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2D Vectors and Geometric Constructions

2D Vectors and Geometric Constructions
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2020-06-02 19:17
PolygonVectorGeometric Construction
This example demonstrates the process of constructing complex geometric figures using 2D vectors and basic elements like circles, squares, and equilateral triangles. Key math concepts include vector operations, linear regression, polygon construction, and geometric transformations. Construction highlights involve commands like LineBisector, Vector, OrthogonalVector, Line, OrthogonalLine, Mirror, Intersect, Polygon, CircumcircleArc, and Midpoint, as listed in the construction summary. Suitable for high school and above learners to understand the integration of vectors, geometric transformations, and computational geometry.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → m
  2. Vector(A, B) → u
  3. OrthogonalVector(u) → v
  4. LineBisector(A_1, A) → l
  5. Line(A, B) → s
  6. OrthogonalLine(Q, s) → q
  7. Mirror(q, m) → q'
  8. OrthogonalLine(D, s) → i
  9. Intersect(i, l) → P
  10. Mirror(i, m) → i'
  11. Intersect(i', l) → H
  12. OrthogonalLine(A, s) → b
  13. OrthogonalLine(J, b) → p
  14. Intersect(q', p) → L_1
  15. Line(H, L_1) → a
  16. Line(I, a) → f_1
  17. OrthogonalLine(F, b) → f
  18. Intersect(i, f) → R
  19. LineBisector(R, P) → n
  20. Intersect(n, i) → T
  21. Mirror(f, l) → f'
  22. Intersect(m, f') → S
  23. Line(K_1, f_1) → g_1
  24. Mirror(f, l) → f'_1
  25. Intersect(q', f'_1) → K
  26. OrthogonalLine(N, f') → h
  27. Intersect(h, g_1) → V
  28. OrthogonalLine(A_1, b) → r
  29. Intersect(i, f') → E
  30. OrthogonalLine(K_1, f'_1) → n_1
  31. Intersect(m, l) → L
  32. OrthogonalLine(B, u, xOyPlane) → g
  33. Intersect(g, r) → C
  34. Mirror(F, l) → F'
  35. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  36. Intersect(i', f') → W
  37. Mirror(p, l) → p'
  38. Intersect(i', f) → G_1
  39. Intersect(m, f) → G
  40. Line(H, L_1) → j
  41. Line(I, j) → k
  42. Intersect(h, k) → M
  43. CircumcircleArc(T, G, H) → c
  44. CircumcircleArc(T, U, I) → d
  45. CircumcircleArc(T, L, K_1) → t
  46. Intersect(t, f_1) → Z,
  47. CircumcircleArc(T, O, V) → e
  48. Intersect(e, f_1) → B_1,
  49. Midpoint(Z, B_1) → C_1
  50. Midpoint(L, O) → D_1
  51. CircumcircleArc(T, D_1, C_1) → c_1
  52. Intersect(d, a) → E_1,
  53. Intersect(e, a) → F_1,
  54. Vector(H, E_1) → w
  55. Polygon(K_1, V, B_1, C_1, T) → poly1, k_1, v_1, b_1, h_1, t_1
  56. CircumcircleArc(T, I_1, J_1) → p_1
  57. CircumcircleArc(T, O, F_1) → q_1
  58. Polygon(K_1, V, B_1, Z) → q1, i_1, v_2, j_1, z_1
  59. Intersect(t, a) → H_1,
  60. Polygon(C_1, Z, H_1) → t1, l_1, m_1, z_2
  61. Polygon(B_1, I, E_1, F_1) → q2, r_1, i_2, s_1, f_2
  62. Intersect(d, p') → M_1,
  63. Polygon(H, E_1, M_1) → t2, g_2, h_2, j_2