MathPlotAI Logo MathPlotAI

Ellipse: Magic Sum = ? (V2)

Ellipse: Magic Sum = ? (V2)
Loading the math board and drawing, please wait…
2016-01-25 20:44
Coordinate GeometryComplex NumberGeometric Construction
This example demonstrates the geometric properties and calculations related to ellipses. Core math concepts include the definition of an ellipse, foci, vertices, vectors, rotation, scaling, etc. Construction highlights involve GeoGebra commands like Focus, Vertex, Segment, Translate, Point, Vector, Dilate, Angle, Rotate, Circle, Intersect, and Center to build the ellipse and auxiliary shapes. Suitable for high school mathematics teaching to understand geometric transformations and properties of ellipses.

GeoGebra Commands & Parameters

  1. Focus(c) → F_1, F_2
  2. Vertex(c) → C, D, E, F
  3. Segment(C, D) → d
  4. Translate(C, (0, b + 4)) → C'
  5. Translate(D, (0, b + 4)) → D'
  6. Point(c) → G
  7. Segment(G, F_1) → e
  8. Segment(G, F_2) → f
  9. Translate(C, (b + 4, 0)) → C'_1
  10. Vector(C, C') → u
  11. Vector(D, D') → v
  12. Dilate(C, If[0 < n < 1, 1 - n, 0], C') → C'_2
  13. Dilate(D, If[0 < n < 1, 1 - n, 0], D') → D'_2
  14. Segment(C'_2, D'_2) → l
  15. Dilate(F_1, If[1 < n < 2, 2 - n, 1], C') → A'
  16. Vector(F_1, A') → w
  17. Translate(G, w) → G'
  18. Segment(A', G') → m
  19. Segment(C, D) → p
  20. Angle(F_2, F_1, G) → α
  21. Rotate(A', If[1 < n < 2, ((-(2 - n)) * α)], A') → A''
  22. Rotate(A', If[1 < n < 2, ((-(n - 2)) * α), 0], A'') → A''_1
  23. Rotate(A', If[1 < n < 2, ((-(n - 1)) * α), (-α)], A') → A''_2
  24. Rotate(G', If[1 < n < 2, ((-(n - 1)) * α), (-α)], A') → G''
  25. Segment(A''_2, G'') → m'
  26. Circle(C', e) → q
  27. Intersect(q, l, 1) → H
  28. Segment(C', H) → r
  29. Segment(F_1, G) → s
  30. Dilate(F_2, If[2 < n < 3, 3 - n, 1], D') → B'
  31. Vector(F_2, B') → t
  32. Translate(G, t) → G'_1
  33. Translate(G, t) → G'_2
  34. Translate(F_2, t) → B'_1
  35. Segment(G'_2, B'_1) → f'
  36. Angle(G, F_2, F_1) → β
  37. Rotate(G'_2, If[2 < n < 3, ((n - 2) * β)], B') → L
  38. Rotate(B'_1, If[2 < n < 3, ((n - 2) * β)], B') → M
  39. Segment(L, M) → f''
  40. Segment(H, D') → a_1
  41. Segment(G, F_2) → b_1
  42. Center(c) → A
  43. Segment(A, G) → c_1
  44. Segment(A, G) → d_1
  45. Dilate(A, If[1 < n < 2, 2 - n, 0], C') → A'_1
  46. Vector(F_1, A'_1) → u_1
  47. Translate(A, u_1) → A'_2
  48. Translate(G, u_1) → G'_3
  49. Segment(A'_2, G'_3) → e_1
  50. Angle(D, F_1, G) → γ
  51. Rotate(A'_2, ((-(n - 1)) * γ), A'_2) → B
  52. Rotate(G'_3, ((-(n - 1)) * γ), A'_2) → I
  53. Segment(B, I) → f_1
  54. Dilate(G, If[2 < n < 3, 3 - n, 0], D') → G'_4
  55. Vector(G, G'_4) → v_1
  56. Translate(A, v_1) → A'_3
  57. Translate(G, v_1) → G'_5
  58. Segment(A'_3, G'_5) → g_1
  59. Rotate(A'_3, If[2 < n < 3, ((-(n - 2)) * γ)], G'_4) → J
  60. Rotate(G'_5, If[2 < n < 3, ((-(n - 2)) * γ)], G'_4) → K
  61. Segment(J, K) → h_1