Equation of Sphere/Rectangular Coordinates/Corollary

Theorem
The equation of a sphere with radius $R$ whose center is at the origin expressed in Cartesian coordinates is:


 * $x^2 + y^2 + z^2 = R^2$

Proof
From Equation of Sphere, the equation of a sphere with radius $R$ and center $\left({a, b, c}\right)$ expressed in Cartesian coordinates is:


 * $\paren {x - a}^2 + \paren {y - b}^2 + \paren {z - c}^2 = R^2$

Setting $a = b = c = 0$ yields the result.