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Geometric construction of the IKASNOVA logo using mirror symmetry and vectors

Geometric construction of the IKASNOVA logo using mirror symmetry and vectors
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2020-08-07 21:53
PolygonVectorTransformationGeometric Construction
This example demonstrates how to construct an IKASNOVA-style logo line drawing by combining classical geometric constructions and symmetry. The key mathematical ideas include vector representation and orthogonality (OrthogonalVector, OrthogonalLine), constructing bisectors and midpoints (LineBisector, Midpoint), using mirror transformation to enforce symmetry (Mirror), and computing intersections and assembling shapes via polygons (Intersect, Polygon). Construction is carried out with GeoGebra commands such as LineBisector, Vector, OrthogonalVector, Line, OrthogonalLine, Mirror, Intersect, Polygon, and Midpoint, along with multiple auxiliary points (e.g., A, B, D, E, G, H, K, S) and text objects (texto1, texto2) to place labels and finalize the graphic composition. Suitable for middle school geometry construction lessons, transformation geometry topics, and beginner-friendly graph-to-design style projects.

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(D, s) → i
  7. Mirror(i, m) → i'
  8. OrthogonalLine(A, s) → b
  9. OrthogonalLine(A_1, b) → r
  10. OrthogonalLine(F, b) → f
  11. Mirror(f, l) → f'
  12. Intersect(i', f') → P
  13. Intersect(i, f') → E
  14. Intersect(m, l) → K
  15. Mirror(f, l) → f'_1
  16. OrthogonalLine(G, f'_1) → h
  17. OrthogonalLine(B, u, xOyPlane) → g
  18. Intersect(g, r) → C
  19. Mirror(F, l) → F'
  20. Polygon(A_1, C, B, A) → c4, a_1, c_3, b_2, a_2
  21. OrthogonalLine(H, f'_1) → k
  22. Intersect(i', f) → J_1
  23. Intersect(f, m) → D_1
  24. Intersect(f, k) → J
  25. Intersect(l, i) → M
  26. Line(L, l) → j
  27. Polygon(S, L, J, R, Q) → poly1, s_1, l_1, j_1, r_1, q
  28. Line(O, l_1) → n
  29. Line(O, s_1) → p
  30. Line(I, q) → t
  31. Line(N, r_1) → c
  32. Line(N, j_1) → d
  33. Intersect(p, t) → T
  34. Intersect(c, t) → V
  35. Intersect(n, d) → W
  36. Polygon(O, T, V, N, W) → poly2, o, t_1, v_1, n_1, w
  37. Vector(W, N) → a
  38. Vector(J, R) → e
  39. Vector(T, V) → u_1
  40. Vector(S, Q) → w_1
  41. Polygon(B_1, C_1, H_1, G_1) → q1, b_1, c_1, h_1, g_1
  42. Polygon(C_1, E_1, I_1, H_1) → q2, f_1, i_1, k_1, m_1
  43. Polygon(E_1, F_1, K_1, I_1) → q3, p_1, q_1, d_1, f_2
  44. Polygon(L_1, M_1, Q_1, P_1) → q4, g_2, h_2, i_2, j_2
  45. Polygon(M_1, N_1, R_1, Q_1) → q5, k_2, l_2, m_2, n_2
  46. Polygon(N_1, O_1, S_1, R_1) → q6, p_2, o_1, q_2, r_2
  47. Polygon(W, B_1, G_1, J) → q7, w_2, s_2, t_2, j_3
  48. Polygon(F_1, N, R, K_1) → q8, c_2, n_3, r_3, d_2
  49. Polygon(V, Q, R, N) → q9, v_2, q_3, r_4, n_4
  50. Polygon(T, P_1, L_1, S) → q10, t_3, f_3, g_3, s_3
  51. Polygon(Q, O_1, S_1, V) → q11, q_4, h_3, i_3, v_3
  52. Midpoint(H_1, I_1) → T_1
  53. Midpoint(C_1, E_1) → U_1
  54. Polygon(U_1, E_1, I_1, T_1) → q12, k_3, l_3, m_3, p_3

AI Drawing Prompt Reference

Create a geometric design that demonstrates how to construct an IKASNOVA-style logo line drawing by combining classical geometric constructions and symmetry. Start with a line segment and its midpoint, then use vectors and orthogonal lines to construct symmetry axes and angle bisectors. Apply mirror transformations to ensure symmetry and calculate intersections. Finally, assemble the shape using polygons, showcasing the application of vectors, orthogonal lines, angle bisectors, and mirror transformations.
The prompt above was compiled from the original drawing commands and is for reference only.