Modifying a Torus (Multiple VS) in GeoGebra Augmented Reality

Here, we explore various ways of modifying the equation of a torus to get some interesting-looking surfaces. In the first screencast (V1), for which point (x,y) in the coordinate plane (i.e. in the plane z = 0) does the blue surface attain maximum value? How can we mathematically show this is true? Enjoy!

V1

V2

V3

V4

V5

V6: Special T/Y to Mathieu Blossier (who helped me with these surface EQ's)

V7

V8