why a circle is being devided into 36 0degrees? why not 100?

Question

i want the derivation behind this

Answer 1

every thing on this world is based on assumption and conventions.in the same way, 360 is just a convention.we must have a standard for calculations and the babylonians found those standards.

Answer 2

Mostly tradition (although I have some more arguments below)

A few decades back there was a movement to change it to 400, and many compasses with 400 grads were sold. They are less common now. Military compasses usually use mils instead of degrees. There are 6400 mils in a circle. I'm sure there are many other systems. One obvious candidate is to say that there is exactly 1 subdivision, and that a 90 degree angle is 1/4 circle.

But actually, there is one division that makes more sense than the others when viewed through the abstract eyes of a mathematician: radians. There are 2*pi radians in a circle, that is approximately 6.2832 radians in a circle. Unfortunately for the mathematicians, few non-mathematicians find this convenient at all.

So let's go back to why 360 degrees have become the "standard". 360 is a convenient number. It is divisible by 4, giving 90 degrees for a straight angle. 90 is a convenient number, being divisible by both 2 and 3, giving us 45 degree angles, 30 degree angles and 60 degree angles. Had we chosen 400 grads (or 100 whatever), we would need to use fractions when talking about a 30 or 60 degree angle. Mils are another good choice, but I guess most people didn't need that kind of precision.

Answer 3

Apparently it is the fault of the Babylonians (around 2000 BC). They used a number system with 60 as the base (where we use 10), or rather with a basis composed of 10 and 6 (they had 10 number symbols, not 59 which would have been inconvenient).

Anyway because of that system, 60 was, to them, a perfectly round number - it would be written as "10" in a system with base 60, meaning "1 time 60 to the 1st power, 0 times 60 to the zeroeth power".

And 360 would have been written as just 60 in their system, and 3600 would have been "100".

Of course it is tough to argue why 360, why not 240 or 420 or other multiples of 60.

Anyway, they used 360, and hey were great astronomers and mathematicians so their culture remained very influential for very long.

As a result we have 360 degrees today for a full circle.

And we also have 60 minutes of each 60 seconds to make an hour (this one works well, for the Babylonians this mean "10" and "10" giving "100").

At the French revolution a new calendar was introduced, and there was an attempt to work with days of 10 hours, divided in 100 minutes of each 100 seconds (so you had 100'000 metric seconds per day, instead of the 86'400 non-metric seconds we use) - but this lasted only 12 years.


Bottom-line: if you're going to invent something a bit too complicated, try to make sure that you do not become so influential, that billions of others will have to continue using it for thousands of years!...

Answer 4

Some of the stuff in mathematics were adapted by usage and some are adapted by convention.

For an example if there is more then one common usage , some one points out the confusion, and a resolution is agreed by the convention. Once that happens every one starts following the same(.....-5,-4,-3,-2,-1, 0,+1,+2,+3,+4,5, +6......).

Some of this example of convention is sign convention shown above. In case of a circle if you divide a circle in to equal parts, say 100 parts and call a single wedged shape a unit of the 100 units, then people will understand it also, but your one unit will be equal to 3.6 time larger then standard unit.

If you have time to look in to the method of standardisation then, you can dig in to it.

Answer 5

As other's have said, 360 is divisible by many factors.

The Babylonian calendar was a lunar calendar with a year of 354 days, but they knew that the solar/stelar year is 365 days and added leap months. Maybe 360 was seen as a practical compromise: between 254 and 365, and a nice round figure, especially to Babylonians who used a base 60 number system.

Answer 6

As a matter of wording, it is not so much that the circle is defined
to be 360 degrees, but the other way around - the degree is a unit of angular measure which is 1/360th of a full "rotation." The degree is derived from the Babylonian base 60 numerical system. Hours and minutes are similarly divided into 60's (of course, there are minutes of time and minutes of angle - there are 60 minutes in a degree, and, similarly, there are seconds of time and seconds of degree - there are 60 seconds in a minute, 3600 in a degree).

Answer 7

this conception was derived much before it was possible to calculate in fractions. 360 is a number which can be divided by 2,3,4,5,6,8,10......but the factors of 100 are only a few (2,4,5,10,20). so it was possible for the then scientists to conduct circle related calculations for a large extent without having any fractional value. this conception has been used to calculate time also in analogue watches. so measuring time easily was a practical demand of that time particularly.

thats why dividing a circle into 360 degrees was(and is) more rational than 100.

Answer 8

Just because 360 has more number of factors, it can be divided into a variety of combinations. This has lead to the early mathematician to choose 360 divisions (basically 12 = 3 x 2 x2, whereas 10 = 5x2 only). This was very useful for them to explain many physical things and aided them in mental computations.

Answer 9

yeah i once asked my proffesor why dont we have a metric clock too.

but it has to do with mental math and what's easier for the masses.

it is easy to divide 360 by 2, 3, 4, 5, 6, 8,9, 10, 12, 15, 18,20, 24, 25, 27, 30, 36, and a whole lot more

while it is easy to divide 100 by some numbers, it is not easy to divde 100 by as many numbers as 360 is.

the iraquies (babylonians) knew this. go figure.

Answer 10

It is all to do with the way we record time - which is based on the old Babylonian system. They believed that the number 6 was very lucky, hence 24 hours, 60 minutes, 60 seconds etc