Harnessing the Universal Geometry of Embeddings: "A new paper shows all language models converge on the same "universal geometry" of meaning. Researchers can translate between ANY model's embeddings without seeing the original text."
https://arxiv.org/pdf/2505.12540
hat tip: Ethan Mollick
A Tour in the Wonderland of Math with Python - A collection of python scripts for drawing beautiful figures and animating interesting algorithms in mathematics.
https://github.com/neozhaoliang/pywonderland
hat tip to Karl Thidemann
One of Robert Boyle's "Curious Mathematical Forms" (1670)
https://x.com/pickover/status/1931542696474079529
hat tip to Karl Thidemann
Expanding Racks from Henry Segerman
Video: https://www.youtube.com/watch?v=iWknov3Xpts
Printable plans: https://www.printables.com/model/1305045-expanding-3-4-5-triangle
Article: https://www.core77.com/posts/137381/Expanding-Mechanisms-Designed-by-Henry-Segerman
Glynn Fractal
https://x.com/pickover/status/1831016941785407558
Glynn Julia Set
https://www.flickr.com/photos/subblue/3647227394
hat tip to Karl Thidemann
Geometric animations
https://x.com/Yann_LeGall
A new tetrahedron that always lands on the same side
https://www.quantamagazine.org/a-new-pyramid-like-shape-always-lands-the-same-side-up-20250625/
hat tip boingboing.net
Culture changes perception: circles or rectangles?
https://www.science.org/content/article/culture-literally-changes-how-we-see-world
hat tip: @BernieDoesIt@mstdn.social
Emily Dickinson’s Herbarium - pressed flowers and designs from a unique poet at an early age
https://iiif.lib.harvard.edu/manifests/view/drs:4184689$1i
hat tip: https://www.themarginalian.org/2017/05/23/emily-dickinson-herbarium/
Geometers Circle - geometric art and tutorials
https://geometerscircle.com/
Kinetic model of a tesseract
https://www.creativeapplications.net/project/round-about-four-dimensions-exploring-the-unknown/
hat tip: https://www.core77.com/posts/137789/An-Eye-Popping-Kinetic-Representation-of-a-Tesseract
Rinus Roelofs' exhibit at the Bridges conference
https://www.facebook.com/1206771269/videos/pcb.10239412001017345/2107838516375795
https://www.facebook.com/1206771269/videos/pcb.10239412001017345/709305988673842
https://www.facebook.com/1206771269/videos/pcb.10239412001017345/1800623344186058
Monday, July 21, 2025
Friday, May 23, 2025
Geometry Links - May 23, 2025
Lunar moth - biological design
https://www.youtube.com/watch?v=puejRndICqQArchimedean Solids in the 15th and 16th Centuries
https://veraviana.net/history-of-science/archimedean-solids/
Specimens of “fancy turning” from 1869
https://publicdomainreview.org/collection/fancy-turning/
hat tip boingboing.net
Geometry homebrew animation
https://x.com/LimbaTrip/status/1905481692619702507
The Schrödinger Equation
https://www.facebook.com/watch?v=1008462380657737
hat tip Gil Friend
Another visualization for one dimensional Gaussian wave packet and Non Relativistic Schrödinger equation
https://x.com/PhysInHistory/status/1922617024246612302
Hopewell Culture and mound-building geometry
https://www.bbc.com/travel/article/20221204-the-us-2000-year-old-mystery-mounds
The Blossom of Dimensions - Meditative 3D Mandelbrot Zoom - Music by Art of Chance
https://www.youtube.com/watch?v=-1x9cGWs9yE
A sculptural desk organizer
https://www.core77.com/projects/136193/KIIR-A-Sculptural-Desk-Organizer-for-Creative-Workspaces
A crow’s math skills include geometry
https://www.npr.org/2025/04/12/nx-s1-5359438/a-crows-math-skills-include-geometry
GeekMom's LED deltoidal hexacontahedron covered with 3D printed diffusers with "two #Pixelblaze controllers work in sync to provide a fast frame rate for patterns on the 1200 LEDs”
https://mastodon.social/@geekmomprojects/114354417573389621
1903 Japanese book of wave and ripple designs
