Parabola, Knot, Conchoid, and Line

Parabola, Knot, Conchoid, and Line
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2020-06-25 03:16
This example demonstrates the geometric relationships and interactive phenomena between a parabola, a knot, a conchoid, and a line. It involves core mathematical concepts such as the definition of a parabola, the parametric equations of a knot curve, the application of a directrix, and intersection calculations in analytical geometry. The construction highlights GeoGebra commands and objects like Line, Circle, Intersect, Point, and Locus. Suitable for high school and above students studying analytical geometry, parametric equations, and curve plotting, as well as for mathematical competitions or teaching demonstrations.

GeoGebra Commands & Parameters

  1. Line(O, xAxis) → f
  2. Circle(O, 1) → c
  3. Intersect(c, f) → B, C
  4. Point(c) → A
  5. Line(A, yAxis) → g
  6. Intersect(g, Segment[B, C]) → D
  7. Line(O, A) → h
  8. Circle(A, r_1) → d
  9. Intersect(d, h) → E, F
  10. Locus(F, A) → loc1
  11. Locus(E, A) → loc2
  12. Circle(A, r_2) → e
  13. Intersect(e, h) → G, H
  14. Locus(G, A) → loc3
  15. Locus(H, A) → loc4
  16. Circle(A, r_3) → k
  17. Intersect(k, h) → I, J
  18. Locus(J, A) → loc5
  19. Locus(I, A) → loc6