Then you must be completely misunderstanding everything because any text I have ever seen defined spherical coordinates using .
So what formulas does your text use to define "polar" and "spherical" coordinates? (The two you post are for spherical coordinates but since there are three coordinates, you should have three formulas, not 2.)
Since linalg123 hasn't got back to us, I will continue myself.
Every Calculus text I have ever seen has defined "polar coordinates" with the formulas
amd
Strictly speaking, "polar coordinates" is defined only in two dimensions but and immediate extension is "cylindrical coordinates" using 'z' as the third variable,
Spherical coordinates are defined by the formulas
It is then easy to see that, in cylindrical coordinates, so that becomes
And in spherical coordinates,
So in spherical coordinates becomes [tex]\rho^2= 2[/itex] or, since , the distance from the origin to the point, is never negative,
.