Vi, you say that "someone just *decided* to make 360degrees in the circle" but while i agree with the relative arbitrarity of 360, you neglect to mention the cool fact that the sum of the digits of the degrees of any nth bisection of a circle gives you a multiple of 9.

n=0: 360deg: 3+6+0=9

n=1: 180deg: 1+8+0=9

n=2: 90deg: 9+0=9

n=3: 45deg: 4+5=9

n=4: 22.5deg: 2+2+5=9

n=5: 11.25deg: 1+1+2+5=9

n=6: 5.5125deg: 5+5+1+2+5=18

n=7: 2.75625deg: 2+7+5+6+2+5=27

n=8: 1.378125deg: 1+3+7+8+1+2+5=27

n=9: 0.6890625deg: 0+6+8+9+0+6+2+5=36

n=10: 0.34453125deg: 0+3+4+4+5+3+1+2+5=27

n=11: 0.172265625deg: 0+1+7+2+2+6+5+6+2+5=36

n=12: 0.0861328125deg: 0+0+8+6+1+3+2+8+1+2+5=36

I find the pattern of the multiples interesting:

1,1,1,1,1,1,2,3,3,4,3,4,4,....

it isn't in the oeis...