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GeoGebra Optimization Example

GeoGebra Optimization Example
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2023-03-22 02:03
TrigonometryCoordinate GeometryOptimizationGeometric Construction
In collections Realidades de GeoGebra
This example demonstrates the process of solving geometric optimization problems using GeoGebra. It involves core mathematical concepts such as angles, triangle constructions, optimization problems, trigonometry, geometric distribution, frequency distribution, and linear equations. The construction highlights commands and objects like Segment, Circle, Intersect, Polygon, Midpoint, and Angle. Suitable for high school and above learners to understand geometric optimization solutions and visualization.

GeoGebra Commands & Parameters

  1. Segment(P, P_1) → c
  2. Segment(D, E) → m_2
  3. Segment(P, P_3) → b
  4. Segment(P, P_2) → a
  5. Circle(P_1, P_3 / verSolucion) → e
  6. Circle(P_3, P_1) → f
  7. Intersect(e, f, 2) → F
  8. Polygon(P_1, P_3, F) → Q, f_1, p_1, p_3
  9. Circle(P_2, P_3 / verSolucion) → d
  10. Circle(P_3, P_2) → g
  11. Intersect(d, g, 1) → G
  12. Polygon(P_3, P_2, G) → R, g_1, p_2, p_4
  13. Circle(P_1, P_2 / verSolucion) → h
  14. Circle(P_2, P_1) → k
  15. Intersect(h, k, 1) → H
  16. Polygon(P_2, H, P_1) → S, p_5, p_6, h_1
  17. Midpoint(G, P_3) → K
  18. Midpoint(P_2, G) → J
  19. Midpoint(P_2, H) → L
  20. Midpoint(H, P_1) → M
  21. Midpoint(P_3, F) → N
  22. Midpoint(F, P_1) → O
  23. Segment(H, P_3) → i
  24. Segment(G, P_1) → j
  25. Segment(F, P_2) → l
  26. Intersect(j, l) → T
  27. Angle(P_1, P, P_3) → α
  28. Angle(P_3, P, P_2) → β
  29. Angle(P_2, P, P_1) → γ
  30. Segment(I_1, U) → m
  31. Segment(V, W) → n
  32. Segment(Z, A_1) → p
  33. Segment(A_1, B_1) → r
  34. Segment(U, V) → t
  35. Segment(W, Z) → d_1
  36. Segment(B_1, P_3) → q
  37. Segment(I_1, C_1) → e_1
  38. Segment(D_1, E_1) → i_1
  39. Segment(F_1, G_1) → j_1
  40. Segment(H_1, J_1) → k_1
  41. Segment(K_1, P_2) → l_1
  42. Segment(I_1, L_1) → n_1
  43. Segment(W_1, P_1) → d_2
  44. Segment(K_1, J_1) → e_2
  45. Segment(H_1, G_1) → f_2
  46. Segment(F_1, E_1) → g_2
  47. Segment(D_1, C_1) → h_2
  48. Segment(L_1, M_1) → i_2
  49. Segment(W_1, N_1) → q_1
  50. Segment(N_1, O_1) → r_1
  51. Segment(O_1, Q_1) → s_1
  52. Segment(Q_1, R_1) → t_1
  53. Segment(R_1, S_1) → a_2
  54. Segment(S_1, T_1) → b_2
  55. Segment(M_1, T_1) → c_2

AI Drawing Prompt Reference

Draw a triangle with three vertices. Construct an equilateral triangle outward on each side of the original triangle, creating three external equilateral triangles. Connect each outer vertex to the midpoint of the opposite side of the original triangle; these three segments intersect at a common point. Then add a series of auxiliary segments around the figure, forming a complex grid of lines and polygons. Label the three interior angles of the original triangle. The final diagram shows a symmetric geometric optimization layout with midpoints, intersections, and multiple polygonal regions.
The prompt above was compiled from the original drawing commands and is for reference only.