Lets say you have a rectangular prism.

Model: LxWxH: 192 x 210 x 212

various rectangular prisms L,W,H

186,205,204

186,206,205

188,210,206

191,209,210

188,208,209

185,207,208

197,204,207

199,211,214

210,192,212 (should be farthest from a match)

384,420,424 (should be perfect match)

How would you pick the one that most closely matches the proportions of the original shape? scale does not matter, only proportions

In the above data set I added one with the same dimensions but in a different order, also a couple where the width is greater than the height.

The solving method should show those value as the least similar.

I also added one that has the exact same dimensions as the original only doubled, it should return the closest match.(perfet match, although there wont usually be a perfect match)

when its two dimensions its much simpler, you could just divide the length/width and pick which ever number is closest to the result of the original model.

I dont need a solution, these numbers are just examples, I am just wanting to know what equation you would use to solve this type of problem.

I am working on a software project where I will need to do a lot of work comparing the difference between sets of numbers.