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Animation Demonstrating Circumcircle and Similarity Transformation

Animation Demonstrating Circumcircle and Similarity Transformation
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2017-06-07 08:19
CircleCalculusTransformationGeometric Construction
This example animates the circumcircle of a general quadrilateral and its similarity transformation. Key math concepts include circumcircle, similarity transformation, indefinite integral, and continuity. Construction highlights involve commands like Rotate, Segment, Circle, Intersect, and Dilate. Suitable for high school and above, aiding in understanding geometric transformations and calculus concepts.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(A, B) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(C, A) → h
  7. Rotate(A, α / 2, B) → A'_1
  8. Angle(A, B, A'_1) → β
  9. Ray(B, A'_1) → i
  10. Segment(B, C) → j
  11. Min({f, j}) → b
  12. Circle(B, (0.2 * b)) → c
  13. Intersect(c, f) → D,
  14. Intersect(c, i) → E,
  15. CircleSector(B, D, E) → d
  16. LineBisector(f) → k
  17. LineBisector(j) → l
  18. Intersect(l, k) → O
  19. Circle(O, C) → e
  20. Dilate(O, If[0 < m ≤ 1, 1 - m, 0], C) → F'
  21. Segment(O, F') → n
  22. Rotate(C, If[1 < m ≤ 3, ((m - 1) * π), (2 * π)], O) → C'
  23. CircleArc(O, C, C') → p
  24. Rotate(C, If[1 < m ≤ 3, ((m - 1) * π), (2 * π)], O) → C'_1
  25. Rotate(O, If[1 < m ≤ 3, ((m - 1) * π), (2 * π)], O) → F'_1
  26. Rotate(F', If[1 < m ≤ 3, ((m - 1) * π), (2 * π)], O) → F''
  27. Segment(F'_1, F'') → n'
  28. Intersect(e, i) → G, H
  29. OrthogonalLine(O, f) → q
  30. Intersect(i, q) → I
  31. Intersect(f, q) → F
  32. OrthogonalLine(O, j) → r
  33. Intersect(j, r) → J
  34. Intersect(r, i) → K
  35. Distance(B, K) → distanceBK
  36. Distance(H, I) → distanceHI
  37. Dilate(B, If[4 < m ≤ 5, 5 - m, 0], I) → B'
  38. Segment(B, B') → s
  39. Intersect(c, f, 1) → L
  40. Rotate(L, If[5 < m ≤ 6, ((m - 5) * β), β], B) → L'
  41. CircleSector(B, L, L') → t
  42. Rotate(d, If[7 < m ≤ 8, ((m - 7) * β), β], B) → d'
  43. Angle(O, J, C) → γ
  44. Angle(O, F, B) → δ
  45. Dilate(I, If[5 < m ≤ 6, 6 - m, 0], K) → I'
  46. Segment(I, I') → f_1
  47. Dilate(O, If[8 < m ≤ 9, 9 - m, 0], I) → O'
  48. Segment(O, O') → g_1
  49. Dilate(I, If[9 < m ≤ 10, 10 - m, 0], F) → I'_1
  50. Segment(I, I'_1) → h_1
  51. Dilate(O, If[10 < m ≤ 11, 11 - m, 0], K) → O'_1
  52. Dilate(O, If[10 < m ≤ 11, 11 - m, 0], J) → O'_2
  53. Segment(O, O'_1) → i_1
  54. Segment(O, O'_2) → j_1
  55. Segment(B, I) → k_1
  56. Dilate(K, If[6 < m ≤ 7, 7 - m, 0], H) → K'
  57. Segment(K, K') → l_1
  58. Midpoint(I, K) → M
  59. Rotate(B, If[11.5 < m ≤ 12.5, ((-(m - 11.5)) * π), (-π)], M) → B'_1
  60. Rotate(I, If[11.5 < m ≤ 12.5, ((-(m - 11.5)) * π), (-π)], M) → I'_2
  61. Segment(B'_1, I'_2) → m_1
  62. Circle(O, C) → ee
  63. Polygon(B, A, C) → poly1, c_1, b_1, a_1

AI Drawing Prompt Reference

Draw a quadrilateral with one fixed side and another side rotating around a fixed endpoint, creating a dynamic similarity transformation. Show the circumcircle of the quadrilateral and the rotation path of points on the circle. Construct the circumcenter and draw segments from it to vertices. Add a slider to control rotation angle and scaling, making the figure animate. Display intersections of the circumcircle with rotating rays, construct perpendiculars, and mark relevant distances. Finally, use sectors and arcs to represent rotation, and label angles.
The prompt above was compiled from the original drawing commands and is for reference only.