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Deltoid Constellation Oscillation

Deltoid Constellation Oscillation
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2016-05-11 17:03
TrigonometryParametric EquationLocus
This example demonstrates the generation process of a deltoid. Key mathematical concepts include parametric equations and trigonometry. Using GeoGebra commands such as Point, Intersect, Circle, Line, OrthogonalLine, Locus, and Mirror, the trajectory of the deltoid can be constructed. Suitable for high school mathematics education and students learning parametric equations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → O
  3. Circle(O, B) → c
  4. Point(c) → J
  5. Line(O, J) → a
  6. Circle(O, C) → d
  7. Circle(B, J) → e
  8. Intersect(c, e, 2) → D
  9. Circle(D, B) → f
  10. Intersect(c, f, 2) → E
  11. Line(O, E) → b
  12. Line(J, E) → g
  13. Intersect(d, b, 2) → A
  14. Intersect(d, b, 1) → G
  15. OrthogonalLine(G, g) → h
  16. Intersect(g, h) → P
  17. Locus(P, J) → loc1
  18. Circle(O, F) → k
  19. Intersect(k, a, 2) → H
  20. Mirror(P, H) → Q
  21. Line(O, Q) → i
  22. Intersect(g, i) → I
  23. Locus(I, J) → loc2
  24. Circle(A, G) → p
  25. Circle(H, J) → q
  26. Line(H, P) → j
  27. Line(A, P) → l

AI Drawing Prompt Reference

Draw a deltoid by first taking a point B on the x-axis, then drawing circle c with O and B as centers. Take point J on c, and draw line a through O and J. Draw circle d with O and C, and circle e with B and J. The second intersection of e and c is D. Draw circle f with D and B, and the second intersection of f and c is E. Draw line b through O and E, and line g through J and E. The second intersection of g and b is P, and the locus of P is loc1. Draw circle k with O and F, and the second intersection of k and a is H. The mirror image of P with respect to H is Q. Draw line i through O and Q, and the intersection of i and g is I, with the locus of I as loc2. Finally, draw circle p with A and G, and circle q with H and J. The intersection of q and p is P, and draw lines j through H and P, and l through A and P.
The prompt above was compiled from the original drawing commands and is for reference only.