Point in a circle

What do you notice? [ignore rounding error in the sum of the areas] Any conjecture(s) ? Proof(s) ? Can the diagonals of the four squares form a quadrilateral? If yes, does the order of the colored diagonals matter? Why or why not? Under what circumstances can the diagonals of the four squares not form a quadrilateral? Can you envision a 'point in a sphere' determining 8 cubes ? Can you imagine a possible relationship between the sum of the volumes of the cubes and the volume of the sphere ? How about a point in a 4D sphere? What questions could / would you put to your students based on this applet ?
This applet was inspired by Juan Carlos Ponce Campuzano