My brother photographed this astonishing lichen, Cladonia pyxidata, or Pixie Cups.

# Personal Blogs

It is generally agreed that the first crossword was composed by Arthur Wynne and appeared in The New York World on 21^{st} 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 *KreuttzwortrĂ¤tsel* (I thinkÂ *rĂ¤tsel* is puzzle)

French mots croissĂŠs

Spanish *crucigramma*

Welsh *croesair*

Here are languages that use crossword as a loan

Yiddish crossvert

Russian KrossowordÂ ĐŃĐžŃŃĐ˛ĐžŃĐ´

Georgian h'rosvordiÂ áá ááĄááá áá

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 Î˝á˝šĎĎÎżĎ nostos = going home andÂ ÎąÎťÎłá˝ˇÎą 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.Â

The modern Greek wordÂ Î˝á˝šĎĎÎąÎťÎłá˝ˇÎą 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.

âMy shares have gone upâ, said Tom again.

âIâve got a loft full of whiskyâ, said Tom dramatically.

âJust turn where I say, and you wonât get lostâ, said Tom forthrightly.

Here's a classic aeroplane parked up at London City Airport earlier this week. It's a 1946Â 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 onÂ r/dad jokes by tjetersÂ

#### 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: SeeÂ *Borage*.Â

What happens if you donât 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.

I don't know why but I was thinking about the word "mog" and wondered where it came from, and whether it is a "real" word, i.e. one I could find in the dictionary (turns out yes). With the help of the Oxford English Dictionary and Wikipedia I managed to piece together a possible etymology.

mog < shortened from moggy

moggy < regional dialect, a young woman, variant of Maggie

Maggie < pet form of Margaret

Margaret < late Latin Margareta

Margareta < classical Latin margarita, a pearl

margarita < ancient Greek ÎźÎąĎÎłÎąĎÎŻĎÎˇĎ (margarites), pearl

ÎźÎąĎÎłÎąĎÎŻĎÎˇĎ < Persian murwÄrÄŤd, pearl

murwÄrÄŤd* *< an old Iranian word
meaning something coming from a shell

Some more geometry!Â

We can inscribe a square in an equilateral triangle so that all itas corners lie on the sides of the triangle. How? Well, consider this sketch.

We draw a chord of the triangle parallel to the base and draw a square with the chord as one of its sides. Then we move the chord vertically downwards, keeping it parallel to the base and with its ends on the sides of the triangle and progressively enlarging the square, until the base of the square lands on the base of the triangle, and we are done.

We can extend the idea to three dimensions and inscribe a cube in a regular tetrahedron.

We take a section parallel to the base and in this equilateral triangle inscribe a square using the method described above, and construct a cube with this square as one of its faces. Then we move the section vertically downwards, keeping its vertices on the sides of the tetrahedron, progressively enlarging the cube, until the base of the cube lands on the base of the tetrahedron, and we are done.

It's conjectured, but I don't think proved, that this gives the largest cube that can be inscribed in a regular tetrahedron, see here.

Rather neat, and It seems to me that an analogous construction would be possible in dimension and beyond, a hypercube in a 4-simplex and so on, but I canât prove it and drawing a picture of even the four dimensional case feels quite a challenge.

No round holes involved, the Square Peg Problem is a deceptively simple mathematical problem, first posed over a hundred years ago. It asks whether every closed curve has an inscribed square, that is, a square with all four of its vertices on the curve, as in the example below.

I've been fascinated by this problem for nearly 50 years. It's easy to state but hard to solve and although solutions have been found for many particular categories of curve, a completely solution is still lacking and it remains an active research topic. There is a good summary of the history and current state of the problem here:

https://diposit.ub.edu/dspace/bitstream/2445/151918/2/151918.pdfRecently I remembered a problem someone showed me many years ago. Given an acute triangle can you always inscribe a square in it? The answer is yes and with the right insight itâs not hard to see why.

The idea is to begin at (a), with a small square that has three vertices on the triangle, the point P and two others on the base of the triangle. In (b) we move P along the side it lies on, while maintaining the same square configuration, and at some stage the point Q must meet the third side of the triangle (c), and we have the desired inscribed square. Rather neat.

It occurred to me that this was a special case of the square peg problem, so I went off and caught up on the latest research, and the summary I referred to above reproduces a number of proofs for different classes of curve. Most of them are quite difficult, some very, but I found one that looked as though it ought to be easy, although I still struggled with it a bit. I wanted to write something about the square peg problem and give a simple and intuitive proof for at least one case, but this one seemed to involve too much maths to be generally accessible.

After a couple of days pondering this, I woke up suddenly in the early hours of the morning with a eureka moment. The proof I'd being looking at is really just the same as the triangle problem above. There is really nothing special about the triangle, it could be any path that starts at a base level, has some ups and downs, and eventually end up at the base level again. It might be a section through a hill for example, like this:

As before we draw squares with two vertices at base level, and a third vertex P which lies on the hillside. We start with a small square, as shown in (d) and move P along the surface of the hill as in (e). In (e) point Q just misses being on the surface, but we carry on and eventually there must come a time, as shown in (f), when Q meets the surface, and we have an inscribed square. Of course we would need to tighten this argument up a bit before it became a rigorous proof, but it's basically correct and quite easy to follow.

Staying with idea of the hill section, the inscribed square means there must necessarily be two points on the hillside with the same elevation whose distance apart equals that elevation.

This attractive little plant likes my front garden wall, where it grows profusely. In the photo itâs intertwined with some actual ivy, at left, and you can see that the leaves of the toadflax really do look like miniature ivy leaves.

This year there is more of the toadflax than I can remember ever seeing before. Perhaps itâs because we have such a lot of rain in the last few months.

### đ

If you try to steal my grapes, then you better watch Shiraz.

âGolden Bouquetâ

Here's a rather neat bit of geometry. If we take a quadrilateral ABCD and join the midpoints of its sides, we get a parallelogram.

This theorem is named after Pierre Varignon (pictured, courtesy Wikipedia), a mathematician of the 17th and 18th century.Â

Varignon was well-connected; it seems he knew Newton and Leibnitz, for example.

Now why should the theorem be true? Well suppose we concentrate just on EH and FG and draw in the diagonal BD, see below

Now there is a theorem that says if we join the midpoints of two side of a triangle the segment so obtained is parallel to the third side and half its length. Looking at triangles ABD and DBC tells us are half the length of the diagonal and parallel to it. Hence HEFG must be a parallelogram.

We can also see that a half is not special, for example if F, G, H and E had been one-third the way along the sides they lie on, instead of one half, we would still have obtained a parallelogram.

Last week I visited Solva, a place in South-West Wales. It's a fishing village and harbour. Up on the cliff overlooking the sea there is an (Iron Age?) fort, it was once an significant commrercila port and centre for lime burning, and it probably has some Viking associations. The name might be derioved from Old Norse Sol = sun and Vo/Voe whichh means inlet in English and so may have had a similar meaning in Old Norse. But the orgin of the name does not seem to be attested - there is no early written evidence - so it's hard to know for sure.

Here is a picture of the estuary by Bill Boaden.

Here is a photo taken by one of our party, showing what it looks like from the shore with the tide out.

From Solva there is a cliff path that takes you to St David's and the cathedral of the monastery founded by the saint. It was a fine day and I would have liked to have walked it, but I am simply not mobile enough.

In my hedge grown these âpinkbellsâ, from bulbs I planted many years ago.

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