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Cissoid of Diocles

Cissoid of Diocles
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2018-07-19 06:16
FunctionCoordinate GeometryGraphing
In collections Phantom Graphs
This example demonstrates the generation of the Cissoid of Diocles. It involves the concept of inverse proportion functions and polar coordinates. Using GeoGebra commands such as Plane, ComplexRoot, and CurveCartesian, the process of generating the curve can be visually illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw the Cissoid of Diocles, a curve defined by parametric equations, consisting of four symmetric branches: two upper and lower, and two left and right. The shape is based on a parameter a, with a reference plane in 3D space and key points derived from complex roots of a cubic equation. The curve exhibits a cusp and asymptote, resembling a leaf or teardrop. Generate the branches by varying parameter t from negative to positive, ensuring symmetry and continuity. This visualization is suitable for demonstrating inverse proportion functions and polar coordinates, with coordinate axes and grid for clarity.
The prompt above was compiled from the original drawing commands and is for reference only.