https://publicdomainreview.org/collection/hamonshu-a-japanese-book-of-wave-and-ripple-designs-1903/
Earlier:
from https://geometrylinks.blogspot.com/2023/05/geometry-links-may-24-2023.html
Hokusai’s Quick Lessons in Simplified Drawing in Three Volumes
https://cdn.flipsnack.com/widget/flipsnackwidget.html?hash=ftcsgji5x&bgcolor=EEEEEE&t=1481362893
https://cdn.flipsnack.com/widget/flipsnackwidget.html?hash=fti4xlqen&bgcolor=EEEEEE&t=1481363446as
https://cdn.flipsnack.com/widget/flipsnackwidget.html?hash=fdcj01ckg&bgcolor=EEEEEE&t=1481364640
Article: https://inaminuteago.com/free-drawing-lessons-great-master-hokusai/
Catalogue Raisonne of Hokusai: http://www.hokusai-katsushika.org/index.html
from https://geometrylinks.blogspot.com/2020/07/geometry-links-july-23-2020.html
Geometric Hokusai from 100 Views of Mt Fuji
Through a Spider Web: https://www.pinterest.com/pin/365495325984645798/
Torigoe: https://commons.wikimedia.org/wiki/File:Hokusai,_Fuji_at_Torigoe.jpg
At Sea (note the Escher transformation long before Escher was born): https://theconversation.com/how-hokusais-great-wave-came-into-the-world-77750
Bastien Dausse, Gravity Explorer
https://www.instagram.com/bastiendausse/?hl=en
hat tip: https://www.core77.com/posts/136812/Acrobatic-Artist-Bastien-Dausses-Low-Tech-Wall-Walking-Invention
Friday, March 21, 2025
Geometry Links - March 21, 2025
Packaging design
https://x.com/gunsnrosesgirl3/status/1876944504051114400A laptop stand from a single sheet of paper
https://www.core77.com/posts/134948/A-Laptop-Stand-Made-from-a-Single-Sheet-of-Recycled-Paper
Animated Mandelbrot zoom video with pastels and sepia pencil
https://www.youtube.com/watch?v=DU3TaKPhPac
Snowflakes: a chapter from the book of nature by Israel Perkins Warren - published in 1863 - with beautiful illustrations
https://publicdomainreview.org/collection/snowflakes-a-chapter-from-the-book-of-nature-1863/
https://archive.org/details/snowflakeschapte00warriala/page/n3/mode/2up
hat tip: boingboing.net
A global classification of snow crystals, ice crystals, and solid precipitation based on observations from middle latitudes to polar regions
https://www.researchgate.net/publication/257132993_A_global_classification_of_snow_crystals_ice_crystals_and_solid_precipitation_based_on_observations_from_middle_latitudes_to_polar_regions which found that snowflakes can be divided into thirty-nine categories, further divisible by 121 subtypes.
Simone Conradi drawings "using mathematics and Python, no generative AI"
https://bsky.app/profile/sconradi.bsky.social
Geometric and other art, some intriguing ideas
https://lovid.org/
Unfold Form - origami reusable concrete form that reduces the need for both concrete and steel
https://ethz.ch/en/news-and-events/eth-news/news/2025/01/zigzags-for-greener-construction.html
https://www.core77.com/posts/135375/Architecture-Student-Invents-Brilliant-Formwork-that-Reduces-Concrete-n-Steel-Usage
Robert Obier’s sculptures and art
https://www.obierstudios.com/portraits
https://www.core77.com/posts/135547/Architect-Industrial-Designer-and-Sculptor-Robert-Obiers-Creations
"The go-to source for physical puzzles"
https://www.puzzlemaster.ca/
hat tip: https://kk.org/cooltools/
Geometric cakes for Ramadan
https://www.bbc.com/travel/article/20240406-kek-lapis-the-most-beautiful-cake-for-ramadan
Animation of the three-body problem
https://mastodon.social/@infobeautiful@vis.social/114155933549054103
Smoke ring geometries
https://x.com/stonersvilla/status/1901635534721605898
Thursday, January 9, 2025
Geometry Links - January 10, 2025
Mathematicians discover new universal class of shapes to explain complex biological forms
https://www.ox.ac.uk/news/2024-09-12-mathematicians-discover-new-universal-class-shapes-explain-complex-biological-formsThe paper itself: Soft cells and the geometry of seashells
