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“My cuddly bear is luminous”, Tom gloated.
This astonishing tiling with 7-fold symmetry is build from identical pentagonal tiles.
I find the way it is constructed fascinating.
The drawing is by Tom Ruen and I think the discoverer of the pattern was Klaassen, who showed in 2016 that a similar pentagonal tiling can be found for any degree of symmetry, see here.
“I’m here”, said Tom presently.
St Neot, d. 877, was was a monk from Glastonbury Abbey who moved to Cornwall to be more isolated (the word monk is from Greek μονος monos = alone). His piety and devotion made him famous and a number of miracle were connected with him. He visited the Pope, and on the latter's bidding found a monastery in Cornwall, where his remains were kept after his death. The relics attracted many pilgrims and an associated flow of income. Here is a rather impressive stained glass window from the church in St Neot's in Cornwall.
About a hundred years on a different monastery was founded in Cambridgeshire, at what was then called Eynesbury (probably after an earlier saint who may have existed called Arnulf) but is now named St Neot's.
Monks from this second abbey seem to have though St Neot's remains would be a useful pull for pilgrims, so they travelled to Cornwall and the saint's remains were (as Wikipedia delicately puts it) "abstracted from Cornwall without permission, and lodged at Eynesbury". In other words monks from Cambridgeshire went to Cornwall, snatched the bones and brought them back home.
Sure enough these relics brought a stead stream of visitors and a healthy revenue flow, but stealing these bones has always seemed to me a rather discreditable and cynical act, and I've often wondered too why the Cornish monks never staged a counter raid. Who knows?
Varignon's Theorom says that if we take any quadrilateral whatsoever and join the midpoints of its sides we (rather surprisingly) always get a parallelogram
I give a neat and I hope fairly intuitive proof here.
Today I read about an elegant generalisation of this theorem. The page I've linked to has much more that this, but in my diagram below, which I drew using Geogebra, I've just illustrated the first case.
For any hexagon, STUVWX in the figure, form a triangle from each group of three adjacent vertices in turn. Mark the centroid, i.e. the centre of gravity, of each triangle, and join them up to form a hexagon A1B1C1D1E1F1 as shown.The each pair of opposite sides of the new hexagon are parallel and of equal length, in other words the new hexagon is analogous to a parallelogram, but with six sides rather than four.
"I seem to be developing tooth decay", said Tom precariously.
Today I picked up a local saying I'd not heard before:
"He's ninety-twelve years old".
Meaning he's very old. I like it, it's vivid and humorous.
I always thought of "Earthling" as a fairly modern sci-fi type of word but I've learned from the excellent "Words Unravelled" podcast and YouTube channel that it was already word in Old English. It meant a ploughman and was still used in that sense until the early 1800s. From about 1600 it came to have the modern sense of someone who lives on the Earth.
It's interesting because it uses the suffix -ling, which has several loosely related meanings. Originally in OE it (usually) implied a person concerned with or related to some particular thing (hence earthling) and we also have hireling (someone hired) and sibling (originally a kinsman, now just a brother or sister of course, and I used to think it was just a modern word, but not so). Starling the bird also seems to use the same construction, and birds crop again below
Nowadays it can just be a diminutive, as in gosling, duckling, sapling or nestling, but can sometimes also have dismissive connotations, the OED gives the examples godling, lordling, kingling, princeling. A princeling is definitely some way down the scale of princeliness (yes it really exists).
Chat GPT threw up quite a few more: weakling, fledgeling, hatchling, seedling, underling, yearling, changeling, foundling, stripling, mostly implying some sort of smallness or weakness.
"I love camping", said Tom intensely.
Sun Dogs are caused by the light from the Sun being refracted by ice crystals. My brother snapped this one a couple of days ago, on the 21st of June.
They appear 22 degrees horizontally from the Sun and if you are lucky one on each side of the Sun, depending where the ice crystals are, although it's commoner to only see one.
What’s the most difficult tongue twister? It’s hard to say.
I'll never forget the time I got wax in my ears. It was a near deaf experience.
My brother photographed this astonishing lichen, Cladonia pyxidata, or Pixie Cups.
It is generally agreed that the first crossword was composed by Arthur Wynne and appeared in The New York World on 21st December 1913. Wynn's pioneering word cross as I think he called it is below.
