Math Photo: Paraboloid Gridlines

Published by MrHonner on

The frame of this stained-glass lampshade reminds me of the gridlines on a parameterization of a paraboloid.  The function

r(u,v) = v cos(u) \textbf{i} + v sin(u) \textbf{j} + v^{2} \textbf{k}; 0 \le u \le 2\pi, 0 \le v \le 4

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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Categories: Photography


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!

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