link: https://soundcloud.com/user-640835231 )

#spherepacking #mastoart #apolloniangasket

Rotating the Apollonial Sphere Packing through the Screen.

#perfectloop #mastoart #spherepacking #mathart #apolloniangasket

Only spheres with even curvature get built from the bottom up.

#spherepacking #mathart #mastoart

Showing circles of radii between r and 2r for shrinking r.

#spherepacking #mathart #codeart #apolloniangasket

Fun with Apollonial Sphere Packings. Here an all-Integer specimen in pastell-prime palette

#spherepacking #apolloniangasket #mathart #codeart #mastoart

March 14 is World Maths Day because in mm/dd format the date is like an approximation of pi 3.14…. aka Pi Day. So here’s a hand-printed block print related to math and pi. It shows the two piles with the two possible close packing of equal spheres, each below a diagram of the plan view of the layout: Face-centered cubic (fcc) and hexagonal close packed (hcp).

#WorldMathsDay #math #maths #mathematics #spherePacking #mathArt #sciart #histstm #linocut #printmaking #PiDay #PiDay2023