Shape of Universe?Geometry Level 3
Suppose that the universe had a beginning in the Big Bang, and currently is expanding. For example, suppose that the universe is in the form of an elliptical paraboloid \(z = x^2 + y^2\) where \((x,y,z) = (0,0,0)\) represents the Big Bang... The question is:
What is the plane tangent to the elliptic paraboloid \(z = x^2 + y^2\) at the point \((x,y,z) = (1,2,5)\)?