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Light in GeoGebra Demonstration

Light in GeoGebra Demonstration
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2013-02-17 14:00
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the refraction of light through a prism and the construction of polygons and 3D shapes using GeoGebra. It involves core mathematical concepts like polygons, trigonometric functions, solid geometry, and coordinate geometry. Key GeoGebra commands used include Polygon, Mirror, Segment, Point, and OrthogonalLine. Suitable for high school and above students to learn geometric optics and 3D shape construction.

GeoGebra Commands & Parameters

  1. Polygon(A, E, F, B) → многоугольник1, a, e, f, b
  2. Polygon(B, F, H, C) → многоугольник2, b_1, f_1, h_1, c
  3. Polygon(C, H, E, A) → многоугольник3, c_1, h_2, e_1, a_1
  4. Polygon(H, F, E) → многоугольник4, e_2, h_3, f_2
  5. Mirror(N, G) → B_3
  6. Mirror(L, G) → C_1
  7. Mirror(K, G) → D_1
  8. Mirror(J, G) → A_3
  9. Polygon(K, B_3, A_3, L) → многоугольник5, k, b_2, a_2, l
  10. Polygon(L, A_3, D_1, N) → многоугольник6, l_1, a_3, d_1, n
  11. Polygon(N, D_1, C_1, J) → многоугольник7, n_1, d_2, c_2, j
  12. Polygon(J, C_1, B_3, K) → многоугольник8, j_1, c_3, b_3, k_1
  13. Polygon(C_1, D_1, A_3, B_3) → многоугольник9, c_4, d_{10}, a_4, b_4
  14. Polygon(S, B_5, A_5, T) → многоугольник10, s, b_5, a_5, t
  15. Polygon(V, C_5, B_5, S) → многоугольник11, v_1, c_5, b_6, s_1
  16. Polygon(W, D_5, C_5, V) → многоугольник12, w, d_7, c_6, v_2
  17. Polygon(U, E_5, D_5, W) → многоугольник13, u, e_5, d_{11}, w_1
  18. Polygon(T, A_5, E_5, U) → многоугольник14, t_1, a_6, e_3, u_1
  19. Polygon(B_5, C_5, D_5, E_5, A_5) → многоугольник15, b_7, c_7, d_9, e_4, a_7
  20. Mirror(G_1, E_1) → L_1
  21. Mirror(F_1, E_1) → M_1
  22. Mirror(H_1, E_1) → N_1
  23. Mirror(J_1, E_1) → O_1
  24. Mirror(K_1, E_1) → P_1
  25. Mirror(I_1, E_1) → Q_1
  26. Polygon(I_1, N_1, L_1, K_1) → многоугольник16, i_1, n_2, l_2, k_2
  27. Polygon(J_1, M_1, Q_1, H_1) → многоугольник17, j_2, m_1, q_1, h_4
  28. Polygon(K_1, L_1, M_1, J_1) → многоугольник18, k_3, l_3, m_2, j_3
  29. Polygon(F_1, O_1, N_1, I_1) → многоугольник19, f_3, o_1, n_3, i_2
  30. Polygon(G_1, P_1, O_1, F_1) → многоугольник20, g_1, p_1, o_2, f_4
  31. Polygon(H_1, Q_1, P_1, G_1) → многоугольник21, h_5, q_2, p_2, g_2
  32. Mirror(Z_1, B_1) → B_2
  33. Mirror(U_1, B_1) → A_2
  34. Mirror(V_1, B_1) → C_2
  35. Mirror(W_1, B_1) → D_2
  36. Mirror(R_1, B_1) → E_2
  37. Mirror(S_1, B_1) → F_2
  38. Mirror(A_1, B_1) → G_2
  39. Mirror(T_1, B_1) → H_2
  40. Polygon(W_1, G_2, H_2, V_1) → многоугольник22, w_2, g_3, h_6, v_3
  41. Polygon(R_1, B_2, G_2, W_1) → многоугольник23, r_1, b_8, g_4, w_3
  42. Polygon(S_1, A_2, B_2, R_1) → многоугольник24, s_2, a_8, b_9, r_2
  43. Polygon(T_1, C_2, A_2, S_1) → многоугольник25, t_2, c_8, a_9, s_3
  44. Polygon(A_1, D_2, C_2, T_1) → многоугольник26, a_{10}, d_{12}, c_9, t_3
  45. Polygon(Z_1, E_2, D_2, A_1) → многоугольник27, z_1, e_6, d_{13}, a_{11}
  46. Polygon(U_1, F_2, E_2, Z_1) → многоугольник28, u_2, f_5, e_7, z_2
  47. Polygon(V_1, H_2, F_2, U_1) → многоугольник29, v_4, h_7, f_6, u_3
  48. Polygon(B_2, A_2, C_2, D_2, E_2, F_2, H_2, G_2) → многоугольник30, b_{10}, a_{12}, c_{10}, d_{14}, e_8, f_7, h_8, g_5
  49. Polygon(O_1, P_1, Q_1, M_1, L_1, N_1) → многоугольник31, o_3, p_3, q_3, m_3, l_4, n_4
  50. Corner(4) → I_2
  51. Corner(2) → J_2
  52. Segment(I_2, J_2) → d
  53. Point(d) → K_2
  54. Segment(I_2, K_2) → g
  55. Point(g) → L_2
  56. OrthogonalLine(L_2, g) → m
  57. Point(m) → M_2
  58. Mirror(M_2, L_2) → N_2

AI Drawing Prompt Reference

Create a demonstration of light refraction through a prism, showing the path of light as it passes through. Start by drawing three connected triangles to form the prism, then use mirror operations to generate multiple symmetric polygons, and finally combine these polygons to form a 3D geometric shape, illustrating the refraction of light and the construction of three-dimensional forms.
The prompt above was compiled from the original drawing commands and is for reference only.