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The word kamplye (pronounced with three syllables) comes from the Greek word for “crooked staff” .
The general formula for kampyle of Eudoxus is:
a2x4 = b4(x2 + y2)
- a and b are nonzero constants,
- (x, y) ≠ (0, 0). In other words, the origin is excluded as a solution to the equation.
This is an open curve that never closes or completes. It is an increasing curve—single, non-repeating curvature .
Derivative of Kampyle of Eudoxus
Geometry of Kampyle of Eudoxus
- The two intercepts are: (0, a, 0), (π, -a, 0).
- The minimum is at (0, a, 0).
- The maximum is at (π, -a, 0).
- There are four points of inflection: (tan-1 ± (√2)/2, ± a(√6)/2, a(√3)/2 .
 Fifty Famous Curves, Lots of Calculus Questions, And a Few Answers.
 Tan, S. (2020). Handbook of Famous Plane Curves Using Mathematica.
 Schwartzman, S. (1994). The Words of Mathematics. An Etymological Dictionary of Mathematical Terms Used in English. Mathematical Association of America.
 Krawczyk, R. Seashell Interpretation in Architectural Forms.
 Lawrence, J. (2013). A Catalog of Special Plane Curves. Dover Publications.
Stephanie Glen. "Kampyle of Eudoxus" From CalculusHowTo.com: Calculus for the rest of us! https://www.calculushowto.com/kampyle-of-eudoxus/
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