So have you ever wondered why there are 360 degrees in a circle? Or why there are 60 minutes in an hour? or 60 seconds in a minute? Seems rather weird doesn’t it. Well, don’t worry – it’s not an evil conspiracy.
Simple Answer: Blame the Babylonians – they used the Sexagesimal system. Don’t get excited – it means that instead of using base 10 (as we do) they used base 60. You can read more about it on wikipedia.
Geek Answer: So the next question is, why 60? Well, 60 has a lot of advantages, especially before the day of calculators. The numbers 1-6 all divide nicely into it – therefore it’s easy to split a circle / hour / minute into fractions and get a whole number back (e.g. 1/4 hour is 15 minutes, and 1/6th of a circle is 60 degrees). Not only that, 10, 12, 15, 20 and 30 all go into it as well! All up, that means you get 12 factors (or easy fractions). That’s awesome. Just don’t ask them to divide by 7… (1/7 = 0.08:34:17:08:34:17: reoccuring)
Compare this to base 10, where you only get 4 (1,2,5,10) – even with 100 you only get 9 (1,2,4,5,10,20,25,50,100).
But why 60? Dustmop (below in comments) points out that farmers probably counted the days in the year long before they cared about algebra. Combined with the fact that 360 is very close to the 365 days in a year, probably lead to the number being used in a lot of primitive seasonal calculations. The Babylonians probably got the idea of using Base 60 from this even earlier origin. If there are ETs out there, I wonder what base they use for chopping up time (considering it’s unlikely that they have the same 365ish rotations per cycle around the sun) and circles (probably radians)?
Update 2009: There is a much more comprehensive explanation here: http://scienceray.com/mathematics/applied-mathematics/why-are-there-60-minutes-in-an-hour/
Update 2013: Ian pointed out in the comments below that that link no longer works. You can still read the article via the Wayback Machine here: https://web.archive.org/web/20100924073459/http://scienceray.com/mathematics/applied-mathematics/why-are-there-60-minutes-in-an-hour/