The perfect shape(bannalia.blogspot.com)

99 pointsby joaquintidesvor 12 Jahren21 comments

bannalia.blogspot.com

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

9 comments

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.

getbreadboxvor 12 Jahren

Yeah, these double walled cups work quite well:

http://www.amazon.com/gp/aw/d/B004NBXR98/ref=mp_s_a_1_1?qid=...

jeyvor 12 Jahren

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

gravity13vor 12 Jahren

Or perhaps solved more purely using Calculus of Variations.

joaquintidesvor 12 Jahren

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

foxliskvor 12 Jahren

that was my first thought too. we developers sometimes get so caught up in development weforget there's a whole world of other tools.

eltetovor 12 Jahren

I was thinking the same thing. It is a good exercise to test a genetic algorithm but a numerical solver could have been used as well.

[deleted]vor 12 Jahren

colordropsvor 12 Jahren

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.

jameshartvor 12 Jahren

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

dpiersvor 12 Jahren

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...

natchvor 12 Jahren

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.

jameshartvor 12 Jahren

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.

twicvor 12 Jahren

So put a stem on it:

http://www.nisbets.co.uk/Arcoroc-Excalibur-Grand-Cuvee-Glass...

dj-wonkvor 12 Jahren

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

nkozyravor 12 Jahren

I can only read this wrong because I found a shot glass "mathematically perfect" earlier this evening.

nine_kvor 12 Jahren

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.

joaquintidesvor 12 Jahren

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.

Someonevor 12 Jahren

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)

mahovor 12 Jahren

I guess that the ratio h_open/h_closed is much bigger for hot beverages, due to evaporative cooling. Of course, this would mean that the optimum shape is even thinner than those that were calculated.

But maybe the shape of tee-cups and coffee mugs is optimal, in its own way? I certainly appreciate that beverages that need quite high temperatures for brewing are cooled down quickly to a drinkable temperature.

[deleted]vor 12 Jahren

dj-wonkvor 12 Jahren

I think shot glasses are optimized to be put into various configurations, such as matrices and triangular matrices: http://www.likecool.com/Home/Accessories/Billiards%20Shot%20...

Mathnerd314vor 12 Jahren

So when is the kickstarter?

[deleted]vor 12 Jahren