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Conic Section Simulation

Conic Section Simulation
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2017-08-28 00:08
CircleFunctionCoordinate Geometry
This example demonstrates the generation process of conic sections. Key mathematical concepts include the definition, equations, and properties of conic sections. Using GeoGebra commands such as InfiniteCone, Rotate, Intersect, etc., the dynamic generation of circles, ellipses, hyperbolas, and parabolas can be shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. InfiniteCone((0, 0, 3), Vector[(0, 0, 0), (0, 0, 1)], π / 6) → a
  2. Point(f) → A
  3. Line(A, g) → h
  4. Point(f) → B
  5. Rotate(B, 30°, A) → B'
  6. Angle(B, A, B') → α
  7. Line(B, h) → i
  8. Line(A, B') → j
  9. Intersect(i, j) → C
  10. Mirror(C, B) → C'
  11. Mirror(C, A) → C'_1
  12. Mirror(C', A) → C''
  13. Polygon(A, C'_1, C'') → 다각형1, c'', a_1, c'_1
  14. Polygon(A, C', C) → 다각형2, c, a_2, c'
  15. Angle(C, C', A) → β
  16. Rotate(C, Slope, B) → C'_2
  17. Line(B, C'_2) → k
  18. Angle(C, B, C'_2) → δ
  19. IntersectPath(xOyPlane, a) → d
  20. Intersect(f, yAxis) → D
  21. Intersect(g, d) → E, F
  22. Intersect(f, d) → G, H
  23. Semicircle(E, F, b) → e
  24. Midpoint(E, F) → I
  25. Rotate(F, π / 2 - Slope, f) → F'
  26. Vector(I, F') → u
  27. OrthogonalPlane(I, u) → l
  28. IntersectPath(l, a) → p
  29. Angle(A, C, C') → ε
  30. Angle(C'_2, B, C') → θ
  31. Line((0, 0, 0), (0, 0, 1)) → m
  32. IntersectPath(l, a) → q
  33. IntersectPath(l, a) → r
  34. IntersectPath(l, a) → s
  35. IntersectPath(n, l) → t
  36. IntersectPath(n, a) → c_1
  37. Point(c'') → J
  38. Line(J, c'_1) → f_1
  39. IntersectPath(l, a) → d_1