This photo is actually from a year ago but I neglected to upload it then and only rediscovered it recently while attempting to explain to an older relative, over the phone, how to attach images to text messages. It's a shallow Showa bowl from Japan, bought when my wife and I visited Tokyo three years ago. We usually hold fruit in it; current contents: three bananas and three lemons.

Doyle spiral explorer: bl.ocks.org/robinhouston/60969

If you slur "Doyle spiral" enough it kind of sounds like "Dora". You can also Möbius transform these things and get double spirals: observablehq.com/@mbostock/dou

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New entry!
Article by Andries de Man
In collections: Easily explained, History, Things to make and do, Unusual computers
Analog calculating machines usually contain lots of gears (differentials), cams, ball-and-disc integrators and rack-and-pinions. But would it be possible to construct such calculating machines only using hinged rods? In the first instance, one would think only linear functions could be...

The ring lemma: en.wikipedia.org/wiki/Ring_lem

New Wikipedia article on the ratio between sizes of adjacent circles in a circle packing, with associated new illustration for the worst-case construction.

Mochizuki will publish his purported proof of the abc conjecture in the journal of which he is editor in chief: nature.com/articles/d41586-020

"The latest announcement seems unlikely to move many researchers over to Mochizuki’s camp."

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A little something that may help... 320 Random Acts of Maths: pocket-sized problems, teasers, curios, provocations, inspirations, etc. For downloads, inc. solutions and slides: bit.ly/2MkTnFM

Semidefinite programming bounds for the average kissing number: arxiv.org/abs/2003.11832

Spheres kiss by touching with no overlap. The kissing # is how many unit spheres can touch a central one, and lattice kissing # is how many can touch in a lattice packing; both are 12 in 3d.

Average kissing # is for finitely many non-unit spheres. It is ≥ lattice kissing # and ≤ 2x kissing #. One of my papers has a slightly better lower bound in 3d, and now we have better upper bounds in many dimensions.

Mathematics as a team sport: quantamagazine.org/mathematics

What a week-long research workshop at Oberwolfach (or Dagstuhl, or many similar retreats) can be like. The workshop in the link is on low-dimensional topology, but the story would be the same for many other subjects.

Last week, instead of attending a Bellairs workshop, we all collaborated remotely. I think we got a fair amount of research accomplished, but I didn't have the same sense of all being brought together to do that one thing.

Monotone subsets of uncountable plane sets: mathoverflow.net/q/356220/440

I ask on MathOverflow about infinite generalizations of the Erdős–Szekeres theorem on the existence of square-root-sized monotone subsets of finite sets of points in the plane.

What happens when half a cellular automaton runs Conway's Game of Life and the other half runs a rolling version of Rule 30 pushing chaos across the border? youtube.com/watch?v=IK7nBOLYzd, via news.ycombinator.com/item?id=2

I wish I could see a larger scale of time and space to get an idea of how far the effects penetrate. If the boundary emitted gliders at a constant rate they'd collide far away in a form of ballistic annihilation but the boundary junk and glider-collision junk makes it more complicated.

New blog post: Backyard sunlight, 11011110.github.io/blog/2020/0

Just a few photos from my garden. There's an optical effect in the one I've attached below that intrigues me: viewed at a large size, all I see is the rosemary foliage; it's only when I blur my vision or look at a smaller thumbnail that the shadow pattern emerges.

Sadly, graph theorist Robin Thomas has died: blog.computationalcomplexity.o

VisMath MathArt: mi.sanu.ac.rs/vismath/mart.htm

Many linked galleries of images of mathematical art, from the 1990s-style web (occasional broken links and all)

3 recent "Did you know?":

... that Chiara Daraio used Newton's cradle to create sound bullets, and ball bearing filled walls to create one-way sound barriers? en.wikipedia.org/wiki/Chiara_D

... that a tetrahedron with integer edge lengths, face areas, and volume can be given integer coordinates?
en.wikipedia.org/wiki/Heronian

... that former college basketball star Amy Langville is an expert in ranking systems, and has applied her ranking expertise to basketball bracketology?
en.wikipedia.org/wiki/Amy_Lang

Two linocut interpretations of a rhombic dodecahedron by the same artist, @joshmillard

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Nines

Minimal-stick examples of the knots $$9_{35}$$, $$9_{39}$$, $$9_{43}$$, $$9_{45}$$, and $$9_{48}$$.

Source code and explanation: community.wolfram.com/groups/-

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If conferences are online only, then they should accept all papers that are above threshold - physical limits disappear. All theory conferences should have acceptance rates > 40%. PC can designate better papers by accepting into different pools (spotlight, reg, garbage, etc).

Also, would be great if each speaker creates a one minute, five minutes, and 20 minutes videos for their talks, this way one can have a one hour video of the whole conference..

New blog post: UCI Ecological Preserve, 11011110.github.io/blog/2020/0, and image gallery, ics.uci.edu/~eppstein/pix/ucie

This is what it looked like yesterday, a short walk from my house:

The four points, two distances problem: theguardian.com/science/2019/o

Can you find all of the ways of arranging four distinct points in the plane so that they form only two distances? The link is not a spoiler but it has a separate link to the solution. "Nearly everyone misses at least one" says Peter Winkler; can you guess the one I missed?

Greedy coloring, now a Good Article on Wikipedia: en.wikipedia.org/wiki/Greedy_c