Thank you for trying to explain it to me. I guess I should say I don't understand how the theoretical meets the practical here. Then again, I'm just a web programmer.
The theoretical. Sure, I read the article about a circle and trying to find the better, smaller circle within it, and I can imagine slicing into the circle to find it. No problem there.
The practical. Also, I noticed how they started off with real-world problems like designing the thinnest, most durable smartphone with the longest battery life.
But I don't see how designing a smartphone has anything to do with a circle, or a circle within a circle, or slicing the larger circle to find the smaller one. If I want to design a smartphone that's thin, then I will seek the thinnest of each of: battery, processor, etc....
Oh, I get it. The thinner I make the phone, the smaller the battery. The larger the battery, the thicker the smartphone. Likewise, thickness and durability are related. I guess I forgot that they have very complex formulae figured out to tell them ahead of time exactly how durable a material will be at a given thickness and a given shape, exactly how much charge a battery of a given size holds, exactly how much charge a given component will consume, etc. So they have all these number floating around, and normally they try different combinations to arrive at the best compromise. Or they have some formulae for doing some of the recombinations for them, but they're slow. And these researchers say that they have found a way to speed that last part up.
I guess industrial designers are a lot further along than I normally imagine them. Normally I imagine them just trying different stuff, sketching it out until looks nice (first on paper napkins, then in 3-D computer programs); then trying different materials; then trying the materials at different thicknesses (or going by past experience, learning that, say, 3mm of magnesium is ideal at this particular point).