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Given two rectangles, and a maximum difference score, tell me whether the aspect ratio of these rectangles are considered similar or not?

For example a $2\times4$ rectangle [ratio $0.5$] and a $2\times3$ [ratio $0.66$] are considered similar, meaning that the difference of $0.16$ is still considered similar.

Also a $4\times2$ rectangle [ratio $2$] and a $3\times2$ rectangle [ratio $1.5$] are both considered similar and the difference is $0.5$ which is much larger than $0.16$ and yet is considered similar.

Another example of a $3\times2.9$ rectangle and a $2.8\times3.1$ rectangle are also considered similar.

How can one give one formula for calculating such a thing?

Further clarification

Let us represent a completely identical ratio with a score of $0$, meaning that there is no change between them

Let's represent a completely different ratio with a score of $1$

Let's say that the largest rectangle can be up to $1000$ width or up to $1000$ height

Example of the same ratio: $2\times3$ rectangle and $4\times6$ rectangle and the like

An example of a completely different ratio: a $1\times1000$ rectangle and a $1000\times1$ rectangle

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There is no mathematical definition for the similarity of aspect ratios. You might consider the ratio of the aspect ratios as a measure of aspect ratio similarity. The closer to $1$ the more similar.

You could then choose a cutoff point for "similar enough", depending on your application.

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  • $\begingroup$ Are you actually saying there is no solution? I could not understand, please explain more. $\endgroup$ – google dev Sep 24 at 5:44
  • $\begingroup$ There is no mathematical definition (I know of) that describes how similar two rectangles with different aspect ratios are. If you need such a measurement in your application you have to invent one. My answer has a suggestion. $\endgroup$ – Ethan Bolker Sep 24 at 11:10

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