# Determine if an aspect ratio is closer to 16:9 or 4:3

I have a number of various different aspect ratios that I would like to categorize into two groups. One group that is closer to 4:3 aspect ratio and another group that is closer to 16:9. Essentially, it's a matter of if ... then 16:9, else 4:3.

Any help would be greatly appreciated. Thanks!

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The question presumably has to do with where the "break point" should be. My choice of break point would be the geometric mean of the two aspect ratios, where the geometric mean of $a$ and $b$ is $\sqrt{ab}$. Thus the break point is at about $1.5396$ to $1$. Another natural candidate is the arithmetic mean $(a+b)/2$, which here is about $1.5556$ to $1$.
Compare your given aspect ratios $u:v$ as $u/v$ to $16/9$ and $4/3$. Pick the closest.