The problem is given in the picture attached. However we are given the equation of a 4 dimensional shape with certain choice given to explain the shape in that dimension.
Equations of different shape such as:
sphere: √(x^2+y^2+z^2) = r
Ellipse: (x-h)/a^2 + (y-k)/b^2 = K
Hyperbola: (x-h)/a^2 - (y-k)/b^2 = 1
The Attempt at a Solution
Well for question one and two, I said 1 ( which is w=x^2+y^2+z^2) is a "a collection of equally spaced concentric spheres" and 2 ( w=√(x^2+y^2+z^2) was "a collection of unequally spaced concentric spheres ".Though I know the difference between both is the radius where one is w and the other is √w. But why does have a radius of √w make the sphere unequally spaced?
My teacher barely touched the topic so I have a hard time figuring out how to visualize these shapes.