I plotted $z = x^2+y^2$ and got this shape. Is there a name for this shape?
How about $z \ge x^2 + y^2$ ?
[Math] the name of this 3D shape
geometry
geometry
I plotted $z = x^2+y^2$ and got this shape. Is there a name for this shape?
How about $z \ge x^2 + y^2$ ?
Best Answer
The surface is a "circular paraboloid" (a special case of the "elliptic paraboloid"). Slices by planes perpendicular to the $z$ axis are (concentric) circles, while slices by planes parallel to the $z$ axis are (identical) parabolas.
It's an example of a surface of revolution, in this case obtained by revolving the basic parabola shape (think $y = x^2$) about its axis.
The filled counterpart would simply be a "solid circular paraboloid".