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Jonathan Goodwin

@joncgoodwin.bsky.social

https://jgoodwin.net

630 Followers  |  748 Following  |  652 Posts  |  Joined: 19.09.2023  |  2.0603

Latest posts by joncgoodwin.bsky.social on Bluesky

It's convenient to redraw Fig. 121(b) as three concentric rings, without crossing edges, as shown in Fig. 122(a). Then it's easy to find a Hamiltonian cycle, such as the one indicated by bold edges in Fig. 122(b). (In fact, Hamilton proved that every such cycle on the dodecahedron is essentially the same as this one; see exercise 9.) Thus we can also redraw the dodecahedron's graph as shown in Fig. 122(c). From that diagram it's obviously Hamiltonian
- that is,
it obviously has a spanning cycle; but it's not obviously planar at first glance.

It's convenient to redraw Fig. 121(b) as three concentric rings, without crossing edges, as shown in Fig. 122(a). Then it's easy to find a Hamiltonian cycle, such as the one indicated by bold edges in Fig. 122(b). (In fact, Hamilton proved that every such cycle on the dodecahedron is essentially the same as this one; see exercise 9.) Thus we can also redraw the dodecahedron's graph as shown in Fig. 122(c). From that diagram it's obviously Hamiltonian - that is, it obviously has a spanning cycle; but it's not obviously planar at first glance.

was acquired in 1911. A similar example, smaller and with more beautiful let-terforms, is object number UC 59254 in the nearby Petrie Museum of University College London [see W. M. F. Petrie, Objects of Daily Use (1927), #288]. What a pleasant coincidence that W. R. Hamilton himself would independently come up with the same concept some 1800 years later, and would proceed to find a closed cycle instead of just a path!
Now fast forward to the ninth century,

was acquired in 1911. A similar example, smaller and with more beautiful let-terforms, is object number UC 59254 in the nearby Petrie Museum of University College London [see W. M. F. Petrie, Objects of Daily Use (1927), #288]. What a pleasant coincidence that W. R. Hamilton himself would independently come up with the same concept some 1800 years later, and would proceed to find a closed cycle instead of just a path! Now fast forward to the ninth century,

are equivalent to the tours of bunches aza3a4a1, a3a4a1a2, and a4a1a2a3 whenever each aj is one of the 28 wedge codes.
Reflection also gives an equivalent tour, whose bunch depends only on the unreflected bunch name. For example, the top-bottom reflection of cycle (1) gives a cycle that belongs to bunch yByD. In general, let p and r be the permutations of wedge codes that correspond to 90° rotation and to top-bottom reflection.
Then a → ap is the mapping discussed in Fig. 123, and we have
a=abodefghijklABCDEFGHIJKLwxyz;

are equivalent to the tours of bunches aza3a4a1, a3a4a1a2, and a4a1a2a3 whenever each aj is one of the 28 wedge codes. Reflection also gives an equivalent tour, whose bunch depends only on the unreflected bunch name. For example, the top-bottom reflection of cycle (1) gives a cycle that belongs to bunch yByD. In general, let p and r be the permutations of wedge codes that correspond to 90° rotation and to top-bottom reflection. Then a → ap is the mapping discussed in Fig. 123, and we have a=abodefghijklABCDEFGHIJKLwxyz;

Idly had the thought “I wonder if Donald Knuth is still doing a Christmas lecture?” And the answer is of course he is, it was yesterday. Eighty-seven years old, still on the wholly Quixotic TAoCP path, and casually spitting out TeX fascicles. www-cs-faculty.stanford.edu/~knuth/fasc8...

05.12.2025 16:38 — 👍 90    🔁 26    💬 3    📌 0

Used Pragmata Pro for the final exam, just to send a message

03.12.2025 17:37 — 👍 0    🔁 0    💬 0    📌 0

When I think back to books that seared themselves upon my brain, it was a mixture of form and content [that cast Searing Ray].

03.12.2025 14:42 — 👍 2    🔁 0    💬 0    📌 0

I think I read a book one time, some kind of dystopia, where people went to theaters to watch film of people being shot in the water. Author implied this was a bad thing, socially.

01.12.2025 23:13 — 👍 1    🔁 0    💬 0    📌 0
Preview
Conquistador (Procol Harum song) - Wikipedia

I have 'issues' with this 'plot' summary: en.wikipedia.org/wiki/Conquis... Isn't a museum or public statuary more likely, with the seemingly contemporaneous details mere flourishes of a piqued imagination?

01.12.2025 23:05 — 👍 0    🔁 0    💬 0    📌 0

I'm still using the one from @kjhealy.co forked from another starter kit, filled with my own customizations that I no longer understand but am terrified to lose or change. It gives me some satisfaction knowing that the frontier models still are terrible at elisp, however.

01.12.2025 22:56 — 👍 0    🔁 0    💬 0    📌 0

Where's your init.el, or god forbid, .emacs.d?