https://academic.oup.com/pnasnexus/article/3/9/pgae311/7754698?login=false
hat tip boingboing.net
Structural modeling kit - magnets and springs
https://molamodel.com/
https://www.core77.com/posts/133959/Architecture-Student-Develops-Structural-Modeling-Kit-Now-Sells-Them-Worldwide
The Geometry of Concepts: Sparse Autoencoder Feature Structure - geometric structure in LLM-learned concepts
https://arxiv.org/abs/2410.19750
First coherent picture of atomic nucleus made of quarks and gluons
https://press.ifj.edu.pl/en/news/2024/10/15/
Online collection of plaid patterns
https://plaid-patterns.com/
hat tip boingboing.net
Kelli Anderson’s imaginative pop-up books
https://www.kellianderson.com/books/
Geometry of tides and rivers
https://www.instagram.com/p/DAEvhs1ynYD/
More at https://www.instagram.com/geometriasagrada.en/
hat tip: boingboing.net
Alhambra Palace and Crystallographic Groups
https://structures.uni-heidelberg.de/blog/posts/2023_01_palace_crystallographic/index.php
hat tip Howard Rheingold
The vault organelle
https://en.wikipedia.org/wiki/Vault_(organelle)
hat tip Massimo @Rainmaker1973
"The Steampunk Whirling Wonder Fidget (Gear Ball)”
https://www.grynalor.com/products/the-steampunk-whirling-wonder-fidget-gear-ball
Maze Generator
https://mazegenerator.net/
hat tip kk.org/cooltools
Moving Geometry from Vera Viana
https://veraviana.net/
Thursday, September 19, 2024
Geometry Links - September 19, 2024
Labyrinth Locator - find labyrinths all around the world
https://labyrinthlocator.org/hat tip: boingboing.net
Abu Dhabi real-time data sculptures of brain waves
https://twitter.com/SCDabudhabi/status/1793232852454351293
"A majestic visualization of the toroidal structure and flow of a smoke ring"
https://twitter.com/Rainmaker1973/status/1804085910763364836
What if we could see spacetime?
https://www.youtube.com/watch?v=YNqTamaKMC8
hat tip: boingboing.net
Simulating Extreme SpaceTimes: black holes, neutron stars, and beyond
https://www.black-holes.org/
Their videos are very good if you’re into spacetime dynamics on the cosmic scales
https://www.youtube.com/c/SXSCollaboration
Aleks Melnyk’s extensive metal stencil products
https://www.amazon.com/stores/AleksMelnyk/page/9D4534FA-EB02-45F9-A5EF-294E88E8A552
hat tip core77.com at https://www.core77.com/posts/132925/Aleks-Melnyks-Pyrography-Stencils
Lunar gravity simulator
https://www.core77.com/posts/133036/Acrobatic-Artist-Bastien-Dausses-Incredible-Low-Gravity-Invention
OCD Art
https://www.core77.com/posts/133324/Fighting-Through-Mental-Struggles-Incredible-Renderings-Created-with-Only-a-Pencil
Bridges Math Art Conference papers online
https://archive.bridgesmathart.org/2024/#gsc.tab=0
hat tip Gwen Turner
3D printed clear radiolaria from Jessica Rosenkrantz
https://mastodon.social/@nervous_jessica/112997128650862037
https://www.instagram.com/nervous_jessica/
https://n-e-r-v-o-u-s.com/
and
Bismuth crystal jigsaw puzzles
https://n-e-r-v-o-u-s.com/shop/product.php?code=410
hat tip: https://www.core77.com/posts/133615/Experimental-Design-Lab-Nervous-Systems-Bismuth-Crystal-Puzzles
Elastic Grid - online interactive Op Art
https://elasticgrid.pinkus.link/
hat tip: boingboing.net
Sunday, June 16, 2024
Geometry Links - June 16, 2024
Optical illusions illuminate neural pathways
https://scitechdaily.com/demystifying-vision-optical-illusions-illuminate-neural-pathways/Peter Lu on Islamic Geometry
Quasicrystals in Medieval Islamic Architecture
https://www.youtube.com/watch?v=rldnu9rNpH8
Girih Tiles: Decagonal Geometry in Seljuq Architecture
https://www.youtube.com/watch?v=6AJx8IVcL_c
hat tip Eleftherios Pavlides
Most detailed (so far) 3D map of the Cosmos
