I have a rather old lamp with a plain conical shade that has fallen apart and two thoughts occurred to me: I could make one of those, and if it's a cone, I could use a conical map projection to decorate it.

So I measured it, and started playing with the idea in Geogebra.

The angles on the right are the standard parallels for an equidistant conic projection. The angles on the left are the parallels where the top and bottom of the shade would be.

Initially I had used the top and bottom of the lamp shade as the standard parallels, but then I realized I could reduce the distortion by moving the standard parallels in a bit. Hence the points F and G. I then tweaked them to get the distance between the projection surface and the sphere about equal at the top, bottom, and middle.

So now I just need to decide if I want to use some real world data or a made up world, and make a map out of it using this projection.

2. Neat! I have seen commercial lampshades done with an older, "Age of discovery"-style map, but had never thought of doing something like that myself.

3. Originally Posted by junius_gallio
Neat! I have seen commercial lampshades done with an older, "Age of discovery"-style map, but had never thought of doing something like that myself.
Yes, though I doubt they would have gone to the trouble of projecting the map onto a surface the same shape as the lamp shade. I readily admit that it's stupendously geeky and obsessive.

4. Maybe so, but I think it's worth doing.

photos!!!

5. Originally Posted by Hai-Etlik
Yes, though I doubt they would have gone to the trouble of projecting the map onto a surface the same shape as the lamp shade. I readily admit that it's stupendously geeky and obsessive.
Oh, no--these weren't projected--when you saw the seam, it was quite obvious that they had cut the shades from material where the map was simply printed as a flat map on a flat sheet. These "lampshade projections" are just too cool!

I second Coyotemax--pics when finished!

6. Crap, I just realized I screwed up. The slant length of the projected cone would be the length of the arc, not the segment. This is going to be a bit more complex.

7. This sounds fun.

8. Originally Posted by dangerdog15
This sounds fun.
Not so fun after a few hours of trying to solve it.

9. OK, I'm pretty sure I've got it this time.

I ended up cheating a bit. I constructed H' such that arc HH' would be the correct length sₒ given any particular H and I, and then adjusted I until H was at the right distance from the y axis.

10. I've decided to do a map of Earth in the style of my Baakoi map. I'm currently putting together some data from free sources in QGIS, then I'll export to SVG and load into Inkscape for styling.

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