New posts in Implicit Function

Explaining the graph of $\sin(x^2) + \sin(y^2) = 1$

plot of $\sin(x) + \sin(y)= \cos(x) + \cos(y)$

Can someone help explain the behaviour of the implicit equation $x^n+y^n-n^x-n^y=0$, specifically the significance of the number 1.9667894071088...?