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Square Construction by ADarkenedAlley

Square Construction by ADarkenedAlley
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2013-04-13 09:04
PolygonCoordinate GeometryGeometric Construction
In collections Square Translation Tessellation
This example demonstrates how to construct a square using GeoGebra, involving core math concepts like polygons, linear equations, natural numbers, integral calculus, exponents, and roots. Key GeoGebra commands used include Polygon, Segment, and Point for geometric construction, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(C, E) → e
  3. Segment(E, F) → f
  4. Segment(F, G) → g
  5. Segment(G, H) → h
  6. Segment(H, B) → i
  7. Polygon(A_1, B_1, 4) → poly1_1, a_1, b_1, c_1, d_1, C_1, D_1
  8. Segment(C_1, E_1) → e_1
  9. Segment(E_1, F_1) → f_1
  10. Segment(F_1, G_1) → g_1
  11. Segment(G_1, H_1) → h_1
  12. Segment(H_1, B_1) → i_1
  13. Segment(D, I) → j
  14. Point(c) → J
  15. Segment(I, J) → k
  16. Segment(K, J) → l
  17. Segment(K, L) → m
  18. Segment(L, M) → n
  19. Point(c) → N
  20. Segment(M, N) → p
  21. Segment(C, N) → q
  22. Polygon(A_2, B_2, 4) → poly1_2, a_3, b_3, c_2, d_3, C_2, D_2
  23. Polygon(A_3, B_3, 4) → poly1_3, a_2, b_2, c_3, d_2, C_3, D_3
  24. Segment(D_2, I_1) → j_1
  25. Point(c_2) → J_1
  26. Segment(I_1, J_1) → k_1
  27. Segment(K_1, J_1) → l_1
  28. Segment(K_1, L_1) → m_1
  29. Segment(L_1, M_1) → n_1
  30. Point(c_2) → N_1
  31. Segment(M_1, N_1) → p_1
  32. Segment(C_2, N_1) → q_1
  33. Polygon(E, C, F_1, G_1, H_1, A, I_1, J_1, K_1, L_1, M_1, N_1, N, B, H, G, F, M, L, K, J, I, D, E_1) → poly2, e_2, e_3, f_2, g_2, h_2, a_4, i_3, j_3, k_3, l_3, m_3, c_4, n_3, b_4, h_3, g_3, f_3, n_2, m_2, l_2, k_2, j_2, i_2, d_4

AI Drawing Prompt Reference

Draw a square by connecting four points to form its sides, and show the geometric relationships inside and outside. First, construct a square, then draw lines from one vertex to the midpoint of the opposite side, and expand outward to create multiple related geometric shapes, including several squares and connecting lines, forming a complex pattern.
The prompt above was compiled from the original drawing commands and is for reference only.