As one simple refutation of H.Baker's asteroidal magic mirror mutterings, it was once proposed you could just put a blob of liquid in space, it'd form a perfect sphere to minimize its surface energy; freeze it, and lo and behold, far superior ball bearings. This project was used as PR hype to "justify" the space program. Actually, they then tried that using the super silly space station or space shuttle (don't get me started on how stupid those things are/were -- as somebody recently pointed out, it is quite annoying being surrounded by everybody who is stupider than I am... which was an exaggeration, I am not actually always smarter than everybody else... but I can tell you that nevertheless this phenomenon in fact does happen in too many cases, and it is indeed very annoying to me that a hell of a lot of people are indeed stupid, with the designers of the USA space program being just one, and that is not anywhere near the "best" such example)... with the conclusion: this is an incredibly expensive way to manufacture incredibly low-quality ball bearings. But anyhow. Ignoring the practical, there are interesting and fun math questions here. Q1. ROTATING blob of fluid in space. Minimizes surface energy. Neglect gravity. What shape do we get? Kind of a spinning version of the Ancient Greek isoperimetric problem. Q2. Let's get electric and magnetic forces involved. Charge the fluid. Now there is electrostatic energy as well as centrifugal and surface tension effects. Q3. And... put it in a magnetic field. Now what? In principle these should form perfectly mathematically-defined blob shapes. What shapes? In practice as NASA found out, there are some severe problems if you actually try this, which your solutions will blissfully ignore. A related problem is, a liquid drop sits on a table. What is its shape? (Min: surface energy + grav'l energy.) This has been solved, and the solution is in principle very useful, because if you actually built a tank out of uniform thickness sheet metal, with that shape, it would be the "optimum" shape of a tank for storing liquid in. "Optimum" meaning: uniform-stress, stores the most liquid with the least sheet metal. In practice it's hard to manufacture so I think this idea never caught on. Similarly the answer to Q1 would be the optimum sheet-metal tank for storing liquid when spinning in zero-grav situation. Yet another question is the shape of fluid self-gravitating blob (constant density fluid) now neglect surface energy. This question was the subject of some brilliant investigations over 100 years ago, which successfully found answers. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)