Circle - 360 degrees. Why not 400?

Question

A circle having 360 degrees. Why not 400? So that each quarter will have 100 degrees ( as rounded to hundred ) 4 x 100 = 400. Why 4 x 90 = 360 only.

Answer 1

I think it's because 30 and 60 degree angles have special properties. With the 400 degree circle, those angles would be 33.3333333333333.......... and 66.666666666666666............. degrees respectively. That's just as much of a pain to work with, if not more. Good night!

Actually, I was just thinking . . . there are 400 gradians in a circle. Someone thought of that before. I just learned that actually . . . it was a random thought that crossed my mind as I was thinking about your question. I think gradians may have been briefly mentioned to me in high school trig but no one EVER made me do calculations with it as far as I remember. And I'm a senior math major. The fact that no one teaches that should tell us something . . . Good night!

Answer 2

Youre so right.

I dont know if anyone truly knows the etymology of the concept of 360° in a circle. It might have something to do with the fact that there are 365 days in our year... 360 just seems naturally close enough of an estimate. One might say that for each day of our year, the Earth moves one degree along its solar orbit... but technically that isnt true due to more specific astronomical facts.

Youre right that 360 is an odd-ball number to use for a circle. Some would argue that 2⋅π radians is more logical. Even though using 2π radians has its mathematically logical basis, it isnt inherently and instinctively more logical. 360 might be an odd-ball number... but so is the irrational number 2π.

All in all, grads (aka gradian) are more logical. An even 400 of those in a circle. Unfortunately, between the layman's insistence on the degree and the mathematicians insistence on the radian, there isnt much use for the grad... otherwise it probably would be more popular.

Answer 3

It came from the division of the night into 12 units due to the rising of astrological constellations. A new constellation rises about every 15 degrees. Then the daytime was added to make 24 hours. 24 x 30 = 360. Also the number system was base 60 because 60 has so many divisors: 1, 2, 3, 4, 5, 6, 10, 12,15, 20, 30, 60.

Answer 4

The division of numbers into 60 and multiples of 60 comes from the Babylonians. Nobody's 100% sure as to why, though one idea is that they used triangles and hexagons to measure certain things, and approximating the circle with a hexagon gives an easy way to divide angles into units of 360.

Answer 5

You can factorize both 360 and 400 to grasp answer to your own question!

360 has maximum equal split whole number divisions, which is a single reason for use of 360 digrees!

A publicly used knowledge need to be effective and simple to apply! It realises "usual mental number application" by all users of it

Answer 6

It originally comes from the design of a sundial. The sundial was numbered according to numbers that had many factors, such as 24 hours (2x12, 3x8, 4x6), and sixty minutes (2x30, 3x20, 4x15, 5x12, 6x10). The sundial is a complete circle, and there are 360 seconds if you go all the way around.

Answer 7

Ok real good answer here, but probably more than you want.
Rephrase that, a little bit more than I want, which is probably a lot more than you want.
http://mathforum.org/library/drmath/view/59075.html
I checked this sites sources, 100% verifiable
Hope this helps, Doug

Answer 8

Man, it's TOTALLY arbitrary. That's why I like radians...radians are logical...Use radians!!!!