Cartesian equation: (x/a)
+ (y/b) = 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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