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Folium of Descartes with Unit Tangent Vector

Folium of Descartes with Unit Tangent Vector
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2019-09-24 09:48
VectorCalculusParametric Equation
This example demonstrates the Folium of Descartes and its unit tangent vector. Using parametric equations, we can intuitively understand the geometric properties of the folium. Key mathematical concepts include parametric equations, vectors, and tangents. GeoGebra commands used include CurveCartesian, Vector, If, and Textfield. Suitable for high school mathematics education and learning about curve properties in calculus.

GeoGebra Commands & Parameters

  1. CurveCartesian(((((3 * a) * sin(t)) * cos(t)^(2))) / (sin(t)^(3) + cos(t)^(3)), ((((3 * a) * sin(t)^(2)) * cos(t))) / (sin(t)^(3) + cos(t)^(3)), t, 0, (2 * π)) → c
  2. Vector(P, P + c'(t) / abs(c'(t))) → u
  3. If(ttog ≟ 1, "Stop Animation", "Start Animation") → Animate
  4. Textfield(sp) → InputSpeed

AI Drawing Prompt Reference

Draw the Folium of Descartes and its unit tangent vector. Use parametric equations to represent the folium, then compute and unitize its tangent vector to draw the unit tangent vector. Finally, control the animation play and stop with a text field.
The prompt above was compiled from the original drawing commands and is for reference only.