Advanced Search

Question: Squircle areas: why does int give so lousy values?

Question:Squircle areas: why does int give so lousy values?

mmcdara 7816 Maple 2015
March 29 2025
2

( squircle is the humoristic name for the 2D open ball of center 0 and radius 1 in Ln norm ).
The equation of the squircle in Ln norm writes  |x|n+|y|n = 1

The attached file gives the exact values of the areas of squircles in norms L2, L4, L100, L1. 
Unless for n=2 the results are dramatically poor (evalf/Int gives the same wrong results).

The function a(n) gives the exact expression of the squircle area in  Ln norm.

squircle.mw
Please Wait...