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Magic Triangle

Magic Triangle
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2020-04-24 19:49
FunctionCoordinate GeometryIntegralGeometric Construction
This example demonstrates a special geometric construction by dynamically adjusting points to showcase triangle properties. It involves core math concepts like coordinate geometry, function graphing, integral calculation, and sequences. Construction highlights include commands like Polygon, Circle, Intersect, Distance, and Segment in GeoGebra. Suitable for high school and above learners to understand the integration of geometric construction and calculus.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Circle(A, Distance[A, B] / 3) → c
  3. Circle(B, Distance[A, B] / 3) → d
  4. Circle(C, Distance[A, B] / 3) → e
  5. Intersect(c, f, 1) → D
  6. Intersect(d, f, 1) → E
  7. Intersect(d, g, 1) → F
  8. Intersect(e, g, 1) → G
  9. Intersect(e, h, 1) → H
  10. Intersect(c, h, 1) → I
  11. Distance(A, B) → AB
  12. Circle(C, r) → k
  13. Circle(H, r) → p
  14. Circle(I, r) → q
  15. Circle(A, r) → s
  16. Circle(D, r) → t
  17. Circle(E, r) → c_1
  18. Circle(B, r) → d_1
  19. Circle(F, r) → e_1
  20. Circle(G, r) → f_1
  21. Intersect(k, h, 1) → J
  22. Intersect(p, h, 1) → K
  23. Intersect(p, h, 2) → L
  24. Intersect(q, h, 1) → M
  25. Intersect(q, h, 2) → N
  26. Intersect(s, h, 1) → O
  27. Intersect(s, f, 1) → P
  28. Intersect(t, f, 1) → Q
  29. Intersect(t, f, 2) → R
  30. Intersect(c_1, f, 1) → S
  31. Intersect(c_1, f, 2) → T
  32. Intersect(d_1, f, 1) → U
  33. Intersect(d_1, g, 1) → V
  34. Intersect(e_1, g, 1) → W
  35. Intersect(e_1, g, 2) → Z
  36. Intersect(f_1, g, 1) → A_1
  37. Intersect(f_1, g, 2) → B_1
  38. Intersect(k, g, 1) → C_1
  39. Segment(J, K) → i
  40. Segment(L, M) → j
  41. Segment(N, O) → l
  42. Segment(P, Q) → m
  43. Segment(R, S) → n
  44. Segment(T, U) → a
  45. Segment(V, W) → b
  46. Segment(Z, A_1) → g_1
  47. Segment(B_1, C_1) → h_1