I like the three color addition! Is this a common property of projective planes (maybe it's trivial?...I'm not used to thinking about the points as repeated like this! 🙂 ) or one of the named adjectives (Desarguesian, etc.)?
In recent years I have mainly reviewed for CS conferences. Now I am reviewing a paper for a mathematics journal and they're asking for a rating out of 100... how can you possibly boil down a scientific paper to a number out of 100? It seems absurd to me. I don't remember doing it in the past (but my memory for such things is bad)
I realise now that the way I have been saying this fact is very ambiguous (I can make it make sense with tone of voice and hand gestures).
I mean to say there is exactly one number that is the successor of a square and whose successor is a cube, or to put it another way, there is exactly one solution to y³-x²=2 with x,y integers.
I learned this fact in a very Ramanujan-esque fashion, as a friend turned 26 and suggested on facebook that it wasn't a particularly interesting number - another friend commented to the contrary, that it was a very interesting number for the given reason. In writing these toots, I learned another fact (that I suspected but somehow never thought to check) that indeed y³-x²=k for k ∈ ℤ has only finitely many integer solutions.
Surely the gaps just grow larger and larger? And surely once you establish that there is no counterexample in the first thousand numbers or so, we can just go home? Which led us on to a nice discussion of the prime-counting function π(n) and the logarithmic integral li(n) and the fact that li(n)-π(n) is positive for very many values (it switches around n=10³¹⁶ according to wikipedia) but turns out to switch signs infinitely often. Well that's my outreach for the week! 2/n
Over the weekend I was canoeing and one of my companions (in another boat) asked me for a maths fact as we paddled along. Many parameters to consider here (background, attention span, lack of blackboard) and I went for: there is exactly one number between a square and a cube. It turned out to be a good choice! The instinctive response was "it must be a small number" - good instinct in my opinion. But then I mentioned that it is not exactly trivial to prove and an objection was raised 1/n
There are (at least) two (apparently) unrelated classes of graphs called "parity graphs". One is the class of graphs in which the size of a maximal independent set is fixed mod 2. The other is the class in which the length of an induced u-v-path is fixed mod 2 for all pairs of vertices u,v. By coincidence, both are somewhat connected to research projects of mine, but the overloaded terminology is annoying.
The slope number of a graph G is the minimum number of distinct gradients of the edges in a straight line drawing of G.
An open problem that is very nice in my opinion: When Δ(G)≤3 the slope number of G is at most 4. For any k there is a graph G with Δ(G)=5 and slope number >k. But what about Δ(G)=4?
Not really my area at all but I like questions like this: where's the boundary?
When I add say 579 and 345, my inner monologue says "eight *nine* one *two* four nine hundred and twenty four!"
Mathematician, computer scientist, bassist, knitter?
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
\) for inline LaTeX, and
\] for display mode.