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Slippery surface 04：Geometric Construction and Optimization

Slippery surface 04：Geometric Construction and Optimization
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2015-05-28 15:42
Solid GeometryDerivativeOptimizationGeometric Construction
In collections Slippery surface
This example demonstrates geometric construction and optimization problems. Key mathematical concepts include derivatives, linear programming, and solid geometry. Construction involves using GeoGebra commands like Polygon, Segment, Intersect, and multiple geometric objects. Suitable for high school students or college undergraduates learning geometry and optimization techniques.

GeoGebra Commands & Parameters

  1. Polygon(E, F, B, N, O, R, S, T, U, V, W, Z, G, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, H, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, I, J, K, L, M, A) → camino, c, m, p, q, i_1, s_1, t_1, c_2, d_2, e_2, f_2, d, g_2, h_2, j_2, k_2, l_2, m_2, n_2, p_2, q_2, r_2, e, s_2, t_2, a_3, b_3, c_3, d_3, e_3, f_3, g_3, f, g, h, j, k, l
  2. Segment(Q, P) → segmento
  3. Intersect(segmento, camino) → corte, corte_1, corte_2, corte_3
  4. Segment(C, D) → llegada
  5. Intersect(llegada, segmento) → corteganador
  6. Vector(ejemplo, ejemplopunta) → ejemplovector
  7. PolyLine(listarastro) → rastro
  8. Vector(controles + (1, 1), controles + (0, 1)) → izq
  9. Vector(controles + (2, 0.5), controles + (2, 1.5)) → arr
  10. Vector(controles + (3, 1.5), controles + (3, 0.5)) → aba
  11. Vector(controles + (4, 1), controles + (5, 1)) → der
  12. Vector(ejemplo, puntoexplicado) → vectorexplicado_1
  13. Vector(puntoexplicado, ejemplopunta) → vectorexplicado_2
  14. Vector(P, P + (i * (Q - P))) → segmentovisible
  15. Polygon((0, 0), (0.8, 0), (0.8, 1.8), (0, 1.8)) → rectangulito, rectangulito_2, rectangulito_3, rectangulito_4, rectangulito_5
  16. Translate(Rotate[rectangulito, 90*°], controles + (5.4, 0.6)) → der_F
  17. Translate(rectangulito, controles + (2.6, 0.1)) → aba_F
  18. Translate(rectangulito, controles + (1.6, 0.1)) → arr_F
  19. Translate(Rotate[rectangulito, 90*°], controles + (1.4, 0.6)) → izq_F

AI Drawing Prompt Reference

Draw a graphic with multiple geometric objects. First, draw a rectangle, then rotate and translate it. Next, draw some line segments and vectors that intersect with the rectangle. Finally, draw arrows and vectors to show their relationships. Ensure the graphic is clear and easy to understand.
The prompt above was compiled from the original drawing commands and is for reference only.