Perfectly Proportioned Donut Hole - A reply

I sent an email off to a Statistics lecturer. He was helpful in letting me know that I was completely off track...


Original Letter:

Hi Lecturer

I wonder if you could point me in the right direction please...

I've been trying to find some information relating to donuts on the internet and particularly the mathworld.wolfram.com website. My question is this, "Is there a perfect proportion between inner and outer donut circumferences?" I found information regarding the torus at http://mathworld.wolfram.com/Torus.html but nothing on in relating to what I search for... I think.

I know that this is a geometry type question, but I hope that you can help in some small way.


Reply:

I’m not aware of any ideas of “perfection” relating to tori. There has been a lot of work (both mathematical, psychological and artistic) on the aesthetic preference for geometric figures divided according to the “golden ratio”. I’m not sure if this ratio has any influence in respect to tori. Certainly there are aspects of topology that distinguish different tori according to the difference in proportion of the circumferences that you mention but that isn’t my area at all! I wonder what a doughnut with a golden ratio of the outer to inner circumefrence would look like? My feeling is that it would probably be quite fat. Not sure. Maybe read up on the golden ratio (or Google both) and see what you find!

Lecturer