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:

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

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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...
Entry: read.somethingorotherwhatever.

The ring lemma:

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:

"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:


Semidefinite programming bounds for the average kissing number:

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:

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:

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?, via

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,

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.

VisMath MathArt:

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?

... that a tetrahedron with integer edge lengths, face areas, and volume can be given integer coordinates?

... that former college basketball star Amy Langville is an expert in ranking systems, and has applied her ranking expertise to basketball bracketology?

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

Source code and explanation:

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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..

The four points, two distances problem:

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?

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