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Element H Geometric Construction and Transformation

Element H Geometric Construction and Transformation
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2020-05-14 00:44
VectorCoordinate GeometryGeometric Construction
This example demonstrates the construction and transformation of element H in geometric transformations. Key mathematical concepts include vector transformation, geometric construction, and spatial point positioning in three-dimensional space. The construction involves using GeoGebra commands such as Rotate, Segment, Intersect, Circle, and Plane to build the element H's geometry, along with objects like Semicircle and Surface for spatial context. This example is suitable for high school students learning geometric transformations and coordinate geometry, useful for teaching and self-exploration.

GeoGebra Commands & Parameters

  1. Rotate(B, 45°, A) → B'
  2. Segment(A, B') → f
  3. Intersect(f, yAxis) → C
  4. Circle(C, 0.1) → c
  5. Segment(A, C) → g
  6. Segment(C, B) → h
  7. Intersect(c, g, 1) → D
  8. Intersect(c, h, 1) → E
  9. Circle(O, straal) → d
  10. Intersect(d, xAxis, 1) → F
  11. Intersect(d, xAxis, 2) → G
  12. Semicircle(F, G) → e
  13. Surface((sqrt(straal^(2) - h^(2)) * cos(t)), (sqrt(straal^(2) - h^(2)) * sin(t)), h + (1.5 * straal), t, 0°, 180°, h, 0, straal) → a
  14. Surface((sqrt(straal^(2) - h^(2)) * cos(t)), (sqrt(straal^(2) - h^(2)) * sin(t)), h + (1.5 * straal), t, 0°, 360°, h, 0, straal) → b
  15. Surface((straal * cos(t)), (straal * sin(t)), hh, t, 0°, 180°, hh, 0, (1.5 * straal)) → i
  16. Surface((straal * cos(t)), (straal * sin(t)), hh, t, 0°, 360°, hh, 0, (1.5 * straal)) → j
  17. Segment(L, M) → k
  18. Segment(L, A) → l
  19. Segment(M, B) → m
  20. CircleArc(N, J, P) → p
  21. CircleArc(N, P, I) → q
  22. Point(q) → Q
  23. Point(q) → R
  24. Point(q) → S
  25. Point(q) → T
  26. Point(q) → U
  27. Line(P, k) → r
  28. Line(Q, k) → s
  29. Line(R, k) → t
  30. Line(S, k) → f_1
  31. Line(T, k) → g_1
  32. Line(U, k) → h_1
  33. Intersect(r, l) → V
  34. Intersect(l, s) → W
  35. Intersect(l, t) → Z
  36. Intersect(l, f_1) → A_1
  37. Intersect(l, g_1) → B_1
  38. Intersect(l, h_1) → C_1
  39. Polygon(V, W, Q, P) → vierhoek1, v, w, q_1, p_1
  40. Polygon(W, Z, R, Q) → vierhoek2, w_1, z_1, r_1, q_2
  41. Polygon(Z, A_1, S, R) → vierhoek3, z_2, a_1, s_1, r_2
  42. Polygon(A_1, B_1, T, S) → vierhoek4, i_1, b_1, t_1, s_2
  43. Polygon(B_1, C_1, U, T) → vierhoek5, j_1, c_1, u, t_2
  44. Polygon(C_1, H, I, U) → vierhoek6, k_1, h_2, i_2, u_1
  45. Plane(O, C, P) → sym
  46. Mirror(V, sym) → V'
  47. Polygon(M, V', V, L) → vierhoek7, m_1, v', v_1, l_1
  48. Polygon(L, A, C, D_1) → vierhoek8, l_2, a_2, c_2, d_1
  49. Mirror(vierhoek5, sym) → vierhoek5'
  50. Mirror(vierhoek8, sym) → vierhoek8'
  51. Mirror(vierhoek1, sym) → vierhoek1'
  52. Mirror(vierhoek2, sym) → vierhoek2'
  53. Mirror(vierhoek3, sym) → vierhoek3'
  54. Mirror(vierhoek4, sym) → vierhoek4'
  55. Polygon(H, A, F, I) → vierhoek9, h_3, a_3, f_2, i_3
  56. Mirror(vierhoek9, sym) → vierhoek9'
  57. Mirror(vierhoek6, sym) → vierhoek6'
  58. Polygon(L, M, D_1) → driehoek1, n_1, l_3, m_2
  59. Segment(G, B) → e_1
  60. Segment(A, F) → g_2