Kampyle of Eudoxus is a family of curves studied by the Greek mathematician Eudoxus in relation to doubling the cube; Eudoxus, a student of Plato, was famous for finding formulas for measuring cones, and cylinders, and pyramids . He also constructed the first mathematical model of the universe .
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.
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