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Phantom Graph of Kampyle of Eudoxus

Phantom Graph of Kampyle of Eudoxus
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2018-07-21 10:28
FunctionCoordinate GeometryParametric Equation
In collections Phantom Graphs
This example demonstrates the construction of the Phantom Graph of Kampyle of Eudoxus, a special type of parametric curve. It uses the combination of complex roots and Cartesian curve equations. The commands used include Plane, ComplexRoot, and CurveCartesian. Suitable for high school mathematics education, particularly in coordinate geometry and parametric equations.

GeoGebra Commands & Parameters

  1. Plane((0, c, 0), (1, c, 0), (0, c, 1)) → p
  2. ComplexRoot((a^(2) * x^(4)) - (b^(4) * (x^(2) + c^(2)))) → z_1, z_2, z_3, z_4
  3. CurveCartesian(0, (t * sqrt((a^(2) * t^(2)) + b^(4)) / b), t, t, -25, 25) → e
  4. CurveCartesian(0, ((-t) * sqrt((a^(2) * t^(2)) + b^(4)) / b), t, t, -25, 25) → f