Re: [math-fun] Unconditionally stable nesting coffee cups?
On Mon, Nov 3, 2014 at 2:13 PM, Michael Greenwald <mbgreen@seas.upenn.edu> wrote: Must the base be larger than the top? Or would it suffice to have a small, very dense, heavy, weight located in the base (small = radius of the weight < radius of the base, heavy = comparably heavy to the weight of water when the cup is full)? Tungsten is pretty cheap and very dense, e.g. I got some 100g tungsten counterweights for $10 each. -- Mike Stay - metaweta@gmail.comhttp://www.cs.auckland.ac.nz/~mikehttp://reperiendi.wordpress.com Amazingly cheap, given it's non-abundance. "This guidance uses the lifting force experienced by the aeroshell to "fly out" any detected error in range and thereby arrive at the targeted landing site. In order for the aeroshell to have lift, its center of mass is offset from the axial centerline that results in an off-center trim angle in atmospheric flight. This is accomplished by a series of ejectable ballast masses consisting of two 75 kg (165 lb) tungsten <http://en.wikipedia.org/wiki/Tungsten> weights that were jettisoned minutes before atmospheric entry.[134] <http://en.wikipedia.org/wiki/Mars_Science_Laboratory#cite_note-spaceflightnow.com_1-134> " http://en.wikipedia.org/wiki/Mars_Science_Laboratory Compared to the transportation costs, I guess it might as well have been solid gold. Alan Adler bought some W for Euler disks. Disappointing. Fun to fondle, though. --rwg
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Bill Gosper