I just looked up the coffee/theorems quote, and Wikiquotes says Bruce Schechter says that this joke originates with Alfréd Rényi <http://en.wikipedia.org/wiki/Alfr%C3%A9d_R%C3%A9nyi>. On Mon, Nov 3, 2014 at 5:13 PM, Michael Greenwald <mbgreen@seas.upenn.edu> wrote:
On 2014-11-03 13:40, Henry Baker wrote:
I don't know the answer to the following question, but it would be fun to come up with one.
"Mathematicians turn coffee into theorems." -- unknown ??
I drink a lot of coffee, but when I shuffle papers on my desk, the coffee cup turns over & spills coffee all over the papers.
Therefore, I'd love a cup design that is strongly resistant to turning over. This implies that the base should be larger than the top,
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)? Couldn't the exact weight and radius of the heavy weight could be computed to keep the center of gravity of a full cup over the base, as long as the cup were not tilted more than some angle theta? For example if the weight of the heavy weight were equal to 1/2 the liquid in the (full) cup, and the height of the cup were 4 times the radius, wouldn't the cup avoid tipping over as long as it wasn't tipped by more than 45 degrees? (Yes, I'm ignoring the fact that the water actually stays level w.r.t to the ground, and not w.r.t. the base of the cup, when it is tipped)
(I'm not sure I buy the real-world requirement that they nest (unless you're talking about disposable cups), but that's no reason to avoid adding this requirement to the problem).
and
that the center of gravity -- even when full of coffee -- is very low.
I also don't have a lot of room for storing coffee cups, so I'd still like them to _stack_ in such a way that they _nest_ & therefore don't occupy as much volume when stored.
Finally, being a human, I'd still like to have a handle through which a finger could fit. The handle needn't touch in two places, so topologically it could be simply-connected.
I envision some sort of "star-like" shape which will nest when the second cup is rotated 2pi/N.
Like I said, I don't have a candidate shape.
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