The 28th June was an auspicious day for a graduation. Not only did the skies produce some amazing sunshine, but it was a mathematically interesting day for at least two different reasons.
The first reason, which actually got a decent amount of news coverage on the BBC and elsewhere, is that June 28th is Tau Day. There is a small but dedicated group of people who believe that pi is the ‘wrong’ number. Not that there is anything wrong with the number itself, 3.14159…, but that we should be using the ratio of the radius to the circumference of a circle, not the ratio of the diameter to the circumference. So they define tau to be equal to 2 times pi (which is 6.28, hence June 28th!), and have even invented their own symbol:
To modern mathematicians, tau is a more natural constant to use than pi because a circle is defined as the set of points which are a fixed distance (the radius) away from a point. For any of you readers who have studied maths beyond AS level (or Highers), you will know that the standard unit of measure of angles is the radian, not the degree. One radian gives an arc on the circle which has the same length as the radius (see picture). Learning to use radians and converting to degrees can be the bane of a young mathematician’s life! How many radians are in a circle? It’s the circumference divided by the radius, which is 2 pi. So 360 degrees is 2 pi radians. That means we get horrible formulas, like a quarter of a circle being pi/2 radians, instead of what you would expect: pi/4. Using tau instead of pi, we do indeed get a much more intuitive measure for angles.
Still, despite all the arguments in favour of tau, I have to say that I don’t think it will ever catch on. Pi is far too engrained in our history and our culture. We made our choice over 2000 years ago and it’s too late to change things now!
A much better reason, I think, that 28th June is interesting is because it is the perfect day of the perfect month. A perfect number is one which is the sum of its divisors (not including itself). So 6 = 1+2+3, while 28 = 1+2+4+7+14. Perfect numbers, as you might imagine, are pretty rare: the next one after 28 is 496, while the next perfect year is not going to be until 8128. The ancient Greeks were the first people to pay attention to perfect numbers, and it was Euclid who noticed that the perfect numbers had the form 2p−1(2p−1), where p is a prime number. He proved that if 2p-1 is prime then the formula 2p−1(2p−1) will always be a perfect number. However, it was not until Euler came along in the 18th century that the converse was shown: that every even perfect number comes from this formula. So every time we find a new perfect number, we find a new prime too!
Graduation was also an exciting day because all of Julia’s family were able to come up and see it. This included her Hungarian grandmother Emily, who we all call Nagyi (which is Hungarian for grandma, pronounced nudge-ee). Although Nagyi could hardly speak any English, she loved the historic atmosphere of the graduations (in the beautiful McEwan Hall) and all the lovely people she met.
I don’t know why this is, but the Hungarian nation produces a surprising number of top-class mathematicians. So it wasn’t very hard to find one at the University of Edinburgh who was happy to chat to Nagyi during the afternoon reception. Our victim was the charming Tibor Antal, who works on modelling biological processes (such as cancer growths) and population dynamics. I hope that he got to tell Nagyi a bit about his research, but I suspect that he spent most of the conversation listening to her life story!
Another thing which surprised Nagyi was how much everyone appreciated her crochet work here. Before she came, I gave her the double challenge of making a Möbius strip and a hyperbolic disc. Although she made two beautiful models, she had absolutely no idea what they represented or why they were important. And yet, when we took them out at the maths reception, everyone was cooing over them in amazement!
To any other mathematicians who have grandmas: I suggest you get them knitting and crocheting and embroidering any mathematical objects you can think of! They really learn something new from it and have fun in the process. One day I’m still hoping to run an interactive maths knitting exhibition where anyone can come along and try it for themselves.
Thank you once again to everyone who sent messages of congratulation for the graduation, and to all my friends and family for being there on a great day. I wouldn’t have been there without you all!