Math Photo: Paraboloid Gridlines
The frame of this stained-glass lampshade reminds me of the gridlines on a parameterization of a paraboloid. The function
transforms a rectangle in the uv-plane into a paraboloid in 3-dimensional space. The horizontal and vertical lines in the uv-plane become the half-parabolas and circles suggested by the lampshade.
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2 Comments
dansmath · May 23, 2014 at 5:20 pm
Cool lamp and good eye – I like grid lines.
But I think your params describe a cone;
You want a v^2 k not v k there. Carry on!
– Dan Bach the Math Jock
MrHonner · May 23, 2014 at 6:22 pm
Right you are–thanks for catching it. That’s what happens when you make late-night updates!