ATMNE18 Hotel Lighting: More GeoGebra Augmented Reality Demos

Topic:
Cone, Cosine
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). Note, for the first screencast, the blue surface has equation . Since the distance between any point (x, y) in the coordinate plane (i.e. the plane z = 0) and the origin = , the intersection of the blue surface 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!) For the second screencast and third screencast, how would you describe the 2 surfaces are used to model these light fixtures? How can we tell? For the third screencast, 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