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Parabolic Waves

Parabolic Waves
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2018-06-23 12:41
FunctionCalculusTransformationGeometric ConstructionSlider Animation
In collections surface 3D /3D-Oberflächen 1
This example demonstrates the generation of parabolic waves. Key mathematical concepts include parabolas, geometric transformations, and integrals. Using GeoGebra commands such as Point, Parabola, Tangent, and Mirror, the example dynamically illustrates the properties of parabolas and their application in wave patterns. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. OrthogonalLine(A, xAxis) → f
  3. Parabola(F, f) → c
  4. Point(c) → S
  5. Tangent(S, c) → g,
  6. Mirror(K_s, g) → G_s
  7. Circle(F, K_s) → d
  8. OrthogonalLine(G_s, xAxis) → h
  9. Sequence((2 * fractionalPart(τ + k / Anzahl)), k, 0, (2 * Anzahl)) → Listτk
  10. Zip(((u * x(A)), 0), u, Listτk) → ListKPkte
  11. Zip(Circle[F, P], P, ListKPkte) → ListKreise
  12. Zip(Mirror[P, g], P, ListKPkte) → ListGPkte
  13. Line(A, F) → i
  14. Zip(OrthogonalLine[P, i], P, ListGPkte) → ListGeraden
  15. Intersect(d, h) → B, C
  16. Point(d) → D
  17. Segment(C, B) → j
  18. CircumcircleArc(B, D, C) → p
  19. Line(F, A) → l
  20. IntegralBetween(sqrt(((2 * abs(x(A))) * (x - x(S)))), (-sqrt(((2 * abs(x(A))) * (x - x(S))))), x(S), 10, false) → a

AI Drawing Prompt Reference

Draw a parabolic wave pattern, demonstrating parabolas, geometric transformations, and integrals. Start by sketching a parabola, then apply transformations to create reflections and tangents. Use a slider to generate a series of circles and points, and reflect these, along with drawing related lines and arcs, to complete the wave effect.
The prompt above was compiled from the original drawing commands and is for reference only.