Personal Blogs

Woodworm. That's a boring life.

I was watching a very interesting lecture on YouTube, From Ronald Ross to ChatGPT: the birth and strange life of the random walk, and the speaker said "WQ" was one of the few letter pairs that do not appear in English words, and then went on to suggest we could neologise a word "cowquake" and imagine a thunder of hooves.

Well, this was a challenge, surely "WQ" must exist in some real words. So of course I went to look for them.

1. Does "cowquake" exist? (You might argue it does now, even if it didn't before).

2. Are there any other words containing "WQ"?

This is what I found on initial investigation.

1. The OED has "cow-quakes", a name for quaking grass, but I guess the hyphen disqualifies it.

However I found a BBC reference to "cowquaker", an 'off the scale thunderstorm' that frightens the cows. So looks like cowquaker exists, even if cowquake is debateable. Still I couldn't find the word in the OED.

2. Googling for words with "WQ" in throws up many acronyms and company names, and the Cornish town Newquay, plus the odd unusual word in other languages. But these don't really count, and the only promising candidates I'd found by this point are "crowquill" and "snowquake". 

A crowquill is a quill pen made not from a goose feather but with a feather from a crow, and the name is now used for a fine-tipped metal nib for map drawing and similar work. The OED hyphenates the word though, and Merriam-Webster makes two words of it, so this is another disputable example.

As for "snowquake" neither the OED nor Merriam-Webster recognise it, although I did find an Urban Dictionary entry:

This is our new planter and some really gorgeous flowers.

Although the Ancient Greek mathematicians discovered an enormous amount about geometry, in modern times a number of rather nice facts have been found that the Greeks didn't know about. One of these is Bottema's Theorem, named for Oene Bottema, a Dutch mathematician of the 20th century. It goes like this 

Suppose we have a triangle, PQR in the diagrams, and draw squares on two of its sides as shown. Draw a line joining the two vertices of the square that lie opposite to the vertex P and mark the midpoint U of the line that joins them.

Then the midpoint lies at the centre of a square resting on the base of the triangle and rather unexpectedly this is true wherever we move move the vertex P. The diagrams above show two positions of P and you can see that the position of U is indeed the same in both cases. 

There are quite a few websites that discuss the theorem and give proofs, and there are also some nice animations and YouTube videos that demonstrate the fact that the midpoint is independent of P's position. 

There are also some published variations on Bottema's theorem, but here is a neat one one I discovered by chance and  which I haven't seen anywhere and which is new, to me at least.

Bottema's theorem works not just for squares but for any regular polygon with an even number of sides. For example, here is an example where the polygons have six sides.

Notice that the midpoint M is now the centre of a third hexagon, rather than a square, resting on the bases of the square, and as with the square case the position of the midpoint does not depend on the position of vertex A.

If we instead erect octagons on the sides of the triangle then the midpoint will again be independent of the location of A, and will be the centre of an octagon resting on the base of the triangle. We can construct analogous configurations for any even number of sides, and the midpoint will always be fixed in the same way. I think that's rather neat and I was pleased when I discovered it.

“If I asked ever so nicely, could I have that sofa and chairs?”, asked Tom sweetly.

Speaking of rain I saw this rainbow this other day. Although rainbows are a familiar sight, when one appeared all the people around me were quite excited, and I was too.

This got me wondering what rainbows are called in other languages. Is the name a compound, similar to the English rain+bow? On a quick look I found some where it was, and one or two rather different. 

German is regen-bogen, evidently cognate with the English. Old English had regnboga, also very close, but it also had scurboga, and recalling that "sc" in Old English was pronounced as "sh" this would be shower-bow, which rather sadly is now lost. I think we shyould bring it back.

In French we have arc-en-ciel, "arc in the sky", so no reference to rain. Italian is arco baleno, which I think means something like "arc-flash", so that's a bit different, but still has the bow theme.

Latin was iris, borrowed from Ancient Greek I think. Iris was personification of the rainbows. Her name may have originally been Wiris, starting with the archaic digamma, a letter lost in later Greek.

Modern Greek has a different word from Ancient Greek and it baffled me at first, ourano toxo. But after some head-scratching I recalled that Uranus was the personification of the sky and toxo means bow (as in toxophilite, one who likes archery, and the word archer must also be related to arcs/bows). So the Greek expresses the same idea as the French arc-en-ciel.

The last one I looked at was Welsh, which has enfys. The etymology of this is trickier. The en- bit could be an "intensifier", a prefix that adds some kind of emphasis to the following element, and the fys part could be connected to finger or ring, so the origin might have been something like great ring.

I don't know what the weather is like where you are but where I am it's

Raining. Again.

I thought of the nursery rhyme

"Rain, rain, go away/Come again another day",

and that set me wondering if there is a similar children's verse in other languages.

When I tried French, I stumbled across the wonderful Mots D'Heures: Gousses, Rames, by Luis d'Antin van Rooten, which the author claims were verses "From the d'Antin Manuscript, Discovered, Edited and Annotated".  [1][2]

Here's Verse 16. Try reading it aloud in your best French accent

Van Rooten provides scholarly note to help us with the archaic language of the verses, for example Verse 16 he explains as

"Queen, Queen, arouse the rabble
Who use their girdles, horrors, as pillow slips."

Here are a couple more titles from the book - can you work them out?

Et qui rit des curés d'Oc?

Lit-elle messe, moffette

[1] Wikipedia

[2] Blue Ridge Journal

“My cuddly bear is luminous”, Tom gloated.

“I’m here”, said Tom presently.

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.

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 love camping", said Tom intensely.