

The perfect shape - joaquintides
http://bannalia.blogspot.com/2014/05/the-perfect-shape.html

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colanderman
Oh, I've heard this one before. Then the physicist fills a balloon with water
and sticks a straw in it, proclaiming it a dynamically optimal system (in the
absence of gravity); and finally the engineer sprays foam insulation on a
glass jar and calls it a day.

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getbreadbox
Yeah, these double walled cups work quite well:

[http://www.amazon.com/gp/aw/d/B004NBXR98/ref=mp_s_a_1_1?qid=...](http://www.amazon.com/gp/aw/d/B004NBXR98/ref=mp_s_a_1_1?qid=1400342097&sr=8-1&pi=SX200_QL40)

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jey
Awesome, but why a genetic algorithm? I wonder if it could be formulated as a
tractable optimization problem instead.

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gravity13
Or perhaps solved more _purely_ using Calculus of Variations.

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joaquintides
I've added a small postscript explaining why calculus of variations (in its
simplest form at least) is not applicable to this problem.

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colordrops
Interesting, this shape matches exactly the yogurt jars sold on the streets in
Beijing. They need to remain cool without refrigeration for long periods of
time.

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jameshart
Then they should be spherical; this shape's optimal only for a container which
is gradually emptying.

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dpiers
A liquid container designed to keep its contents cool as long as possible?
Sounds like a the job for a dewar flask. I've left drinks out in this
overnight and they were still cold in the morning:

[https://shop.funraniumlabs.com/products/665ml-fmj-
textured-v...](https://shop.funraniumlabs.com/products/665ml-fmj-textured-
variant-rugged-stein-of-science.html)

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natch
Perfect all depends on what you're optimizing for.

If you want a glass that doesn't tip over easily, this isn't so great.

Theory versus practice. The best entrepreneurs are able to see past the theory
and grapple with practical considerations.

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jameshart
Take this shape, minimize thermal conductivity to its surroundings but enable
it to stand safely on a flat surface, and what you have got is a _stemmed wine
glass_.

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dj-wonk
I may be reading this wrong, but I think this means that a shot glass is
mathematically perfect.

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nine_k
I'd notice that this must also describe the best shape of a glass to keep a
beverage _hot_. But, unlike shot glasses, tea and coffee cups look very
different.

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joaquintides
As you correctly point out the problem is entirely symmetrical to that of
keeping a hot beverage as hot as possible. If we take the different problem of
trying to cool a hot beverage, the optimum, pathological solution would be a
glass with 0 height and infinite width --studying this problem with the
additional constraint that width be limited to some predefined value might
make for an interesting followup article.

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Someone
I would add the constraint that the surface is convex, too. Without that, one
could build some 3D fractal, and get infinite area for any given volume.

Alternatively, complicate things by taking the width of the glass into account
or model convection more realistically (a square meter of glass close to other
glass of similar temperature will not lose much heat)

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Mathnerd314
So when is the kickstarter?

