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Symmetry Number for Two Overlapped Ellipses

Symmetry Number for Two Overlapped Ellipses
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2019-05-31 16:35
TransformationGeometric Construction
This example demonstrates the symmetry number for two overlapped ellipses. Key mathematical concepts include the geometric properties and symmetry of ellipses. Using GeoGebra commands such as Line, Ellipse, Midpoint, Point, Segment, Rotate, Angle, Intersect, Polygon, etc., the construction of two overlapped ellipses is illustrated. Suitable for high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Ellipse(A, B, C) → c
  3. Midpoint(A, B) → D
  4. Point(c) → E
  5. Segment(D, E) → g
  6. Rotate(E, 90°, D) → E'
  7. Angle(E, D, E') → α
  8. Line(D, E') → h
  9. Intersect(c, h, 2) → F
  10. Segment(D, F) → i
  11. Rotate(E, 180°, D) → G
  12. Angle(E, D, G) → β
  13. Segment(D, G) → j
  14. Rotate(G, 90°, D) → G'
  15. Angle(G, D, G') → γ
  16. Line(D, G') → k
  17. Intersect(c, k, 2) → H
  18. Segment(D, H) → l
  19. Polygon(E, F, G, H) → q1, e, f_1, g_1, h_1
  20. Circle(D, a) → d
  21. Intersect(c, f, 2) → K
  22. Intersect(c, f) → J, L
  23. Segment(E, C) → m
  24. Segment(H, C) → n
  25. Segment(F, C) → p
  26. Segment(G, C) → q
  27. Line(I, M) → r
  28. Mirror(E, r) → E'_1
  29. Mirror(F, r) → F'
  30. Mirror(G, r) → G'_1
  31. Mirror(H, r) → H'
  32. Polygon(E'_1, F', G'_1, H') → q1', e'_1, f', g'_1, h'
  33. Mirror(c, r) → c'
  34. Mirror(d, r) → d'
  35. Mirror(D, r) → D'
  36. Mirror(E, r) → E'_2
  37. Segment(D', E'_2) → g'
  38. Mirror(D, r) → D'_1
  39. Mirror(F, r) → F'_1
  40. Segment(D'_1, F'_1) → i'
  41. Mirror(D, r) → D'_2
  42. Mirror(G, r) → G'_2
  43. Segment(D'_2, G'_2) → j'
  44. Mirror(D, r) → D'_3
  45. Mirror(H, r) → H'_1
  46. Segment(D'_3, H'_1) → l'
  47. Mirror(E, r) → E'_3
  48. Mirror(C, r) → C'
  49. Segment(E'_3, C') → m'
  50. Mirror(H, r) → H'_2
  51. Mirror(C, r) → C'_1
  52. Segment(H'_2, C'_1) → n'
  53. Mirror(F, r) → F'_2
  54. Mirror(C, r) → C'_2
  55. Segment(F'_2, C'_2) → p'
  56. Mirror(G, r) → G'_3
  57. Mirror(C, r) → C'_3
  58. Segment(G'_3, C'_3) → q'
  59. Mirror(A, r) → A'
  60. Mirror(B, r) → B'
  61. Mirror(K, r) → K'
  62. Mirror(J, r) → J'
  63. Mirror(L, r) → L'

AI Drawing Prompt Reference

Draw two overlapping ellipses and then construct their symmetry axes, midpoints, intersection points, and rotated points. Finally, use these points to form a quadrilateral. Specifically, draw a line segment, rotate points around this segment, construct angles, draw tangents, find intersections, and connect these intersections to form the quadrilateral.
The prompt above was compiled from the original drawing commands and is for reference only.