Go out on the streets and ask the average person “How many degrees in a full circle are there?” and you’ll probably get the answer 360 (although you may come across a few confused faces but let’s gloss over these!). This is something we learn from the early days at school - there are 360 degrees in a full circle, 180 in a half turn, 90 in a quarter turn and yeah you get the picture.

A right angle triangle (that is one with a 90 degree angle) can be the stuff of nightmares after mountains of dull trigonometry questions!

*But now here’s the question; why are there 360 degrees in a circle? *Why *is* a circle broken up into 360 degrees?

Have you ever thought about that? Like, what makes 360 so special? Who decided we should use 360 and why did we listen to them? If a strange (and English speaking, obviously) alien landed on Earth and asked you “Why do you odd earthlings measure angles out of 360?” could you answer him?

Have a think to yourself for a second before you read on: why do you think we use 360?…

Well the cheat answer to this question (and arguably the biggest reason) is because it’s tradition - everyone uses 360 degrees and so that’s what we teach our children, it would be madness to teach them anything else. 360 has been around since at least the Ancient Greeks so why would we want to use anything different?

But this really is a cop out - someone must have started using 360 first and so why did they pick that number? Well the answer to this question is actually fascinating because in truth no-one really knows why. We don’t have any definitive answers. But there are a lot of very good theories and ideas, here’s two of the best:

The Sun and the Earth (not to scale in the slightest).

Firstly there are 365 days in the year and 360 is very close to this - in fact several ancient calenders had precisely 360 days in the year. Ancient astronomers broke up the path the sun traveled in a year into 360, one part for each day, and bang - this became a degree.

The first few divisors of 360…

Secondly another theory is that 360 was an ideal number to choose because it has so many divisors; every number less than 10, apart from only 7, divides into 360 - making calculations so much easier.

Have a read of some of the other theories for why we use 360 here. Perhaps it’s a combinations of all these reasons?

So are you convinced that 360 is a good choice now? We’ve found a few reasons but it’s not really convincing is it, I still don’t think we’d be able to convince our alien friend as to why we really use 360. Don’t get me wrong I love degrees (this blog’s title even takes its name from them!) but really there’s just no mathematical reason for defining 360 degrees to be a full circle.

This is where radians come into play. You see almost all mathematicians don’t actually use degrees to do real “science stuff” they instead use something called radians. What are radians and why are they better? Well click here to find out…

Posted on Friday 22 March 2013.