ATMNE18 Hotel Lighting: More GeoGebra Augmented Reality Demos

These 2 screencasts were taken inside the Crowne Plaza Hotel. This was the site of the 2018 Association of Mathematics Teachers of New England (ATMNE18) conference (Dec 6 - 7, 2018 in Warwick, Rhode Island, USA). [br][br]Note, [b]for the first screencast[/b], the [b][color=#1e84cc]blue surface[/color][/b] has equation [math]z=-1.4\cos\left(\sqrt{x^2+y^2}\right)[/math]. [br]Since the distance between any point ([i]x[/i], [i]y[/i]) in the coordinate plane (i.e. the plane z = 0) [br]and the origin = [math]\sqrt{x^2+y^2}[/math], the intersection of the [b][color=#1e84cc]blue surface [/color][/b]and any plane that contains the z-axis will be a cosine wave. (This is why it looks like a cosine wave in all directions!) [br][br][br]For the [b]second screencast [/b]and [b]third screencast[/b], how would you describe the 2 surfaces are used to model these light fixtures? How can we tell? [br][br]For the [b]third screencast[/b], how do the equations ensure these 2 surfaces don't overlap or leave any gaps (despite one that may seem to appear)?
First Screencast
Second Screencast
Third Screencast
Fourth Screecast

Information: ATMNE18 Hotel Lighting: More GeoGebra Augmented Reality Demos