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Packing Geometric Shapes

erich-friedman.github.io

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Re: Packing Geometric Shapes

#3

Post by paulpauper »

It would seem like this can be done by solving various optimization formulas via plane geometry? The radicals arise from solving maximization polynomials assuming it's a constructable solution.

Re: Packing Geometric Shapes

#5

Post by martyvis »

activatedgeek wrote: post #4

What are some examples of efficient packing results that led to or inspired practical solutions?

One I can think of is circles-in-circles where you are bundling wires or optical fibre cores into cables. (And probably for tensile cables used in bridges and so on)

Re: Packing Geometric Shapes

#8

Post by whatever1 »

paulpauper wrote: post #3

It would seem like this can be done by solving various optimization formulas via plane geometry? The radicals arise from solving maximization polynomials assuming it's a constructable solution.

You are right there is a field of optimization dedicated to solving this problem to guaranteed optimality.

However, Multi dimensional bin packing problems are the some of the hardest non linear optimization problems.

Re: Packing Geometric Shapes

#9

Post by cycomanic »

activatedgeek wrote: post #4

What are some examples of efficient packing results that led to or inspired practical solutions?

Communications theory is largely about how to pack circles/spheres efficiently in multiple dimensions. So arguably pretty much all of the modern society is based on efficient packing.
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