James Tanton gave a great talk at the JMM (Joint Math Meeting) in San Diego on
how many degrees are in a Martian Year?
but he didn't quite answer his title question. I found an excerpt of the talk on YouTube but still didn't quite answer the question, though he could have.
The talk was
How many degrees are in a Martian Year?
Here is an excerpt on You Tube: here
I feel the urge to explain and complete the talk.
Why do we earthlings have 360 degrees in a circle? Because there are 365.25 days in a year and nobody wants to work with that number so they round off. They could have chosen 360 or 365 or 370 but since 360 has the most divisors, it wins. (There is a different measure, gradians, of which there are 400 in a circle- also a nice round number, but 360 is rounder via the criteria we will soon explain.) So why pick 360? It has the most divisors.
There are 668 martian days in a martin year. So you might think they would pick 670 or 660 for there degreees. But thats Base 10 thinking! So the answer depends on what Base the Martians use. Lets assume that, like us, it depends on the number of fingers they have on their hands. We also assume they have two hands with the same number of fingers on them (would aliens look like us or not? Here are some thoughts: here and here). Two fingers on a hand seems like two few, and ten seems like too many so lets assume there base is either
3 fingers per hand: base 6. 668-base 10 is 3032 base 6. 3020 is answer- divided by 2,3,5
4 fingers per hand: base 8. 668-base 10 is 1234 base 8. 1240 is answer- divided by 2,3,4,8.
5 fingers per hand: base 10 668. Lets go with 660- divisible by 2,3,5
6 fingers per hand: base 12 668-base 10 is 478-base 12. 470 is answer- divided by 2,3,4,5
7 fingers per hand: base 14 668-base 10 is 35A in base 14. 140 is answer- leave it to you.
Any other good candidates or methods for this?