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Geogebra Geometry Construction Example by JM Arranz, JA Mora, M Sada y R Losada

Geogebra Geometry Construction Example by JM Arranz, JA Mora, M Sada y R Losada
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2023-03-19 02:34
TriangleCirclePolygonVectorGeometric Construction
In collections geometriadinamica.es
This example demonstrates dynamic geometric construction and visualization using GeoGebra, involving core math concepts like perimeter, vectors, exponential functions, correlation, and similar triangles. Key GeoGebra commands and objects used in the construction include OrthogonalLine, Circle, Intersect, Ellipse, Point, Angle, Translate, Vector, Sequence, Element, Segment, Polygon, Midpoint, and Line. Suitable for high school and above mathematics learners for understanding geometric constructions and dynamic demonstrations.

GeoGebra Commands & Parameters

  1. OrthogonalLine(C, xAxis) → z2
  2. Circle(C, 0.62) → z0
  3. Intersect(z0, z2, 1) → Z4
  4. Intersect(z0, z2, 2) → Z3
  5. Ellipse(Z3, Z4, 0.65) → zElipse2
  6. Point(zElipse2) → Z
  7. Intersect(zElipse2, z2) → Z7, Z8
  8. Angle(Z8, C, Z) → zAngInc
  9. OrthogonalLine(C, yAxis) → z1
  10. Intersect(z0, z1, 2) → Z2
  11. Intersect(z0, z1, 1) → Z1
  12. Ellipse(Z1, Z2, 0.65) → zElipse1
  13. Point(zElipse1) → XY
  14. Translate((0, 0), v) → O
  15. OrthogonalLine(O, yAxis) → d
  16. Point(d) → G
  17. Vector((0, 0), G) → w
  18. Sequence(PuntoEsfera[C, XY, Z, radio, 0, (s * α)], s, 0, n) → puntosA
  19. Sequence((x(w) + x(Element[puntosA, s]), y(w) + y(Element[puntosA, s])), s, 1, n + 1) → puntosB
  20. Sequence(Segment[Element[puntosB, s], Element[puntosA, s]], s, 1, n) → aristas
  21. Element(aristas, 5) → a5
  22. Point(a5) → J
  23. Element(aristas, 1) → a1
  24. Point(a1) → A
  25. Element(aristas, 2) → a2
  26. Point(a2) → B
  27. Element(aristas, 3) → a3
  28. Point(a3) → D
  29. Element(aristas, 4) → a4
  30. Point(a4) → E
  31. Element(puntosB, 5) → B5
  32. Element(puntosB, 1) → B1
  33. Element(puntosB, 2) → B2
  34. Element(puntosB, 3) → B3
  35. Element(puntosB, 4) → B4
  36. Intersect(zElipse1, z1) → Z5, Z6
  37. Segment(Z5, Z6) → z4
  38. Segment(Z7, Z8) → z3
  39. Intersect(zElipse2, zElipse1, 1) → zPunto1
  40. Intersect(zElipse2, zElipse1, 4) → zPunto2
  41. Polygon(B1, B2, B3, B4, B5) → poly2, a, b, c, e, f
  42. Segment(zPunto1, zPunto2) → zSeg2
  43. Angle(Z6, C, XY) → zAngRot
  44. Sequence(Angle[Element[puntosB, s + 1], Element[puntosB, s], Element[puntosA, s + 1]], s, 1, n) → angulos
  45. Sequence(If[s > 1 ∧ Element[angulos, s - 1] > 180° ∧ Element[angulos, s] > 180°, false, If[s ≟ 1 ∧ Element[angulos, n] > 180° ∧ Element[angulos, s] > 180°, false, true]], s, 1, n) → aristasVisibles
  46. Element(aristas, 1) → a1b
  47. Polygon(A, B, D, E, J) → poly1, g, h, i, j, k_2
  48. Element(aristas, 2) → a2b
  49. Element(aristas, 3) → a3b
  50. Sequence(If[Element[angulos, s] > 180°, false, true], s, 1, n) → carasVisibles
  51. Angle(B1, B2, B3) → β
  52. Element(aristas, 4) → a4b
  53. Polygon(A, D, B) → poly3, b_1, a_1, d_1
  54. Midpoint(A, D) → I
  55. Angle(H, I, F) → γ
  56. Element(aristas, 5) → a5b
  57. Polygon(J, A, E) → poly6, e_1, j_1, a_3
  58. Midpoint(B1, B4) → M
  59. Line(M, a5) → l
  60. Intersect(j_1, l) → N
  61. Angle(L, N, F) → δ
  62. Vector(B1, B5) → z
  63. Vector(B5, B4) → m
  64. Vector(B4, B3) → p
  65. Vector(B3, B2) → q
  66. Vector(B2, B1) → r
  67. Line(P, a5) → s
  68. Line(Q, a5) → t
  69. Line(R, a5) → c_1
  70. Line(S, a5) → f_1
  71. Line(T, a5) → g_1
  72. Intersect(k_2, s) → U
  73. Intersect(j, t) → V
  74. Intersect(i, c_1) → W
  75. Intersect(h, f_1) → A_1
  76. Intersect(g, g_1) → B_1
  77. Polygon(Q, R, S, T, P) → poly4, q_1, r_1, s_1, t_1, p_1
  78. Polygon(B5, B4, B1) → poly5, b1, b5, b4
  79. Intersect(t_1, b5) → C_1
  80. Intersect(q_1, b5) → D_1
  81. Polygon(B1, B3, B2) → poly7, b2, b1_1, b3
  82. Intersect(t_1, b2) → E_1
  83. Intersect(r_1, b2) → F_1
  84. Line(C_1, a5) → h_1
  85. Line(D_1, a5) → i_1
  86. Line(E_1, a5) → k_1
  87. Line(F_1, a5) → l_1
  88. Intersect(j_1, i_1) → G_1
  89. Intersect(j_1, h_1) → H_1
  90. Intersect(b_1, k_1) → I_1
  91. Intersect(b_1, l_1) → J_1
  92. Polygon(H_1, U, V, G_1) → poly8, h_2, u_1, v_1, g_2
  93. Polygon(G_1, W, J_1, I_1, H_1) → poly9, g_3, w_1, j_2, i_2, h_3
  94. Polygon(J_1, A_1, B_1, I_1) → poly10, j_3, a_2, b_2, i_3
  95. Polygon(U, B_1, A_1, W, V) → poly11, u_2, b_3, a_4, w_2, v_2

AI Drawing Prompt Reference

Draw a coordinate plane with a point C as the center and two perpendicular axes. Construct a circle centered at C with a given radius, and obtain intersection points with the directions determined by the perpendicular lines to the axes. Use these points to define two ellipses that share the same shape parameter (one built from a pair of intersections on the same vertical reference, and another from a different pair). Take key points from each ellipse and compute two ellipse–ellipse intersection points to form a segment between them. Mark an angle at the center involving the intersection on one ellipse and a reference point on the horizontal base. Then define a translation direction from the origin to a selected point and use it with a parameter step to generate two sequences of points along the construction’s shifting pattern. Connect corresponding points from the two sequences to form edges, pick several specific points from these edges, and finally draw two polygons: one from the selected outer points and another involving the center-related point set, using the earlier ellipse intersection segment as part of the structure.
The prompt above was compiled from the original drawing commands and is for reference only.