The Problem of the Moving Triangle

Posted in Cute Problems, mathematics with tags , , on August 16, 2018 by telescoper

I found this nice geometric puzzle a few days ago on Twitter. It’s not too hard, but I thought I’d put it in the `Cute Problems‘ folder.

In the above diagram, the small equilateral triangle moves about inside the larger one in such a way that it keeps the orientation shown. What can you say about the sum a+b+c?

Answers through the comments box please, and please show your working!


Say A Little Prayer

Posted in Music with tags on August 15, 2018 by telescoper

Aretha Franklin, the Queen of Soul, is gravely ill. You could do worse than say a little prayer for her…

Update: I’ve just heard the sad news that Aretha Franklin died today (Thursday 16th August 2018)  at her home.

R.I.P. the Queen of Soul.

Results Day Advice!

Posted in Education with tags , , , , on August 15, 2018 by telescoper

Today’s the day in Ireland that students get the results of their school Leaving Certificate examinations and, over the other side of the Irish Sea, tomorrow is when A-level results come out. For many there will be joy at their success, and I particularly look forward to meeting those who made their grades to get into Maynooth University shortly.

Others will no doubt receive some disappointing news.

For those of you who didn’t get the grades you needed or expected, I have one piece of very clear advice:


In particular, if you didn’t get the Leaving Certificate points you needed for entry to your first University in Ireland or the A-levels needed to do likewise in the United Kingdom, do not despair. There are always options.

For example, in Ireland, you could try looking at alternative choices on the Available Courses, where any places remaining unfilled in particular courses after all offers have been made and the waiting lists of applicants meeting minimum entry requirements have been exhausted, will be advertised.

In the United Kingdom the Clearing system will kick into operation this week. It’s very well organized and student-friendly, so give it a go if you didn’t make your offer.

D.G. Bradman b Hollies 0

Posted in Cricket, History with tags , , on August 14, 2018 by telescoper

It was on this day 70 years ago (i.e. on 14th August 1948) that the great Australian batsman Sir Donald Bradman played his last Test innings, against England at the Oval. He didn’t know it would be his last knock but Australia won the match by an innings so he never got to bat again in the match, which was the last in the five-match Ashes series that Australia won 4-0.

Bradman needed only to score four runs to finish with a Test batting average of 100, but he was out second ball to the legspinner Eric Hollies, for a duck, and his average was stuck on 99.94.

Here’s a short video of Bradman’s last Test innings, featuring commentary by John Arlott:

Two things struck me when I watched this just now. One is that Norman Yardley’s decision to give Bradman three cheers at the start of his innings may have seemed very sporting at the time, but I’m sure it put the batsman off and I wonder if that was Yardley’s calculated intent?

The second striking thing is the poor state of the pitch, with huge footmarks clearly visible. Although Hollies was bowling round the wicket presumably to exploit them, it’s not clear these played a role in Bradman’s dismissal. It looks to me that he played a loose shot at a full delivery, probably a googly that turned a little. Nevertheless it is worth remembering that batsmen of Bradman’s era had to play on uncovered wickets. I won’t dwell on this point for fear of starting to sound like Geoffrey Boycott, but it does reinforce just how remarkable Bradman’s average really was. Add to that the fact that England had been bowled out on that strip in their first innings for just 52!

Eric Hollies may have been a good bowler, but his record with the bat was at the opposite extreme to Bradman, scoring a total of 37 runs in 13 Test matches, at an average of 5.28. His total of 1,673 runs in first-class matches was 650 fewer than his haul of wickets, and only once (in 1954) did he reach 30 in an innings. In fact, he did not reach 20 in any innings between 1946 and 1953, and equalled an all-time first-class record, between July 1948 and August 1950, of seventy-one consecutive innings without reaching double figures.

Although Australia won the Ashes convincingly in 1948, the Australian camp was not entirely harmonious. The tension therein largely originated in the fact that Bradman was a Protestant and there was a Catholic faction in the touring party that didn’t like him for essentially tribal reasons. Indeed, I’m told that some former Australian players in the Press Box burst out laughing when `The Don’ was out for a duck that day.

The Mother of Civilisation Library Project

Posted in Uncategorized on August 13, 2018 by telescoper

When I was packing books at my Cardiff residence last week I set aside a few I no longer needed. This morning I put them in a parcel which I took to the post office and sent to the Mother of Civilisation Library Project in Sindh (Pakistan).

In case you weren’t aware, the Mother of Civilization Library is a volunteer organisation in the Indus Valley around Sindh, in the southern part of Pakistan. Their project is to help and facilitate a libraries program in Sindh by collecting books. They contacted me a while ago about making a donation, and I’ve finally done it!

If you have any spare new or used books that you would like to send to the Library program, I’m sure they’d be thrilled to receive them! Your donation could do much to stimulate and encourage the growth of learning, especially among the young generation of students.

Please send books to:

Rashid Anees Magsi, Project Manager, Mother of Civilization Library

Street: Sobho Khan Magsi,

City: Radhan Station Dadu,

Province: Sindh,

Postal Code: 76310,

Country: Pakistan

P. S. If you send a donation from the UK be sure to say that you are sending books – the cost is much lower if your parcel contains only books than if it contains other items of the same weight.

Royal Society University – Science Foundation Ireland University Research Fellowships

Posted in Uncategorized on August 13, 2018 by telescoper

It is now time for a quick public information broadcast.

Did you know that the Royal Society has teamed up with Science Foundation Ireland to enable early career researchers in Ireland access to the University Research Fellowship (URF) scheme?

This scheme provides five years of research funding (with the possibility of renewal) and has proved to be a stepping stone to their first permanent academic position for a great many scientists.

This scheme covers, but is not limited to, physics and astronomy. For full details of the scheme, see here.

The deadline if you want to apply to hold a URF in Ireland is 12th September 2018, which is just a month away so get cracking!

You could go a lot worse than applying to hold your URF in Maynooth!

Oh, and five years residency in Ireland qualifies you for citizenship. Just saying…

A Message for your Resit

Posted in Uncategorized on August 12, 2018 by telescoper

It’s the time if the year for repeat examinations at Maynooth University and resit examinations at Cardiff University (note the slightly different nomenclature).

There’s only a couple of students taking my own papers but I will be marking a few other papers in Maynooth so here’s a message for all students taking resits or repeats over the next couple of weeks: