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Thales and the Pyramids

Thales and the Pyramids
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2020-02-25 03:07
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates how Thales measured the height of the pyramids using geometric methods. It involves core math concepts like geometric construction, similar triangles, vectors, and coordinate geometry. Construction highlights include commands/objects like Line, Point, Segment, Vector, OrthogonalLine, Rotate, Angle, Intersect, Ray, Translate, Midpoint, Polygon, Circle from GeoGebra. Suitable for high school and above learning geometric proofs and real-world applications.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. Point(a) → D
  4. Segment(C, D) → b
  5. Point(b) → F
  6. Vector(F1, I1) → v
  7. Point(b) → E
  8. OrthogonalLine(E, a) → c
  9. Point(c) → G
  10. OrthogonalLine(F, a) → d
  11. Segment(E, G) → haut
  12. Point(d) → H
  13. Segment(F, H) → persona
  14. Line(H, a) → e
  15. Line(G, a) → f
  16. Point(e) → I
  17. Point(f) → J
  18. Rotate(I, α, H) → K
  19. Angle(I, H, K) → β
  20. Rotate(J, α, G) → L
  21. Angle(J, G, L) → γ
  22. Line(G, L) → g
  23. Line(H, K) → h
  24. Point(haut) → M
  25. Point(haut) → N
  26. Point(haut) → O
  27. Point(haut) → P
  28. Line(M, g) → i
  29. Line(N, i) → j
  30. Line(O, j) → k
  31. Line(P, k) → l
  32. Line(B, haut) → m
  33. Intersect(g, a) → U
  34. Intersect(h, a) → V
  35. Ray(V, H) → s
  36. Ray(U, G) → t
  37. Segment(E, U) → a1
  38. Segment(F, V) → b1
  39. Vector(F1, C1) → u
  40. Translate(E, u) → E1
  41. Translate(G, u) → D1
  42. Translate(H, v) → H1
  43. Translate(F, v) → G1
  44. Angle(F, V, H) → δ
  45. Angle(E, U, G) → ε
  46. Midpoint(b1) → J1
  47. Midpoint(a1) → K1
  48. Midpoint(persona) → L1
  49. Midpoint(haut) → M1
  50. Line(R, s) → p
  51. Line(Q, s) → q
  52. Intersect(a, p) → S
  53. Intersect(q, a) → T
  54. Line(N1, t) → r
  55. Intersect(r, a) → O1
  56. Segment(Q, T) → c1
  57. Segment(R, S) → d1
  58. Segment(N1, O1) → e1
  59. Intersect(a, xAxis) → P1
  60. Line(G, a) → f1
  61. Point(f1) → Q1
  62. Point(a) → A1
  63. Point(a) → B1
  64. Polygon(A1, B1, S1, T1) → poly1, a1_1, b1_1, s1, t1
  65. Circle(D, 4) → k1
  66. Intersect(k1, a1_1) → W1, Z1
  67. Polygon(G, Z1, W1) → poly2, w1, g_1, z1
  68. Segment(W1, U) → h1
  69. Polygon(G, W1, Z1) → poly3, z1_1, g_2, w1_1
  70. Point(t) → U1
  71. Segment(W1, D) → g1
  72. Point(a1_1) → A_1
  73. Midpoint(D_1, C_1) → E_1
  74. Vector(E_1, C_1) → z
  75. Vector(E_1, D_1) → u_1
  76. Segment(D_1, C_1) → a_1
  77. Segment(U, D_1) → b_1
  78. Segment(W1, F_1) → c_1
  79. Segment(D, C_1) → d_1