This is a straight-out plug for David Treeby, a colleague and good friend and ex-student. David was a Monash undergraduate and eventually went into teaching, doing a (very good) PhD with the Mathologer along the way. David now teaches at Polo Grammar Scotch College, where he is able to do great stuff. We have a different post ready to go on David’s work, as soon as he gives the green light, but something else came up.*
David has had some astonishingly strong minions students; he stretches them and they stretch him. Two of these recent students are Arthur Sun, now an undergrad at Cambridge, and Edward Wang, now an undergrad at Melbourne. (In this instance, the minions are quickly outgrowing Gru.) Together, David and Arthur and Edward pondered a problem, a variation of a problem that Martin Gardner wrote about:
Given four sticks of length between 0 and 1, what is the probability that no three sticks can be used to form a triangle?
Experimentally, the probability appeared to be 1/6 but they had no idea why. They experimented further and the corresponding probability for N sticks appeared to be 1/(F1 x F2 x … Fn), the reciprocal of the product of the first N Fibonacci numbers. Then, together with Aidan Sudbury, a retired Monash mathematician, they proved this to be true.
David and Arthur and Edward and Aidan wrote up their work, submitted it for publication and posted the preprint. Their work has just been featured in a lovely article in Scientific American.
One can get into the deeper meaning of this, but we’ll leave it as the good news story it is.
*) There are other, bad news posts to write about David and some of the nonsense he has had to endure. These posts will not be written, and I will confine the distasteful allusions to this footnote.
As a former student, I can confirm he is very inspiring. Well done team on the paper!
Thank you, and please you a (fake if you like) name. No “anonymous”.
Ah, yep will do in future.
No worries. Thanks, Jasmine (or “Jasmine”).
This is indeed a very nice achievement.
I have another question for your consideration. A middle school student once proposed to me this solution to trisecting an angle with straightedges and compasses. Let POQ be the acute angle to be trisected. From a point A on PO, drop a perpendicular to OQ, meeting OQ at B. On the edge AB, construct an equilateral triangle ABC with C and O on opposite sides of AB. it is claimed that COQ is one third of POQ. I am looking for the simplest possible refutation, one that can be explained to middle school students with minimal knowledge of geometry and no knowledge of trigonometry. (This is a nice question to pose to students in a mathematics club.)
You can send me an email at barbeau@math.utoronto.ca .
Choosing a specific acute angle such as 60 degrees should suffice…?
Congratulations to David & co for the result. I’d be interested in the “bad news” if you do decide to write a post about it.
Thanks, RFS, and sorry to tease. It seemed misleading to not indicate that David had had some nonsense to manage, but I won’t be posting on it.