Hm. Interesting. I would figure it out by cutting out some shapes and seeing how they fit together; it's certainly possible to do it that way.

If I went to math I would think of it as a problem of circumferences - what do I want the circumference of each level to be, and then how do I want each separate piece to look and how many do I want. Once you have cylinders (or angled cylinders) you've made (in your head) by joining your repetitive pieces together, then can't you join them at whatever angle you like, that's aesthetically pleasing? Or, if you like, at an angle determined by the circumference of the next level; any difference in circumference between the level above and the level below would require an angled level. I wouldn't think you'd have to figure out the angles to design it, rather that the design would determine the angles.

Well, I'm sure this is all obvious. Just interesting to me to think out loud about how to do it, since I am not the type to try to work out the math. I am an epidemiologist and do plenty of statistics, goodness it's a relief to do things with my hands instead of figuring them out with my head!

Figuring out is fun, though, huh. No matter how. I love it that your cat is named Protein. That is special.

have a good afternoon,
fruitbat

Well, it's definitely an issue of circumferences, to an extent. Each level would need to join to the level below it, obviously---but I think the question becomes how to angle the sides of an isoceles trapezoid so that, when you join them in a circle, the top of the circle and the bottom of the circle are the correct circumferences to match up to the rows above and below. The further away from vertical (like the bottom row) the pieces are, those pieces must be narrower at their tops.

Several of these trapezoids:

will fit together at their edges differently than several of these trapezoids:

... this is probably really easy, and I feel like a caveman trying to understand fire, but maybe if I talk it through (blog it through?) enough the answer will magically come to me.

Oh, and "Protein" is all Don's fault---she was his cat first. Her full name is Textured Cat Protein. I'd probably be surly too, if I were her :D

My son is marrying a gorgeous, artistic, mathematical genius, who also happens to be a great cook and an inspired writer.

We got that lamp at a craft show at Wheaton Plaza in the early '90's. I think Babybastard has the companion to it.

Wow, I didn't know Dan had a kickass new girlfriend... she sounds like someone I'd like to meet ;)

(lest someone decide I can't take a compliment: thank you!)

As with most math problems, its a matter of figuring out which parts of the equation you want to define, then figuring out the rest from there. For example, your graphics above are one of the first things you'll want to fix-what shape each piece will be. You'll probably then want to figure out how long you want each piece to be. Once you have the definite shape for each piece, the rest is fairly easy, especially if you cut the pieces out first and play with them as Fruitbat suggests. :)

I would say start with the pattern you like on a 2d pitch like your trapazoid pieces above and then consider the z axis pitch and bend.

OR just messure all the ones on that lamp and take it from there, not as fun I'd gather though.

Michelle,

Check out this url for a good description on how to design a multi-layered lamp shade of any number of sides. No math or tables required, just careful drawing. The example shows a three layer nine sided lamp.

http://www.karal.com/glass/lampshade-design/stained-glass-lamp-designer.html

Cheers, Bruce.

Wow. That's totally perfect, and there's a ton of other interesting glass stuff on that site. The writing is fun too... from the Techniques page: "If you are not orgasmic with your line drawing don't expect to be blissed out by the coming of your projects completion!"

Bruce, it's always a happy day when you stop by with one of your tips. Thanks ;D

Found a post today on rec.crafts.glass regarding lamp design. Similar to the karal.com site except moreso, it's written by someone who seems very good at what he does, but less good at explaining it in print. Still worth a link for the sake of future reference, though:

"Pi x diameter you desire divide by panels SIMPLE, yes?"

and from the same gentleman:

"Rough rule of thumb (and the rest of the fingers) is if I have to make more than 5 of the same accurate straight line pieces, I set up a jig."

I oft find that dancing a little jig makes everything go better!

More useful lampshade design links:

Dale Grundon's site provides some useful tools. One is a spreadsheet that will help you calculate dimensions for basic flat-panel lamps. Another is a full-fledged design program called TierMaker which aids in the design of tiered lamps, like the one I have been puzzling about, and which looks very useful:

And there's some serious lampshade math going on at this site, though it appears to directly address only the design of flat panel lamps, not tiered ones.

I am also uncovering references to angled grinding of lamp tile edges using a specialty lamp bit... but there's some question as to whether angle grinding is necessary or even desirable, so I'm just going to pretend I didn't see anything on that topic for right now.