(x/a)n + (y/b)n = 1
Click below to see one of the Associated curves.
|Definitions of the Associated curves||Evolute|
|Involute 1||Involute 2|
|Inverse curve wrt origin||Inverse wrt another circle|
|Pedal curve wrt origin||Pedal wrt another point|
|Negative pedal curve wrt origin||Negative pedal wrt another point|
|Caustic wrt horizontal rays||Caustic curve wrt another point|
The curve drawn above is the case n = 4. For even integers n the curve becomes closer to a rectangle as n increases. For odd integer values of n the curve looks like the even case in the positive quadrant but goes to infinity in both the second and fourth quadrants.
The case n = 2/3 is the Astroid, while the case n = 3 is the (so-called) Witch of Agnesi.
The case n = 5/2 has been associated with the Danish architect and poet Piet Hein (inventor of the Soma Cube) under the name of superellipse and have been used for a variety of purposes, including motorway bridges and other architectural applications.
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