On any sphere. w/ 360 degrees per each circumference solve for x the total of one degree points, regardless of volume, on each and every sperical surface

Question

 I take a golf ball.  I design it with exactly one dimple per degree of any proposed circumference.  Many of the

various circumferences intersect, which means subtracting 2 degrees from all but the first circumference.  With

my question I'm inserting a condition that every dimple is exactly one degree from every other dimple.  

 

I've searched this question online and am thwarted by not being able to pose it in a manner that a search

will solve it.

 

Any sphere, no matter whether the radius is one inch or one mile will have, as a math truth, exactly 360 degrees

on any circumference.  The distance between the points that represent the degrees points may be micro inches or

acres, but 360 is the max. 

 

Now this given, how many of these points, these acres for instance, are there on any and every sphere?

 

And why can't I find this one and only answer online.

I think it is 360 x 358 = 128,880

Answer 1

Consider a sphere and a Great Circle that create two hemispheres.  Around this circle circle would be 360 dimples.

Suppose this is similar to the Earth and this is the equator.  Do not count these points.

 

For each of these points on the equator, consider the great circle that goes from the equator through the poles, i.e. the North and South poles.  The poles would be on all these circles.  For each of these circles there are 178 dimples on the hemisphere from N to S.  A hemisphere is considered because there would no duplicated dimples. Since there are 360 points on the equator, then each of these has 178 dimples, which would be 360*178 dimples.  Add to this the two dimples for the poles.  Then the total number of dimples would be 360*178 + 2 = 64082