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Timetabling choreography with maths

Earlier this week my sister-in-law (“SIL” from now on) sent me an email asking for help. She’s a dance teacher, and her class need to rehearse their group pieces before their exam. She’d been trying to work out how to timetable the groups’ rehearsals, and couldn’t make it all fit together. So of course, she asked her friendly neighbourhood mathmo for help.

My initial reply was cheery and optimistic. It’s always good to let people think you know what you’re doing: much like one of Evel Knievel’s stunts, it makes you look even better on the occasions you succeed.

I’d half-remembered Katie’s friend’s Dad’s golf tournament problem and made a guess about the root of the difficulty she was having, but on closer inspection it wasn’t quite the same. I’m going to try to recount the process of coming up with an answer as it happened, with wrong turns and half-baked ideas included.

Factor Conga

Quite a few designery visualisations of the prime numbers have been put out on the web recently, to varying degrees of success. Most of the time they look pretty but don’t tell you very much; the most recent example I can think of is El Patrón de los Números Primos by Jason Davies.

A few weeks ago Brent Yorgey posted on his excellent blog The Math Less Traveled some really nice “factorization diagrams“, along with the code to produce them. Straight away, anyone with a text editor and a knack for fancy web coding set to work making the animated version that was so clearly required.

Stephen von Worley has made, I think, the nicest one. He calls it the Factor Conga. Sit back and enjoy the mysteries of the natural numbers as they dance their beguiling dance!

 

Dance Your PhD: Cutting Sequences on the Double Pentagon

As a mathematician (and not just any kind of mathematician – a PURE mathematician), I heard of the “Dance Your PhD” contest and immediately burst out laughing. As much as there is some nice pure mathematical dancing out there (see, for instance, this series of videos of different numerical sorting algorithms interpreted through dance), the idea that someone’s mathematical PhD research could be conveyed via bodily gyration was both fantastical and hilarious.