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Animation 55: Parabola, Tangents, and Geometric Constructions in Motion

Animation 55: Parabola, Tangents, and Geometric Constructions in Motion
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2016-06-20 10:01
AngleTransformationSlider Animation
This GeoGebra example presents a composite animation involving a parabola, tangent lines, circles, angles, and various geometric transformations, demonstrating the dynamic interplay among geometric elements. The core mathematical concepts include properties of parabolas and their tangents, orthogonal lines, circles and arcs, vectors and dilations, as well as angle and distance measurements. The construction utilizes commands such as Line, Slope, PointIn, Parabola, OrthogonalLine, Point, Tangent, Intersect, Circle, Ray, Distance, Dilate, Vector, Segment, CircleSector, Angle, CircleArc, and Rotate, creating numerous objects labeled A through L and beyond, with sliders or animation driving parameter changes. This resource is suitable for high school and undergraduate students to explore analytic geometry, function graphs, and geometric transformations, and serves as a valuable tool for teachers designing dynamic lessons or mathematical experiments.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Slope(a) → b
  3. PointIn(d) → C
  4. Parabola(C, a) → e
  5. OrthogonalLine(C, a) → f
  6. Point(e) → D
  7. Tangent(D, e) → g,
  8. OrthogonalLine(C, f) → h
  9. Intersect(e, h, 1) → E
  10. Intersect(e, h, 2) → F
  11. Line(D, f) → i
  12. Circle(D, 1) → k
  13. Intersect(k, i, 2) → G
  14. Ray(D, G) → j
  15. OrthogonalLine(D, f) → l
  16. Intersect(f, l) → H
  17. Distance(C, D) → m
  18. Circle(D, (2 * m)) → p
  19. Intersect(p, j, 1) → I
  20. Dilate(C, If[0 < n ≤ 1, 1 - n, 0], D) → C'
  21. Vector(C, C') → u
  22. Dilate(D, If[1 < n ≤ 2, 2 - n, 0], I) → D'
  23. Vector(D, D') → v
  24. Distance(C, D) → o
  25. Circle(D, (0.3 * o)) → q
  26. Intersect(q, g, 2) → K
  27. Segment(C, D) → r
  28. Intersect(q, r, 1) → J
  29. CircleSector(D, J, K) → s
  30. Angle(J, D, K) → α
  31. CircleArc(D, J, K) → t
  32. Circle(D, J) → c_1
  33. Intersect(c_1, g, 1) → L
  34. CircleSector(D, L, J) → d_1
  35. CircleArc(D, L, J) → f_1
  36. Circle(D, C) → g_1
  37. Intersect(g_1, g, 1) → M
  38. Intersect(g_1, g) → N, O
  39. Vector(D, N) → w
  40. Vector(D, O) → u_1
  41. Intersect(a, f) → P
  42. Angle(B, P, C) → β
  43. Rotate(d_1, If[2 < n ≤ 3, ((n - 2) * α), α], D) → e_1
  44. Rotate(s, If[2 < n ≤ 3, ((-(n - 2)) * (180° - α)), (-(180° - α))], D) → s'