What connects Leeks, Chives, Shallots and Garlic? They’re all relatives of the Onion. So you could call them the Onion’s kin.

# Personal Blogs

This is a solution to the question I asked on 13 June, what is the rectangle of largest area that can be inscribed in an equilateral triangle of side 1?

Intuitively we might guess that the rectangle concerned is a square but it turns out that it isn't.

Suppose the. base of the rectangle is as shown in Fig. 1. Then we can use trigonometry to show its height is sqrt(3)t and find its area. Fig. 2 shows a graph of the area against t, which is a parabola with a line of symmetry as show, and a vertex P which corresponds to the maximum area. The graph must pass through the point where t = 0, so the width of the rectangle is 1 and its height and therefore area is 0. It must also pass through the point where t = ½ and the width of the rectangle is 0 and therefore its area is again 0. By symmetry the vertex of the parabola must be half-way between these values of t, so the maximum is when t = ¼.

This rectangle has an area which is exactly 50% of the are of the triangle. It's interesting to compare this with the area of the largest *square*, which is very close, at about 49.7% of the area of the triangle. I drew the diagram below in GeoGebra showing the rectangle in black and the square in brown. You can see how small the difference is.

What bird sounds out of breath. The Puffin.

Suppose we start with an equilateral triangle of area 1 and draw a rectangle in it, how large can the area of the rectangle be?

Someone at the pub said what does ‘whelm’ mean? You can overwhelm or underwhelm, but can you whelm? Is whelming some kind of middle way?

A bit of research reveals that originally there was just whelm, a disaster that could happen to a boat or ship, meaning it could be overcome by weight of water and sink. Overwhelm just added the sense of a mass of water descending on the vessel.

So what about underwhelm? Well it seems to be a humorous coinage, first recorded in 1956. Here’s a couple of quotations the OED gives for whelm and underwhelm.

*a*1513 R. Fabyan New Cronycles Eng. & Fraunce (1516) II. f. clxxxviii By the Mysgydynge of the Sterysman he was set vpon the Pylys of the Brydge, and the Barge whelmyd.

1956 T. K. Quinn *Giant Corporations* viii. 61 He wrote..commending the action of one of the giant corporations for a..price reduction at a time when prices were rising. I was underwhelmed, and investigated.

I went out with an amorous fruit last night. It was a romantic date,

I had a terrible dream in which I was a cocktail made by incompetent bar staff. Woke up feeling badly shaken.

We were doing a crossword at the bar and someone said “Alarm a relative”.

I though what can that mean? I had this vision of frightening aged aunts or something like that. But the answer turned out to be “alpaca”.

For more Mondegreens visit

https://en.wikipedia.org/wiki/MondegreenI was fascinated to read that researchers have succeeded in sequencing the genome of a man from Pompeii who died in the AD 79 eruption of Vesuvius. There is a really good article at

His genome was similar to that of others living in Italy at the time but with some genes shared by people in modern Sardinia. The authors of the original part commented “Further ancient genomes from Pompeii could help to reconstruct the genetic history of an ancient Roman city frozen in time.”

That’s the fascination of Pompeii: it’s a time capsule. And this research is a new window into it.

I loved you more than worms can say.

I never saw this until today, but it seems to have been going the rounds for some years and generated a lot of discussion. Googling the first phrase gets over 2 million hits.

*A man buys a horse for £60 and sells it for £70. He then repurchases for £80, and sells it for £90.*

*Has he gained or lost, if so by how much? Or has he broken even?*

Sometimes it’s a goat or a pig etc.

*9 students and 9 professors attend a dinner at which they sit at a round table. The organisers wish to arrange the seating so that no one is seated between two professors. Is this possible to meet this condition?*

Solution: Imagine we have found an arrangement that meets the conditions. Ask every other person to stand up, so 9 people will be standing. Then we cannot have two professors separated by only a single seated person, otherwise that person would be flanked by professors. But this means only 4 of the 9 standing persons can be professors.

However the same reasoning can be applied to the 9 people who are sitting down, so we can only accommodate 8 professors altogether, leaving one professor unaccounted for.

Consequentially no arrangement can exist that meets the given condition.

Snow and ice

Isn’t nice.

At the Karma Restaurant we serve just desserts.

9 students and 9 professors attend a dinner at which they sit at a round table. The organisers wish to arrange the seating so that no one is seated between two professors. Is this possible?

… and this is what I got

I managed to get an exclusive story about ice cream. It was a scoop.

My mate was very skinny. We called him Finn.

Two herrings walked into a bar. Well, they got kippered.

What follows Fryday? Fatterday.

For several hours there has been almost no wind in my garden, the wind speed is effectively 0 km/h.

I think this must be quite unusual, although the Hairy Ball Theorem tells us that there must always be a point on the earth where the wind isn't blowing at any given moment.

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