Equation of Sphere/Rectangular Coordinates/Corollary
< Equation of Sphere | Rectangular Coordinates(Redirected from Equation of Sphere/Corollary)
Jump to navigation
Jump to search
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 in Rectangular Coordinates, the equation of a sphere with radius $R$ and center $\tuple {a, b, c}$ 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.
$\blacksquare$
Sources
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Descartes