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Chris Purcell

@ccppurcell.mathstodon.xyz.ap.brid.gy

7 followers 0 following 39 posts

Mathematician, computer scientist, bassist, knitter? [bridged from mathstodon.xyz/@ccppurcell on the fediverse by fed.brid.gy ]

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 07/10/2026

When I'm thinking about AI in mathematics I end up thinking about the moon landings. It's not a perfect analogy. But there are some parallels. We tend to look back at them as a somewhat collective achievement of humanity; we're right to, I think. But the concentration of wealth in one place due […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 09/08/2026

Does anyone else sing "sudo apt update / sudo apt upgrade" to the tune of "autoglass repair / autoglass replace" in their head?

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 28/07/2026

All farms are solar farms, but some are more efficient than others.

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 18/05/2026

I just learned the sad news that my former postdoc advisor Zdeněk Ryjáček has passed away. I recommend checking out his paper (link below) On a Closure Concept in Claw-free Graphs. It's short and clear, and proves the surprising result that the Matthews-Sumner conjecture (that every 4-connected […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 27/04/2026

@robinhouston just a follow up that I have had it 3d printed and asked my colleague whether he could take it with him next time he's in Slovakia or suggest an alternative route. If he agrees perhaps I will email prof Jendrol, would you like to be cc'd in that email?

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 14/04/2026

Just a heads up about Orbán. What happened here in the Czech republic is that the populist Babiš was ousted after a long time in power, due to the growing discontent with his corruption and incompetence. The centre right, pro European party that took over were too ideologically opposed to the […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 17/03/2026

Ten years ago today I was in Dublin for St. Patrick's day and visited Broom Bridge where Hamilton scored the formula for quaternions for the first time. A friend of mine with Irish heritage happened to ask me today about fields and division rings, about which he'd read in an encyclopedia […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 04/02/2026

I've become interested in polyominoes recently and have had a few questions about them I couldn't easily find answers to. Here's one: Let's call an n-omino "balanced" if its 2 colouring has \\(\lfloor\frac{n}{2}\rfloor\\) cells of one colour and \\(\lceil\frac{n}{2}\rceil\\) cells of the other […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 26/01/2026

So the X pentomino fits into a rectangle which is smaller than its "bounding box". In this case we have a square of area 8, where the bounding box would be a 3x3 square. I suppose it's the smallest example, but is there an easy proof? I can imagine doing each […] [Original post on mathstodon.xyz]

The X pentomino at a 45 degree angle sitting inside a square. The convex corners of the pentomino touch the square, which has area 8 if the pentomino has area 5.

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 21/01/2026

@robinhouston ok I'll see what I can do! I'll ask my colleague about printing the monochromatic version, we can always try the 2-colour version some time in the future.

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 21/01/2026

@christianp He hasn't done it in school; we've mentioned square numbers before. This is conceptually similar: oeis.org/A014080 numbers which are the sum of the factorials of their digits.

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 21/01/2026

@robinhouston I can't promise anything but I might be able to get one of these printed and given to prof Jendrol. I know someone with a 3d printer and while I don't know him personally, I have several short paths to him (e.g., he gave a talk here in Plzen in 2024). I don't know the first thing […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 21/01/2026

What are some examples of non-trivial finite sequences, whose definition could be understood by a child? I'll leave the definition of non-trivial vague, but as an example "positive integers less than 10" is trivial. I mentioned that there are infinitely many prime numbers to the 7yo (he had […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 13/11/2025

Here's a blatantly false statement: Let G be a cubic #graph embedded in the plane with a proper 3-edge colouring. Colour a vertex black if the clockwise ordering of the colours of its incident edges is rgb and white if the ordering is rbg. Then the number of black vertices is equal to the […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 21/10/2025

I use arxivist.com (check it out) which scores arxiv posts according to some likes and dislikes you enter on the website, and emails you the top 5 per day. Most days, the top 5 have a score between 90 and 120 but occasionally the scores are all rather small and I think it's a glitch. But I am […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 19/09/2025

I've been reading a lot of Terry Pratchett recently and it's affected my writing. I've written two wry footnotes in the manuscript I've been working on! A similar phenomenon: I've been learning the mandolin and it's affected my bass playing. Suddenly using my ring finger a lot more and today I […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 25/07/2025

The only semi-regular* spherical* polyhedra are the Platonic solids*, Archimedean solids, prisms, antiprisms and that one almost-Archimedean solid. I think the proof of this is relatively straightforward and purely combinatorial. I found a reference for it but it's very recent. Any ideas for […]

Original post on mathstodon.xyz

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Reposted by Chris Purcell

Christian Lawson-Perfect @christianp.mathstodon.xyz.ap.brid.gy · 22/06/2025

It's me! On #numberphile! Talking about my favourite polyhedron! youtu.be/3X2aQIMx5bs?feature=shared After many years never being able to line up doing numberphile video, I was really glad that Brady and I ended up in the same place to do this. I love the animations and especially the […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 18/06/2025

Do people tend to underestimate or overestimate thirds? Does it vary a lot? I consistently underestimate thirds; when tasked with cutting an orange into thirds I cut off what looks like a third then cut the remainder in half. The first third is consistently smaller. Actually I cut oranges into […]

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 01/06/2025

When Jesus said the first will be last and the last will be first, was he referring to pushdown automata?

