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Sivas Şifaiye Geometry: Coordinate Construction with Equilateral Triangles and R

Sivas Şifaiye Geometry: Coordinate Construction with Equilateral Triangles and R
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2020-08-18 00:04
TrianglePolygonCoordinate GeometryGeometric ConstructionGraphing
In collections Fatin Uluengin - muqarnas
This example demonstrates how to build an ornamental, module-like geometric figure in the coordinate plane by combining line segments and polygons whose structure is governed by equilateral-triangle relationships. Key mathematical ideas include equilateral triangles (equal-length/angle constraints), geometric construction using points and segments, and assembling larger designs from repeated coordinate-defined parts. Construction-wise, it uses GeoGebra commands Segment, Point, PolyLine, and Polygon: Segment and Point generate the defining edges and vertices, PolyLine builds the polyline skeleton, and Polygon creates closed multi-sided regions. The listed objects (e.g., A, B and multiple indexed components such as S_4, T_4, U_4, V_4, W_4, Z_4, A_5–L_5) reflect layered or repeated sub-constructs that together form the final pattern. Suitable for secondary-school geometry construction, coordinate geometry practice, and classroom demonstrations of modular geometric design.

GeoGebra Commands & Parameters

  1. Segment(S_4, T_4) → n
  2. Segment(U_4, T_4) → p
  3. Segment(V_4, W_4) → q
  4. Segment(Z_4, W_4) → r
  5. Segment(A_5, B_5) → s
  6. Segment(C_5, B_5) → t
  7. Segment(D_5, E_5) → a
  8. Segment(F_5, E_5) → b
  9. Segment(G_5, H_5) → c
  10. Segment(I_5, H_5) → d
  11. Segment(J_5, K_5) → e
  12. Segment(L_5, K_5) → f_1
  13. Point(yAxis) → M
  14. PolyLine(C, D, M, N, O, P, Q, R, S, T, U, V, E, W, F, G, H, I, J, K, L) → f
  15. PolyLine(Z, A_1, M, H_1, P, I_1, J_1, K_1, L_1, M_1, U, N_1, E, O_1, B_1, C_1, D_1, E_1, F_1, J, G_1) → g
  16. Point(f) → M_5
  17. Polygon(M_5, E_1, D_1, C_1) → vierhoek1, m_5, e_1, d_1, c_1
  18. Polygon(E_1, T_4, C_1, D_1) → vierhoek2, g_1, t_4, h_1, i_1
  19. Point(g) → Q_1
  20. Point(g) → R_1
  21. Point(g) → T_1
  22. Point(g) → V_1
  23. Point(g) → Z_1
  24. Point(g) → A_2
  25. Point(yAxis) → B_2
  26. Point(g) → C_2
  27. Point(g) → D_2
  28. Point(g) → F_2
  29. Point(g) → H_2
  30. Point(g) → J_2
  31. PolyLine(P_1, Q_1, G_1, A_2, B_2, C_2, H_1, D_2, E_2, F_2, G_2, H_2, A_1, I_2, J_2, N_1, K_2, L_2, R_1, S_1, T_1, U_1, V_1, W_1, Z_1) → h
  32. Point(yAxis) → V_2
  33. PolyLine(M_2, N_2, W_2, Z_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2) → i
  34. Polygon(U_1, S_2, R_2, Q_2) → vierhoek3, u_1, s_2, r_2, q_2
  35. Polygon(S_2, B_5, Q_2, R_2) → vierhoek4, j_1, b_5, k_1, l_1
  36. Point(i) → I_3
  37. Point(i) → K_3
  38. Point(i) → M_3
  39. Point(i) → N_3
  40. Point(i) → P_3
  41. PolyLine(M_2, H_3, P_3, Q_3, R_3, S_3, G_3, I_3, J_3, K_3, L_3, M_3, V_2, N_3, O_3) → j
  42. Point(yAxis) → A_4
  43. PolyLine(T_3, U_3, E_4, F_4, G_4, V_3, W_3, Z_3, H_4, A_4, B_4, C_4, D_4) → k
  44. Polygon(G_5, J_3, I_5, W_3) → vierhoek5, g_5, j_3, i_5, w_3
  45. Polygon(I_5, H_5, G_5, W_3) → vierhoek6, m_1, h_5, n_1, p_1
  46. Point(yAxis) → K_4
  47. PolyLine(I_4, U_3, J_4, H_4, K_4, B_4, L_4, F_4, M_4) → l
  48. Point(yAxis) → P_4
  49. PolyLine(N_4, O_4, P_4, Q_4, R_4) → m
  50. Polygon(N_5, J_4, O_5, O_4) → vierhoek7, n_5, j_4, o_5, o_4
  51. Polygon(P_5, N_5, O_4, O_5) → vierhoek8, p_5, q_1, r_1, s_1

AI Drawing Prompt Reference

Draw a decorative modular geometric figure on a coordinate plane, built from equilateral-triangle relationships. Start with several pairs of line segments that form triangle edges. Place a point on the vertical axis as a central reference. Then create two polyline skeletons that outline a symmetric shape, and place multiple points along these polylines to serve as vertices for later polygons. Using these points and existing segment endpoints, construct several quadrilaterals that are adjacent to each other, forming repeating modular units. Finally, add more polylines connecting points on the vertical axis to previously generated vertices to complete the layered, symmetric pattern. The overall design combines line segments, polylines, and polygons, emphasizing geometric construction and coordinate positioning.
The prompt above was compiled from the original drawing commands and is for reference only.