What is the full range of values? I find it easiest to think in terms of an angle of one of the corners, so 0-90 in degrees. Note that the graph only covers half of that range, somewhat arbitrarily.

The important realisation that the ratio of cutting corners that is maximised at 45° is not shown by the graph, which is a shame.

You don't have to use trig to show that, but I think it helps.

Edit: as a side point, as I was thinking about this, I realised that you've discovered the maximum relative error of an L1 norm vs an L2 norm, which is fun