What kind of equations can be solved simply by using things in nature? Letting the physics do the solving, so to speak. My question is not very thought out at the moment, but perhaps there are some examples where one has gleaned on the solution's manifestation in nature before in math? I am thinking of a science program I saw a decade ago or so where the architect used soap bubbles to try to minimize the area between the main structure. Perhaps crystals or similar things can be used to get voronoi diagrams. Things like that. Do you have any examples?
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The origins of the field of Calculus of variations came from nature.
One of the first problems posted was the Brachistochrone problem. This asks what the time minimizing path between two points A and B are where an object is traveling under only the force of gravity.
The calculus of variations also can be used to find the time/energy minimizing curves in other scenarios. For example the catenary problem. When you hang a cord between two points what is the shape of that curve.
Zaros
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But how can you use nature to solve the Brachistochrone problem? – TonyK Dec 10 '16 at 01:27
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@TonyK That's a good point. I don't know of a time where the brachistrone problem is solved in nature. There is probably an analog somewhere but I can't come up with one off the top of my head. The catenary does come up though. – Zaros Dec 10 '16 at 02:05
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Yes, catenaries are everywhere. But I doubt that cycloids can be found in nature. – TonyK Dec 10 '16 at 02:10
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They're found in nature just not in the manner in which they appear in the brachistrone problem. It wasn't the best example but it's historically important. – Zaros Dec 10 '16 at 02:22
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Where are cycloids found in nature? Bearing in mind that nature never got around to inventing the wheel. – TonyK Dec 10 '16 at 02:29
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Things roll. There are a ton of roughly circular things that roll. – Zaros Dec 10 '16 at 03:27