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Trefoil Knot Surface by Juan Carlos Ponce Campuzano

Trefoil Knot Surface by Juan Carlos Ponce Campuzano
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2018-03-05 12:27
Solid GeometryCalculusParametric Equation
This example demonstrates the construction of a trefoil knot surface. A trefoil knot is a fundamental concept in topology, representing a closed curve in three-dimensional space. Using parametric equations and derivatives, the surface of the trefoil knot is constructed. The example utilizes commands such as CurveCartesian, Derivative, and Surface, making it suitable for high school mathematics education and research.

GeoGebra Commands & Parameters

  1. CurveCartesian(fx(t), fy(t), fz(t), t, 0, (4 * π)) → f
  2. Derivative(fx) → dfx
  3. Derivative(fy) → dfy
  4. Derivative(fz) → dfz
  5. CurveCartesian(0, ((-dfx(t))) / sqrt((dfx(t) * dfx(t))), 0, t, 0, (4 * π)) → v1
  6. CurveCartesian((dfx(t) * dfz(t) / sqrt(((dfx(t) * dfz(t)))^(2) + ((dfx(t) * dfx(t)))^(2))), 0, ((-dfx(t)) * dfx(t) / sqrt(((dfx(t) * dfz(t)))^(2) + ((dfx(t) * dfx(t)))^(2))), t, 0, (4 * π)) → v2
  7. Surface(gx(t, theta), gy(t, theta), gz(t, theta), t, 0, (4 * π), theta, 0, (2 * π)) → knotS