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The function x²ⁿ + y²ⁿ = 1 is the unit-circle for n=1, but approaches the unit-square as n→∞pic.twitter.com/AVx8wt8XaY
Here's the proof. When n is large, then x²ⁿ≈0 and y²ⁿ≈0 for all |x|,|y|<1. So everything not strictly equal to 1 will get mapped to 0, as n→∞. Therefore the the limiting solutions to x²ⁿ + y²ⁿ = 1 are (±1,y) with |y|<1 (x, ±1) with |x|<1 QED
sorry! i didn't mean unit-square! just.. a square with area 4
Is there a relation to l_p norm?
This is the lp norm unit ball indeed. For p->0 the (non convex) balls shrinks toward two segments.
This is a beautiful riddle The two limits don't commute (the progression and the length integral)
THANKS BUT WILL IT HELP FIGHT THE ROBOTS
Squircle ;-)
Thinking about morphology: "cubphere" or even "hypercubpheres" or "cubhyperspheres" (ugly words;-)) x^(2n)+y^(2n)+z^(2n)=r^2 etc.
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