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Linkage

Dec 31, 2025

  • The code that revolutionized orbital simulation (\(\mathbb{M}\)), video by braintruffle on how updating velocity and position sequentially rather than in parallel causes orbital simulations to preserve symplectic invariants and thereby become much more stable.

  • The mathematics of optimal gift-wrapping (\(\mathbb{M}\), via). First, imagine a cubical gift…

  • How to cage an egg, a well-known paper by Oded Schramm on polyhedra with edges tangent to a given smooth convex body, leaves Robin Houston asking: should you cage your eggs?

  • ACM starts showing unwanted and unlicensed AI summaries on its digital library publications (\(\mathbb{M}\), see also, via).

  • Computing in Geometry and Topology, a diamond open access journal in computational geometry and computational topology that I co-founded a few years ago, is now listed in DBLP (\(\mathbb{M}\)).

  • This season’s green starts to come back to the UCI Ecological Preserve, after the usual dry brown summer and fall (\(\mathbb{M}\)).

    A view looking south at sunset from the northwest corner of the UC Irvine Ecological preserve. A footpath extands from the lower left towards the San Joaquin Hills in the upper right, through bright green new growth of low plants, with a rebar-and-wire fence to the right of the path separating the preserve from an industrial park. Another hill rises above the path to the left, with dry brown mustard stalks on its lower slopes and live oaks rising dark green above them. The sky shades from dark blue at the top left to yellow towards the horizon on the right, with scattered pink sunset clouds.

  • As a follow-up to my recent post constructing regular link-irregular graphs, Jannis Harder proves that almost all dense random regular graphs are link-irregular (\(\mathbb{M}\)).

  • Lean formalization of Chvátal’s conjecture on stars vs intersecting subfamilies in independence systems (\(\mathbb{M}\)).

  • Bottom-up power pylon looks like an origami crease pattern.

  • A genus-zero surface with bounded curvature enclosing less volume than the unit sphere (\(\mathbb{M}\)), called the “amogus surface” in the Mastodon post but sadly not in Matthew Bolan’s arXiv preprint.

  • Quadratrix of Hippias, now a Good Article on Wikipedia (\(\mathbb{M}\)). This is a curve swept out by the crossing point of two moving lines, one rotating and one translating. The ancient Greeks discovered that if you have a copy of this curve already, you can use it to trisect angles and construct a square with the area of a given circle, two classical geometry problems that are impossible with compass and straightedge alone. As I wrote on an earlier blog post, you can also see curves like this when you take a photo of a spinning airplane propellor using a camera with a rolling shutter:

    Rolling shutter phenomenon on a grounded Yak TD, CC-BY 2.0 image by Soren Ragsdale, 9 January 2009, https://commons.wikimedia.org/wiki/File:Rolling_shutter_n%C3%A4idis.png

  • Ametameric (\(\mathbb{M}\)), a 16-color accessible color palette intended for syntax-colored text, with nice visualization of all pairwise color contrasts under different color vision deficiencies.

  • CNRS dumps Clarivate’s bibliographic databases including Web of Science and Journal Citation Reports (\(\mathbb{M}\)), explaining “We have worked for free to lock ourselves collectively into a paid system, but no more!”

  • Young redwoods near Big River Beach (\(\mathbb{M}\)).

    The late afternoon sun backlights a stand of young coast redwood trees on the north bank of the Big River near Mendocino, California. Ferns grow on the forest floor below them. Through the trees can be seen glimpses of the river and the tree-covered ridge rising behind its south bank.

  • Doubly dual shuffles (\(\mathbb{M}\)), four different ways of implementing the Fischer–Yates random permutation algorithm. The discussion goes into why you might choose one over another depending on whether you want to leave items in place after they’re permuted once, or whether the stream of items to be permuted has unknown length.

  • Disproof of the odd Hadwiger conjecture (\(\mathbb{M}\)), new preprint by Marcus Kühn, Lisa Sauermann, Raphael Steiner, and Yuval Wigderson. This is the one on the relation between clique minors (with paths of odd length between designated seed vertices) and coloring. They construct graphs for which the chromatic number is higher than the odd clique minor size by a factor of roughly \(\tfrac32\).

  • David Eppstein

Geometry, graphs, algorithms, and more