Hyperboloid of One Sheet: Equation x^2 + y^2 + 1

This is an equation of a 3D surface called a 'hyperboloid of one sheet'. It is a smooth, continuous surface that extends infinitely in all directions. The surface is shaped like a saddle, with two 'arms' that curve downward and away from each other, and a 'saddle point' in the middle where the surface is tangent to the xy-plane. The equation does not define any particular point on the surface, but rather describes the entire surface as a whole.