Hypocycloid

Vector-Fields

Changing Coordinates

Generalize to S^2 to R^3

Steeographic projection drom s1 to R

Standart Defintion of Sphere Volume

V=4/3 pier^3
delta V is Approximation pie y^2 deltav


Volume approximation is Summation in r pie y^2 delta x
V=integral from r0 to r pie y^2 dy where r^2=x^2+y^2
V=integral -r tor pie(r^2-x^2) dx

V= pie [r^2+x^3/3] between -r to r

the volume in spherical coordinates dv= r^2 sin(theta) dr d(theta) d(phie)

the volume in general is 52.4% or pie/6 approximation 0.5236