Consider unfollowing that person that always leaves you feeling worse about things.

Sorry, that's Panckoucke with a P. (I have no idea where that M came from.)

Here's his actual theorem statement: "Every rectilinear polygon can be split into as many triangles as it has sides, minus two."

The earliest PROOF of the polygon triangulation theorem that I'm aware of is an unpublished 1899 manuscript of Dehn! See maths.ed.ac.uk/~v1ranick/paper

...Following a rabbit hole inspired by the Numberphile's recent video on Dehn invariants: youtube.com/watch?v=eYfpSAxGak

A triangulated polygon, from Les Amusemens Mathématiques by André-Joseph Mancoucke, 1749. This is the earliest appearance I know of the theorem (stated without proof) that every simple polygon can be triangulated by diagonals. In particular, Mancoucke predates both Meister's (1770) and Poinsot's (1809) seminal treatises on polygons.

Depressingly hilarious.

No, you're not allowed to say "Well, at least we don't have these problems in MY department!"

thelastpsychiatrist.com/2011/0

Impostor Syndrome Exhibit 10 (and technically 11):

i'm here to chew ass and kick bubblegum and I'm all out of correctly rendered quotations

I’d tell you a Fibonacci joke, but it’s probably as bad as the last two you’ve heard combined.

This is not entirely my idea, the original paper includes a subdivision of an annular region. The provided code is all Mathematica though, which I don't have a copy of, so I coded up a quick&dirty version in OpenFl and threw it on Neocities

it is very dirty: double click to split a cell, scroll your mouse to cycle through cells

roywig.neocities.org/truchet/v

Survey on fusible numbers: arxiv.org/abs/1202.5614

Fusible numbers are what you get from 0 by operations $f(x,y)=(x+y+1)/2$ restricted to $|x-y|<1$. They model a puzzle of measuring time intervals using 1-minute fuses whose ends you can light when another fuse burns out, and are well-ordered with unknown order type. @jeffgerickson calls his (wrong) conjecture "one of my bugs that really should be better known" and points out the lack of progress since 2012: mathstodon.xyz/@jeffgerickson/

euro-math-soc.eu/news/18/11/16
Turkey has arrested Betül Tanbay (the former president of the Turkish Mathematical Society), accusing her of implausible crimes, as they have already done with so many others, especially other academics. The EMS asks the "research community to raise its voice against this shameful mistreatment of our colleague, so frighteningly reminiscent of our continent's darkest times". So count me as one of the voice-raisers.

Intuitive illustrations of possible control flows of a computer program. From Herman Goldstine and John von Neumann, _Planning and Coding of Problems for an Electronic Computing Instrument_, Part II, Volume 1 (1947).

Two new arXiv preprints:

The first shows that if a graph $G$ has a non-crossing straight-line drawing (a.k.a. Fáry drawing) in which some set $S$ of vertices is drawn on a single line then, for any point set $X$ of size $|S|$, $G$ has a Fáry drawing in which the vertices in $S$ are drawn on the points in $X$.

The second shows that, in bounded degree planar graphs, one can always find such a set $S$ of size $\Omega(n^{0.8})$.

Survey on fusible numbers
Article by Xu, Junyan
In collection: Easily explained
We point out that the recursive formula that appears in Erickson's presentation "Fusible Numbers" is incorrect, and pose an alternate conjecture about the structure of fusible numbers. Although we are unable to solve the conjecture, we succeed in establishing some basic properties...
URL: arxiv.org/abs/1202.5614
PDF: arxiv.org/pdf/1202.5614v1
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