Base 60 (sexagesimal) - Numberphile

Key Takeaways

so the number we're talking about now is 60 now it's quite a big number so you may not meet it all the time but you do use it a lot when telling the time because of course there are 60 seconds in a minute 60 minutes in an hour but why 60 why this random number 60 well it all goes back to the Babylonians thank you Babylonians because what they wanted back then is a very nice number that divides quite easily so if you think about the number 60 what go what divides it cleanly one of course two 3 four five and six in fact it's the smallest number that's divisible by all of these well why is this important because you can take a half of it you can take a quarter of it you can take a fifth of it you could take a third of it you can divide 60 up in a lot of ways so if you're cooking in this base you can cook with lots of fractions of that so if you don't want to cook a whole meal you can cook half a meal or a third of a meal or you know things like that it's again if you're telling time you can have quarter of an hour you can have 20 minutes you can have half an hour you can have 3/4 of an hour it all divides 60 very nicely and when you don't have computers you need a number that you can divide nicely so you get nice round numbers at the end of it so because they're easier to work with so I mean 60 why if 60 is so nice why do we use 10 you you just asked my next question go on tell me why well the idea is that we use 10 because we have 10 fingers so you can just count along as you're a child you'd count 1 2 3 3 4 5 6 7 8 9 10 but what's it thought is that the Babylonians actually counted in to 60 on two hands they would use each knuckle on one hand to count to 12 and then count the number of 12 on the other so you'd go 1 2 3 4 5 6 7 8 9 10 11 12 one set of 12 and then you do it again 1 2 3 4 5 6 7 8 9 10 11 12 two sets of 12 and again and again until you get five sets of 12 which is 60 highly divisible and you can use it on your hands so when the Babylonians were working with this number 60 they were also very good astronomers and what they found is that the year is pretty much 360 days so that's the length of time it takes for the the Earth to go a full circle and that's what why the the circle is divided up into 360 degre and further each degree is then divided up into 60 minutes you can have an arc minute which is a 60th of a degree and that further is then 60 seconds 60 Arc seconds of that 60 Minute I wonder if we we came close to living in a world where 60 became our base like I say it's very very difficult I mean you could write well there's 57 we we use it two numbers for a Babylonian to write 57 they would have to write one 2 3 4 5 6 one two three four five six seven it's a lot easier to write like that than that so these are how they they drew their numbers because they had little stylus that they would hit into clay and the stylus had a triangular end so their stylus would look something like that and so when they were doing ones they'd use the tip and go 1 2 3 4 5 6 seven all the way up to 10 and a 10 that turn the stylus on the side and create one of those shapes so each one of those is 10 each one of these is a one and so there we have 57 good that's their version of a Sharpie exactly yeah which really good 1 2 3 four five