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Castle del Monte - Central Building and Towers

Castle del Monte - Central Building and Towers
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2019-12-26 17:24
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric construction of the central building and towers of Castle del Monte. Key mathematical concepts include polygons, equilateral triangles, and geometric constructions. Using GeoGebra commands such as Polygon, Distance, and Segment, precise geometric shapes can be constructed. Suitable for middle school and above students to learn geometric constructions and solid geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  2. Distance(C, D) → CD
  3. Segment(F, B) → n
  4. Segment(E, A) → p
  5. Intersect(n, p) → O
  6. Segment(O, A) → q
  7. Segment(O, B) → r
  8. Circle(O, q / phi) → c
  9. Intersect(c, q) → I,
  10. Intersect(c, r) → J,
  11. Segment(I, J) → s
  12. Polygon(I, J, 8) → poly2, t, L, M, N, P, Q, b, d, e, f_1, g_1, h_1, i_1, K
  13. Line(O, f) → k_1
  14. OrthogonalLine(O, j) → l_1
  15. Line(I, J) → j_1
  16. Line(H, G) → m_1
  17. Intersect(j_1, m_1) → R
  18. Mirror(R, k_1) → R'
  19. Line(N, M) → n_1
  20. Mirror(m_1, l_1) → p_1
  21. Intersect(n_1, p_1) → S
  22. Intersect(p_1, j_1) → T
  23. Distance(R, T) → RT
  24. Distance(T, S) → TS
  25. Line(R', k) → q_1
  26. Line(S, i) → r_1
  27. Line(T, g) → s_1
  28. Line(R, m) → t_1
  29. LineBisector(G, F) → a_1
  30. Mirror(R', a_1) → R''
  31. Mirror(R'', l_1) → R'''
  32. Mirror(R''', k_1) → U
  33. Mirror(U, l_1) → U'
  34. Polygon(R'', R''', U, U') → q1, r'', r''', u, u'
  35. Segment(R', R'') → b_1
  36. Segment(R''', S) → c_1
  37. Segment(T, U) → d_1
  38. Segment(U', R) → e_1
  39. Polygon(R'', F, 8) → poly3, f_2, W, Z, A_1, B_1, C_1, g_2, h_2, i_2, j_2, k_2, l_2, m_2, V
  40. Polygon(E, R''', 8) → poly4, n_2, E_1, F_1, G_1, H_1, I_1, p_2, q_2, r_2, s_2, t_2, a_2, b_2, D_1
  41. Polygon(S, D, 8) → poly5, c_2, K_1, L_1, M_1, N_1, O_1, d_2, e_2, f_3, g_3, h_3, i_3, j_3, J_1
  42. Polygon(C, T, 8) → poly6, k_3, Q_1, R_1, S_1, T_1, U_1, l_3, m_3, n_3, p_3, q_3, r_3, s_3, P_1
  43. Polygon(U, B, 8) → poly7, t_3, W_1, Z_1, A_2, B_2, C_2, a_3, b_3, c_3, d_3, e_3, f_4, g_4, V_1
  44. Polygon(A, U', 8) → poly8, h_4, E_2, F_2, G_2, H_2, I_2, i_4, j_4, k_4, l_4, m_4, n_4, p_4, D_2
  45. Polygon(R, H, 8) → poly9, q_4, K_2, L_2, M_2, N_2, O_2, r_4, s_4, t_4, a_4, b_4, c_4, d_4, J_2
  46. Polygon(G, R', 8) → poly10, e_4, Q_2, R_2, S_2, T_2, U_2, f_5, g_5, h_5, i_5, j_5, k_5, l_5, P_2
  47. Segment(U_2, J_2) → m_5
  48. Segment(V, I_1) → n_5
  49. Segment(J_1, U_1) → p_5
  50. Segment(V_1, I_2) → q_5