I hear your point that phrasing in terms of angles may be more understandable. The x-axis in my plot shows the ratio of lengths of the longer to the shorter of

I hear your point that phrasing in terms of angles may be more understandable. The x-axis in my plot shows the ratio of lengths of the longer to the shorter of the two non-hypotenuse sides (yes, typing this out it does sound convoluted). This ratio is 1 when those two sides are equal length, which implies that the two corners are 45°. So the plot does show that the return to cutting corners is maximized at 45°-45°-90°, but indirectly. It's not an arbitrary decision that the graph only covers half the angle range. That's a consequence of the decision to label the shortest side "a" and the longer one (non-hypotenuse) "b". If those labels were applied to specific sides then you could explore the full angle range, but it would be redundant. I'm open to the idea that people might find this easier to understand though. I think the natural way to refer to the sides of a triangle is by their length, which lead to my formulation. If you feel like plotting your formulation, here's my source code (in R): https://gist.github.com/masonicboom/dafeb49b3c1d4c44998969ef6c2a2e05 https://gist.github.com/masonicboom/dafeb49b3c1d4c44998969ef.... Cheers!