Why are there 360 degrees in a circle? (Maths tutorial)

This is a simple maths tutorial answering the question of why there are 360 degrees in a circle. You can find the written tutorial here:
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There are three theories as to why there are three hundred and sixty degrees in a circle. The first is that 360 is simply an easy number to work with because it's divisible by so many other numbers (24 in fact). But then why 360 and not 720 or 1080, which are divisible by more?

The second theory relates to the solar and lunar calendar. There are 365 days and 355 days in each respectively - and 360 is the number that's right in the middle, and once again much easier to work with.

Lastly, if you were to take the radius of a circle and make an equilateral triangle with it (identical sides and angles) you'd find that six of them fit beautifully into the circle. In the past, people used the sexagesimal system which has a base of 60 (we use the decimal system now, that has a base of 10). It's thought that each of these triangles were arbitrarily given the value of 60. And 6 x 60 = 360.

So there you have it, three theories as to why there are 360 degrees in a circle.At the end of the day, it doesn't really matter why we use 360 - what's important is that you know how to measure angles and use them when needed. Check out this tutorial to learn how:

The trivia is cool though, isn't it?

You can turn the captions / subtitles on and off in the bottom right hand corner.

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[switzerlandful]

Yes. I was reading about 360 recently. Seems it has lots of cool qualities. It is...
>a Highly Composite Number
>a Superior Highly Composite Number (which is an even tighter restriction)
>a Colossally abundant number
>a refactorabal number
>a 5-smooth number
>the lowest # that you can put all natural numbers 1-10 into except for 7.
and add "0" and you have the number of seconds in an hour.

[utubeballbag]

Cool vid I asked this in a civil engineering maths class today and the lecturer didn't know the answer and everyone laughed at me as if I was crazy lol

[rezasenohawan]

360 -> 3+6+0=9
180-> 1+8+0=9
45-> 4+5 = 9
22, 5-> 2+2+5=9
but wait there's more
11, 25-> 1+1+2+5 = 9 and 11+2+5 =18-> 1+8=9
5, 625 -> 5+6+2+5 = 18 > 1+8=9
and so on

[hosambadawy]

thanks for this amazing video, love it, i have a small note* at 0:34 (it there were 100 degrees in a circle the degrees per minute would be 0.1388 not 4.157)

[jibster]

well also the triangle is the only polygon with the property to fit n amount of times in a circle creating no gaps or dents in the end shape!

[zhenminliu]

I must be obtuse: by my arithmetic, each minute should be 6 degrees, but she says 1/2 degree to a minute. What am I missing?

[davidcouke]

It's 360 because every single fraction of it equals to 9. 180 degrees = 9, 90 degrees = 9, 45 degrees = 9. 22.5 degrees =9. 11.25 degrees equals 9 and so on.... 9 is universal unity. You're welcome.

[angelocoppola]

by who and when it was decided 360 should be the right number ? Thank you for your time

[jamesantonywhitehead]

Great Start but no further to the development of the -
Theory 1 -
The idea of time is limiting the human species to a introspective view of the universe.
Hours, minutes and seconds are units divisible of the whole. If this ideology is correct why change to base ten in years, though base 12 was used before this.
Theory 2 -
More of theory 1 reinforcing an outdated idea.
Theory 3 -
We do not have 10 fingers and ten toes; 8 finger 2 thumbs ten toes yes, this is to show that this is a construct.

If you want to know why there is no different; it is because any other ideas are burnt out of existence.
People were killed in the past to suggest otherwise.
By all means I can be wrong; can you be?

[dereksrightdelt]

Should have been 320, it’s easier to keep halving it lol. 320 160 80 40 20 10 5 2.25 vs like 360 180 90 45 and then like 22.5 and then I don’t even wanna try to go further lol

[oooooo]

if we had 100 degrees in a circle than we should have had 10 or 20 hours per day and that’s neat

[rifayafatima]

If we draw a diameter it will be 180* but if we take two radius & make an angle at the Centre it will be 360*!..

[jootpepet]

I didnt need to know this but thanks i guess

[fungipolo]

so there is no exact answer to why there are 360 degres in a only said there are 3 theories. Well in my book that don't mean squat! That explanation holds as much water as the theory that you can not do complete 180 in life less you have 360 degrees....lmao. So it's kinda of weird if you ask me that all our physics and such is based on a number that no one can explain. Is that Weird or What, ....lol

[kirkclarke]

If there are 90 degrees in a right angle then there are 180 degrees in a circle

[sharminakhter]

Circle has two part . Each is 180 degree . Thats why circle is 360 degree