01.12.2025 22:46 — 👍 1    🔁 0    💬 1    📌 0
Preview
Questioning Minds “The most intellectually exhilarating work published in 2018 . . . A lasting treasure.” —Michael Dirda, The Washington PostHugh Kenner (1923–2003) and Guy Davenport (1927&#8…

www.counterpointpress.com/books/questi... is one of the most heavily annotated volumes of letters I've ever seen

01.12.2025 16:49 — 👍 2    🔁 0    💬 2    📌 0

"A good grip on the insolubility of the quintic" is a charming phrase I just read on HN. Where else would you find them?

01.12.2025 15:47 — 👍 0    🔁 0    💬 0    📌 0

Two irrational (surdic) irritations: innumerate posters mocking some high school student with a near-perfect SAT for not getting into college of choice vs. equally innumerate columnist mocking UCSD for its math placement policies.

01.12.2025 15:10 — 👍 2    🔁 0    💬 0    📌 0

Do they have ballot referendums (-da) where you live? Because, I tell you, voting on every millage chaps my hide!

01.12.2025 00:37 — 👍 0    🔁 0    💬 0    📌 0

I have a faint resemblance to Steve Spurrier, and I used to get a predictably outraged reaction from freshman at UF when I would tell them that I easily could have coached the team to a victory over Marshall or whoever the first-week sacrifice was.

01.12.2025 00:29 — 👍 0    🔁 0    💬 0    📌 0

My main hobby (tennis) gives me access to the opinions of non-academic educated Louisianans, at least on occasion, and nothing seems to matter them to more than coaching buyouts, salary contracts, and what they would do if they were in charge (as it should be).

01.12.2025 00:28 — 👍 0    🔁 0    💬 1    📌 0

I know this is very obvious, but all the talk about football coaches is emergent marketing: children watch football to imagine themselves as the players (possibly cheerleaders, band, drunken spectators), adults want to be coaches, refs, announcers, and, most of all, athletic directors.

01.12.2025 00:26 — 👍 1    🔁 0    💬 1    📌 0

Speaking of citations, what is going with the extensive Beckett bibliography here: ctan.math.illinois.edu/macros/latex...?

30.11.2025 20:20 — 👍 2    🔁 0    💬 1    📌 0

A common, mildly melancholy experience despite my familiarity with bibliometrical precepts is finding a detailed, lucid reading published in a major journal and then noticing it's been cited <5 times, often none at all.

30.11.2025 20:14 — 👍 9    🔁 1    💬 0    📌 1

That Carol didn't notice =~ 800m dying shows a lack of midichlorians, at the very least. Wonder how that'll develop.

30.11.2025 17:01 — 👍 2    🔁 0    💬 0    📌 0

Sometimes I read about flint-knapping and conclude "that wasn't real."

28.11.2025 04:01 — 👍 1    🔁 0    💬 0    📌 0

Collecting: "Right after the free form piano solo, the time signature of the fanfare preceding the trumpet solo is, per bar, 4 4 , 7 8 , 9 8 , 4 4, 7 8 and 4 4, then transitions to a section in 5 8 for 6 bars, then goes into 6 8 for one bar. The song stays in 4 4 after that.[original research?]"

27.11.2025 22:47 — 👍 0    🔁 0    💬 0    📌 0

A good day to work on annual evaluation. In "what did I learn" section: "a death yak at the Lair stair will take the Kahlúa out of your coffee!"

27.11.2025 16:40 — 👍 3    🔁 0    💬 0    📌 0

If your game had a psychoplasmic tendrils mechanic, perhaps I'd give it a shot.

26.11.2025 16:14 — 👍 1    🔁 0    💬 0    📌 0

ordering a fanta and Kirkland brand Canadian whiskey whisky in honor of the etymological tidbits in recent Pluribus

25.11.2025 00:20 — 👍 1    🔁 0    💬 0    📌 0

if you teach in an academic department are there committees...are there?

25.11.2025 00:18 — 👍 0    🔁 0    💬 0    📌 0

The financial press always tells the truth: " ‘We’re physicists who are also capitalists,’ says quantum CEO" --> more where that came from (ft.com)

24.11.2025 14:34 — 👍 2    🔁 0    💬 1    📌 0

all text-to-video aspires to the condition of a Tim & Eric clip, and it very well may reach the Cinco horizon soon.

24.11.2025 02:31 — 👍 2    🔁 0    💬 0    📌 0

Thank you. I did not know it. I am temperamentally adverse to utilitarianism, which often maps on to a political disposition that I strongly oppose, so it's a troubling concept.

23.11.2025 17:04 — 👍 0    🔁 0    💬 0    📌 0

I thought it was a very lucid review. My interest in these movements relates primarily to their co-development with statistical/probabilistic ideas first and then computational ones. Moral ambiguity and statistical inference, type of thing. The construction of the genius-as-utilitarian.

23.11.2025 16:15 — 👍 2    🔁 0    💬 1    📌 0

My favorite compiler flag is "-Wtautological-constant-out-of-range-compare"

23.11.2025 16:09 — 👍 1    🔁 0    💬 0    📌 0

I'm reading this with the aid of a great philosopher who created pandoc.

23.11.2025 15:58 — 👍 2    🔁 0    💬 1    📌 0

I am sure the transition will be seamless

22.11.2025 19:16 — 👍 0    🔁 0    💬 0    📌 0

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