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Phantom Graph Trisectrix of Maclaurin

Phantom Graph Trisectrix of Maclaurin
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2018-07-20 07:38
FunctionCoordinate GeometryComplex Number
In collections Phantom Graphs
This example demonstrates the Phantom Graph Trisectrix of Maclaurin, a special curve constructed using complex roots and Cartesian curve equations. It utilizes commands like Plane, ComplexRoot, and CurveCartesian. Suitable for high school mathematics education, particularly in coordinate geometry and complex numbers.

GeoGebra Commands & Parameters

  1. Plane((0, c, 0), (1, c, 0), (0, c, 1)) → p
  2. ComplexRoot((c^(2) * (a + x)) - (x^(2) * ((3 * a) - x))) → z_1, z_2, z_3
  3. CurveCartesian(t, sqrt((((-12 * a) * t^(2)) + ((9 * a^(2)) * t) + (4 * t^(3))) / ((2 * a) - t)), sqrt(((-6 * a^(3)) * t) + ((3 * a^(2)) * t^(2)) + ((2 * a) * t^(3)) - t^(4)) / ((2 * a) - t), t, -25, 25) → b
  4. CurveCartesian(t, sqrt((((-12 * a) * t^(2)) + ((9 * a^(2)) * t) + (4 * t^(3))) / ((2 * a) - t)), ((-sqrt(((-6 * a^(3)) * t) + ((3 * a^(2)) * t^(2)) + ((2 * a) * t^(3)) - t^(4)))) / ((2 * a) - t), t, -25, 25) → e
  5. CurveCartesian(t, (-sqrt((((-12 * a) * t^(2)) + ((9 * a^(2)) * t) + (4 * t^(3))) / ((2 * a) - t))), ((-sqrt(((-6 * a^(3)) * t) + ((3 * a^(2)) * t^(2)) + ((2 * a) * t^(3)) - t^(4)))) / ((2 * a) - t), t, -25, 25) → f
  6. CurveCartesian(t, (-sqrt((((-12 * a) * t^(2)) + ((9 * a^(2)) * t) + (4 * t^(3))) / ((2 * a) - t))), sqrt(((-6 * a^(3)) * t) + ((3 * a^(2)) * t^(2)) + ((2 * a) * t^(3)) - t^(4)) / ((2 * a) - t), t, -25, 25) → h