User:Park ceol oung/sandbox

To do that, we define the sphereical coordinates inside the S. Assume 3 independent vectors which originate in the center of S. And in orthography and normalization, these vectors can make a rectangular coordinate system. And this 3 dimensional rectangular coordinate system can be translated into 3 dimensional sphereical coordinates. Now in these sphereical coordinates, we can define an angle. And within this angle, we can project a point from the center of S to ∂S, Then I can call the projected point as. And we will call this point as ‘a’. And I will call a point near ‘a’ which is on the ∂S as ‘b’. Then ‘b’ is on the surface. So to express ‘b’, I can use polar coordinates which originates at ‘a’. So ‘b’ is expressed as (w,L) where ‘L’ is a finite length from ‘a’ and ‘w’ is an angle which specifies a specific point within a distance ‘L’ from ‘a’. And to express ‘b’, we first define ‘a’ so ‘b’ is expressed as (,w,L) which is an sum of coordinates of and (w,L). Now we will show the 4 coordinates are indepandant.