https://news.ucsc.edu/2024/04/desi-universe-mapped.html
Video fly-through
https://www.youtube.com/watch?v=jRYUt9nE9b0
Kirby Urner’s slide deck on tetrahedral tessellators, Bucky Fuller's esoteric geometry of the B, E, A, S and T modules
https://docs.google.com/presentation/d/13QLfgKo6kyX0j0K0RJ7W0uisB0ZyeBiK-_qbzytipck/edit
Ancient Egyptian Calligraphy: A Beginner's Guide to Writing Hieroglyphs by Henry George Fischer
https://books.google.com/books?id=rWlk49hUmDIC&printsec=frontcover#v=onepage&q&f=false
hat tip Dr. Kirsten D. Dzwiza https://youtube.com/@antikemagie, https://www.instagram.com/antikemagie/, https://www.antikemagie.com/
Editorial Comment: a beautifully clear primer
Bacterial art
https://www.theguardian.com/artanddesign/gallery/2024/may/18/beautiful-bacteria-encounters-in-the-microuniverse-tal-danino
Twisted Torque Tensegrity
https://pretenst.com/construction/2024/04/23/torque
Rinus Roelofs' sculptures
https://www.facebook.com/photo?fbid=10233940204345848&set=pcb.10233940206985914
https://www.facebook.com/photo/?fbid=10234067851536948&set=pcb.10234067854537023
The Playful Eye: An Album of Visual Delight by Julian Rothenstein, Mel Gooding (Chronicle Books 2000): "a virtual feast of games and visual tricks gathered from around the world.”
hat tip kk.org/cooltools
Daniele Barresi, champion carver
https://www.danielebarresi.net/carving
https://www.instagram.com/danielebarresi_artist/
Folding Camping Table, with a tensegrity element
https://www.core77.com/posts/132550/A-Nifty-Folding-Camping-Table
Custom rotating nozzles for 3D printing different textures in clay
https://www.core77.com/posts/132566/Producing-Crazy-Textures-by-3D-Printing-Clay-With-Custom-Rotating-Nozzles
https://www.instagram.com/piotr_wasniowski/
Friday, May 3, 2024
Geometry Links - May 4, 2024
The marble floors of the Florence cathedral
https://www.reddit.com/r/ArchitecturePorn/comments/13dkqmy/the_16th_century_optical_illusion_of_florence/https://www.reddit.com/r/ArtefactPorn/comments/qgsl9u/the_marble_mosaic_floor_of_the_florence_cathedral/
hat tip Monica Raymond
The Splash of a Drop - an 1895 study of drops of water splashing on a flat surface and the forms they make
https://publicdomainreview.org/collection/the-splash-of-a-drop-1895/
hat tip boingboing.net
Editorial Comment: I bet Doc Edgerton knew this work and, if you don’t know Doc Edgerton, you should.
The New Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of Its Creators by Alexander Sofer
https://link.springer.com/book/10.1007/978-1-0716-3597-1
hat tip Edmund Harriss
Souper Connect - A modular human-shaped block that can interlock and connect in endless ways
https://www.kickstarter.com/projects/hbb/hbb-human-building-blocks
hat tip core77.com
Cella - a Bauhausian Toy
https://www.youtube.com/watch?v=E7y9_rHrBnc
https://www.core77.com/posts/131781/Cella-A-Bauhausian-Toy
Stable torqued tensegrities from Gerald De Jong
https://www.facebook.com/photo/?fbid=10161035601318948&set=a.10150243650853948
Collaborating for Comprehensivity by CJ Fearnley, one of the founders of the Synergetics Collaborative
PDF version: https://drive.google.com/file/d/1bapsUhFtRDSPdAW6zRBe7omBlcghz-yi/
Amazon Kindle: https://www.amazon.com/dp/B0CW1K18B5/k
One painting, youth to age, depending upon perspective
https://www.instagram.com/reel/C5cfny9Mjc8/
hat tip Joan Mokray
Kagen Sound’s wooden puzzle boxes
https://www.youtube.com/watch?v=_NreYBwzRQk
hat tip boingboing.net
Root systems drawings
https://images.wur.nl/digital/collection/coll13/
hat tip http://kk.org/cooltools
Roman dodecahedron theories
https://www.washingtonpost.com/world/2024/04/30/roman-relic-norton-disney-dodecahedron-theories/
hat tip Amy Edmondson
From Art to Math: The Polymorphisms of the Polymorphic Elastegrity
Subscribe to:
Posts (Atom)