Monthly Archives: March 2015

eclipse chasing

The last total solar eclipse visible from the mainland United Kingdom occurred on 11 August 1999, with the path of totality passing through part of Cornwall. I took a few days off work (at the time I was working on a short-term contract for a software company in Dublin) and joined some friends who were going to try to see it.  In the event it didn’t really work out: we saw some of the partial phase before the clouds thickened and it wasn’t until a few hours later, well after the end of the eclipse, that the sky cleared again. So apart from seeing the overcast sky go briefly dark, and trying to guess which topical pieces of music the local radio station would play (Moonlight Shadow by Mike Oldfield and Here Comes the Sun by the Beatles) it all came to naught. In retrospect, I’d have seen much more of the eclipse if I’d stayed in Dublin, which had clear skies and got about 90% totality. (Also, I wouldn’t have had to camp overnight in a tent, which I don’t remotely enjoy.)

Today’s eclipse, while partial, was a much better occasion. I heard from friends elsewhere that some parts of the UK were overcast, but Coventry had pretty clear skies throughout, apart from some thin, hazy clouds for a short while in the middle, and I was able to watch the whole thing from start to finish.  I dragged my telescope (a 130mm Newtonian reflector) out onto the drive and carefully set it up, projecting onto a pad of paper.

2015-03-20 08.53.03 2015-03-20 09.06.52
08:53am 09:06am

(If you look carefully at the second image you can see a sunspot.)
I also took the opportunity to try that thing with a colander. The holes in the colander act like a sort of unfocused pinhole camera, and project lots of slightly fuzzy copies of the partial eclipse:
2015-03-20 09.18.29

The eclipse progressed over about the next hour and a half:

2015-03-20 09.22.06 2015-03-20 09.26.26
09:22am 09:26am
2015-03-20 09.42.07 2015-03-20 10.34.01
09:42am 10:34am

And finally finished at about 10:40am:
2015-03-20 10.38.50
At about quarter past ten, I smelled burning plastic and noticed a thin wisp of smoke drifting out of the end of the telescope. The sun’s image had drifted half out of the field of view (where it would have remained if I’d ever got around to buying some batteries for the equatorial drive motor), and was now focused on the lens casing. Oops. The lens itself is ok, but the casing is now slightly melted.
2015-03-20 10.22.40
And that, boys and girls, is why we must never, ever look directly at the sun, especially not through a telescope or binoculars.

Ramanujan’s construction for almost squaring the circle

I have ambivalent feelings about Pi Day. Certainly, anything that gets people talking about mathematics is broadly a Good Thing. And clearly a lot of people have tremendous fun, and really enter into the spirit of things, and jolly good for them. But, says a curmudgeonly voice in my head, it’s a little bit contrived. If you use base ten to represent numbers, and if you use the American month-then-day convention to represent dates, then the 14th of March gives actually a pretty rough approximation to the value of pi. (On the other hand, if you use the day-then-month ordering, the 22nd of July yields a more accurate approximation.) But this year, the sequence you get is 3/14/15, which is better than usual, especially if you happened to be looking at your clock at 9:26:53 precisely.
(I wasn’t – we went on holiday to the Peak District for the weekend, so at the numerologically significant second I was helping install a 14-month-old child into a car seat, ready to head off into one of the more scenic bits of Derbyshire for a couple of days.)
Anyway, the Aperiodical had a competition to find interesting methods of approximating pi. This looked great fun, but I totally failed to get around to doing anything about it. Many others were, as usual, better organised and motivated than me, and a list of some of their attempts can be found here.
But earlier today, in Ian Stewart‘s very readable textbook on Galois Theory, I found a nice ruler-and-compass construction, due to Ramanujan, of an approximate solution of the age-old, impossible problem of squaring the circle. This evening, I gave it a go with a moderately sharp HB pencil, a 30cm ruler, a pad of graph paper, and some compasses that were originally part of a geometry set and pencil case I got in the mid-1980s for opening a “Griffin Savers” account at the local branch of the Midland Bank (long since amalgamated into international tax-evasion facilitators HSBC).
And this is the result.

image

The construction is as follows: First draw a circle with centre O, and let AB be a diameter. Now M is halfway along OA and T is 2/3 along OB. P is vertically above T, and then the length BQ is equal to that of TP. TR and OS are parallel to BQ, the length of AD is equal to that of AS, and then draw AC tangent to the circle with the same length as RS. Now mark E so that BE is the same length as BM, and mark X so that EX is parallel to CD.
Once you’ve done all that, says Ramanujan, the square with side BX should be very nearly equal to the area of the circle you first thought of.
So I did all this, very carefully measured BX (~15.8cm) and OB (9 cm), and got a value of about 3.082 for pi, which isn’t that far off the correct value. With a sharper pencil and a larger piece of paper, I reckon I could probably have got a bit closer to the correct answer. I need to think further about why this construction works, and I might even get around to writing more if I figure it out.
(Also, go and visit Derbyshire sometime, because it’s very pretty.)