Unrelated but on the topic of squircles, an interesting factoid:

Among all squircles having arbitrary exponents (|x|^p + |y|^p = 1), PI (3.14159...) is the smallest value of ratio of circumference to diameter.

There is a paper on this with the pithy title "π is the Minimum Value for Pi": https://www.tandfonline.com/doi/abs/10.1080/07468342.2000.11...