How to limit aspect ratio of web player in Facebook integrated canvas

I am trying out my Webplayer based game in Facebook’s new integrated canvas- right now it is set up to fill the entire window and scale automatically. Which is working nicely, but…

My game is only designed to be viewed in landscape mode, in the 4/3 - 16/9 range.
The space it’s in is usually about square by default (because of the sidebar) and can be resized so it’s taller than wide.

What I want to happen is if you resize the window so that the canvas width is less than 4/3 of the canvas height, it clamps the player height to 3/4 of the player width, and if you resize it so the window height is less than 9/16 of the width, it clamps the player width to 16/9 of the player height.

This should be a common thing for people to want to do with their Unity web game but as usual
I could find nothing useful in the Facebook developer documentation, and figuring out how to make anything Facebook SDK related work right on my own is always a massive headache, so I’m asking about it here.

I had the exact same question as you and this was the first place that I landed. After some addition searching, I found the perfect solution here: