Had a rough couple of days: two paper rejections and then found a couple of papers that make a large chunk of my current project obsolete. Ah well.

Don't ask me how I got to it but the wikipedia page for the BCG vaccine uses a square root symbol instead of a tick en.wikipedia.org/wiki/BCG_vacc

I noticed some weird behaviour on whatsapp (android). I just sent three messages with respectively 20, 30, 40 words to the same contact. The message boxes had different widths but multiple lines. When I go away and come back, they are all fixed width, but when I then scroll up and back down, the sizes are different again.

I know this is pretty trivial, but initially I just noticed the different sizes and wondered if there was in interesting reason. Now I'm very confused. Any ideas?

One idea I had: if you take a cycle and add a path between two of its vertices, you get a graph with three cycles. If you repeat, you either get six or seven depending on the choice of vertices. That means you can only achieve four or five cycles by gluing two graphs at a vertex, which I used to figure out a₄ and a₅.

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Here's a sequence that doesn't appear to be in the oeis (unless I erred). Let aₙ be the size of the smallest graph with exactly n cycles. The first few terms are: 3,5,4,6...
a₅ is pretty hard to figure out by hand (I think the answer is 8) but it's easy to check that a₆=5 a₇=4.
A trivial upper bound on aₙ is 2n+1. I think there should be a not too difficult upper bound of O(√n).
Anyone know anything else?

My office mate and I failed, in quick succession, to correctly divide 60 by 5. Time to go home I guess.

Nowadays every mathematics article goes online somewhere, and I would guess that the vast majority of article-reading is done on a screen of some kind. But the format stays the same, i.e. a long linear pdf of results, even if the dependencies between sections, lemmas, theorems etc are more like a tree. Has anyone done something like a mini wiki for an article, or in place of an article?

I wonder which has been written/typed more in human history: "(" or ")". Obviously parentheses are accidentally left open, but on the other hand it's quite common for Russians (and presumably others) to type "))))))))" as a form of emoticon. Do these balance out? Are there other times that one gets used without the other?

Or have I got it wrong and 2m is the distance in America too? I'm sure I heard 6ft a lot when I was there last month...

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In Europe the recommended distance is 2m, in America 6ft (which is approx 90% of 2m). Are humans good enough at distance estimation for this to make a difference? Probably there are too many other factors to figure this out from data.

Sorry if this turns out to be a silly question, but I couldn't find (or think of) an answer.

Suppose I add edges at random to a set of vertices until I have a connected graph. What is the expected number of cut vertices?

I'd be interested to know if there's a spike in sci-hub traffic what with universities being closed. It's often quicker to paste a doi into sci-hub than go through the remote access rigmarole. Or so I'm told...

Drawing a blank:

Is there a name for the "all-or-none" logical operator? Or more specifically its negation, which is XOR for 2-inputs but I want the general case.

Met a woman who seemed to think of herself as a non-math person (though she didn't say it out loud), whose son had asked her how many points were in a circle. I didn't want to give a boring closed answer, so, thinking of eg the ℓ₁ norm, I started to say "it depends..." and she finished the sentence saying "..on how many dimensions you have?" :D

Needless to say, I congratulated her on an excellent observation!

On my next birthday I'll be 25... sorry I mean 2^5

Came across quite a nice little graph that I feel should be "known" if anyone is interested:

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