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 22/05/2025

Just booted up an old windows machine that hasn't been turned on in about 5 years, and before that wasn't on for at least another 5. It's not connected to the internet or anything (we've moved since it was last on). And yet when I go to turn it off... "Installing update 1 of 20" how? How and why?

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 17/05/2025

nopq rst uvwxy zabc def ghij klm now I know my ROT13 next time will you sing with me?

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 16/05/2025

Just a follow up on chatgpt's approaches. Without going into boring detail it first tried the decimal test directly, although it tricked me into thinking it had converted to decimal first! I said the answer was wrong and that it should try a different approach, and I hinted that it is not […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 16/05/2025

Since AI doing mathematics is in the news again (I guess it never stops these days) I tried my usual test on chatgpt: test divisibility by 3 in base 15. I think I've posted about this before, but I would expect to get a good high schooler to figure this out with only a raised eyebrow at the […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 14/05/2025

The empty sum is 0, the empty product is 1, the empty claim is true.

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 07/05/2025

Does anyone know of any article dealing with binary strings that have \\(n\\) 0's and \\(n\\) 1's but are neither Dyck words nor inverse Dyck words (obtainable from a Dyck word by swapping 0 and 1)? They seem to be connected to questions similar to the following: how many equivalence classes of […]

Original post on mathstodon.xyz

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 17/04/2025

@johncarlosbaez I suppose that was too much to hope for... thanks for the link I will check it out! It's still a little odd to me that there are no obvious cones here, nor in @greganSF 's list of proofs. Am I just thinking about it in the wrong way? Can we extract some cone from the calculations […]

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 17/04/2025

Here's a stupid #geometry / #astronomy question. Planetary orbits are ellipses (under the obvious simplifying assumptions) which are conic sections. So what's the cone? There are infinitely many cones that fit of course. But is there one that best explains? To put it another way, is there a neat […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 08/04/2025

@skewray I'll look into the connection with "constructibility" thank you!

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 07/04/2025

No one answered my question the other day but I'm sure someone here will know the answer or at least be interested so I'll try again with some hashtags: #math #geometry #mathematics If I know the sin and/or cos of an angle, what can I deduce about the "rationality" of the angle. Are there […]

Original post on mathstodon.xyz

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 04/04/2025

An angle is rational if it is \\(q \pi\\) for some rational \\(q\\) and irrational otherwise. Do sin and cos behave differently for rational vs irrational angles? Are there known necessary and/or sufficient conditions for \\(\theta\\) to be rational, given \\(\sin \theta\\) or \\(\cos \theta\\)?

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 20/03/2025

[holocaust] @johncarlosbaez it's an extreme case, and macabre, but the Warsaw Ghetto Hunger Study comes to mind. I hope (and believe) conditions in America will not get that bad, but it's an example of hunkering down for sure. They also managed to overcome a typhus epidemic, which is rather […]

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 10/03/2025

@thedansimonson @johncarlosbaez Google proves new result: the category hierarchy collapses at the first level!

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 01/02/2025

My usual test of #chatgpt is to give it a huge number and ask if it's even or odd. It recently passed the test. Inspired by a hacker news post about doing fizzbuzz by converting to base 15, I gave it a number in base 15 and asked it to check divisibility by 3. It failed miserably and doubled […]

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 10/01/2025

@leahstokes.bsky.social my gf is reading this and coincidentally we watched Godspell the other day, which includes the parable of the sower. Interestingly, that parable is about hearing a message and not listening to it!

Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 04/12/2024

@MartinEscardo Would you be satisfied if the question was: "simplify (left hand side) as much as possible, so that it is in the form (right hand side)"? I think that is the intention, but maybe I missed something and my version is also not great...

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 15/11/2024

I asked the 6yo to colour a map with no adjacent countries getting the same colour. Of course its dual was K_4 so four colours were used. I asked if he could use just three colours. He got colouring straight away. I decided to cushion the coming blow by saying "it might be hard" "No, it's […]

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 07/11/2024

It's time to scrap the tube zones www.the-londoner.co.uk/its-time-to-…

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 16/10/2024

Hotel: we "care about your free time" so why don't you "check in online from the comfort of your own home!" Translation: we "want to pay fewer staff" so why don't you "do this labour for us, for free!"

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Chris Purcell @ccppurcell.mathstodon.xyz.ap.brid.gy · 12/10/2024

I've been studying a bit of spherical geometry, especially trigonometry, and it's very interesting. Triangles are determined by their angles! And there's a neat formula for the area of a triangle given its angles, namely 𝑅²(α+β+γ−π) (this is Girard's theorem). The usual sin and cosine rules […]

Original post on mathstodon.xyz