You can see it still had a way to go before it evolved into its modern form. If you decide to have a go and get stuck there are some leads here.
In the more than a hundred years that have passed, crosswords have found their way into most of the world's newspapers, or so I imagine. This set me wondering about what the word for crossword is in other languages. The only one I knew was Greek stavrolexo, which is a literal translation, the stravo bit means cross (as in the name Stavros) and the lexo bit mean word (think lexicon).
This way of exporting a word to another language is called a calque. The alternative is for the target language to adopt the original as a loanword. English has thousands of loanwords, think of bistro, delicatessen, opera, wok, tomahawk, safari, sushi, taco, kiwi, bungalow, budgerigar (not forgetting calque.)
I tried a few sample European languages to see whether crossword because a calque or a loanword and fond a mix. The main reason I stuck to European languages is that outside that group it's harder for me to decide if something is a calque. Lots of languages seem to just use the loanword but there could be ones that have a completely independent word for the concept, I can't really tell.
Here are the calquesI I found, apart from the Greek
German Kreuttzworträtsel (I think rätsel is puzzle)
French mots croissés
Spanish crucigramma
Welsh croesair
Here are languages that use crossword as a loan
Yiddish crossvert
Russian Krossoword Кроссворд
Georgian h'rosvordi კროსვორდი
I used to think nostalgia meant a kind of sentimental hankering for times gone by, our own times or a past age of our romantic imagining. But it seems that when it first came into English in the 1700s it meant homesickness, derived from Ancient Greek νόστος nostos = going home and αλγία algia = pain (as in neuralgia for example), and it only came to mean longing for a time rather than for a place during the last century.
The modern Greek word νόσταλγία does indeed refer to homesickness but I haven't been able to find with certainty whether this has come directly from Ancient Greek or is a back-borrowing from English or perhaps French,
At any rate it is a beautiful word, with a lovely wistful feel to it, and its original meaning of homesickness is the one I prefer.
“My shares have gone up”, said Tom again.
“I’ve got a loft full of whisky”, said Tom dramatically.
“Just turn where I say, and you won’t get lost”, said Tom forthrightly.
Here's a classic aeroplane parked up at London City Airport earlier this week. It's a 1946 de Havilland Dragon Rapide, one of only around nine airworthy examples left. This one is normally based at Duxforn in Cambridgeshire.
Gaspard Monge was a French mathematician of the 18th and 19th century, a man of many parts who was a friend of Napoleon and took part in the latter's expedition to Egypt. He gave his name to a theorem in geometry which is easy to see in this illustration from Wikipedia (image by Jason Quinn).
Although it is usually presented as as theorem about circles and tangents it seems more general than that. Here is my drawing of an analogue for equilateral triangles, produced using GeoGebra.
For any pair of triangles, the lines drawn through pairs of corresponding points meet at a point, and for any set of three triangles taking the triangles in pairs produces three such points that all lie on the same line.
I don't think equilateral triangles are special, as far as I can see we could choose any shape.
Monge's theorem can also be generalised to three dimensions (four spheres and six cones, one for each pair of spheres, all of whose vertices lie on a common plane), and indeed to higher dimensions, although it obviously gets harder to visualise.
What tasty dish is this?
Scroll down for solution
Chicken Sees A Salad
based on joke posted on r/dad jokes by tjeters
Herb and Spice-themed Daffynitions
Anise: Sibling's daughter.
Borage: Jail term.
Chervil: Type of rodent, often kept as a pet.
Chicory: Deception.
Cloves: Fings you wear.
Cumin: Opposite of going.
Fennel: Tapering tube for guiding liquids.
Mace: Small rodents.
Marjoram: Impaired your molasses-based alcoholic spirit.
Rosemary: Got up in a cheerful mood.
Sage: Reason why I'm not as sprightly as I once was.
Thyme: See Borage.
What happens if you don’t pay your spice bill? They send the bay leaves round.
Our old friend Tom has been at it again.
"Are all your pies this small?" asked Tom tartly.
After I'd thought of that one I wondered if Chat GPT knew about Tom Swifties. It does and came up with quite a decent effort when prompted with "pie" and "Tom Swifty".
"This pie is half-baked," Tom said crustily.
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