Square Puzzle

Square Puzzle
Loading the math board and drawing, please wait…
2023-01-18 06:21
This example demonstrates a square puzzle, involving the geometric properties of a square. Using GeoGebra commands such as Intersect, Point, and Polygon, various parts of the square can be constructed. Suitable for middle school and above students, this example is useful for geometric construction and learning about squares.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Midpoint(h) → E
  5. Midpoint(g) → F
  6. Midpoint(f) → G
  7. Midpoint(i) → H
  8. Centroid(poly1) → I
  9. Segment(H, C) → j
  10. Segment(E, B) → k
  11. Segment(F, A) → l
  12. Segment(G, D) → m
  13. Intersect(j, m) → J
  14. Intersect(j, k) → K
  15. Intersect(k, l) → L
  16. Intersect(l, m) → M
  17. Polygon(H, J, D) → t1, d, h_1, j_1
  18. Polygon(K, E, C) → t2, c, k_1, e
  19. Polygon(B, F, L) → t3, l_1, b, f_1
  20. Polygon(G, M, A) → t4, a, g_1, m_1
  21. Polygon(A, M, J, H) → q1, a_1, m_2, j_2, h_2
  22. Polygon(J, D, E, K) → q2, j_3, d_1, e_1, k_2
  23. Polygon(L, K, C, F) → q3, l_2, k_3, c_1, f_2
  24. Polygon(L, M, G, B) → q4, l_3, m_3, g_2, b_1
  25. Polygon(L, M, J, K) → q5, l_4, m_4, j_4, k_4
  26. Rotate(B, aa, F) → B'
  27. Rotate(F, aa, F) → F'
  28. Rotate(L, aa, F) → L'
  29. Polygon(B', F', L') → t3', l', b', f'
  30. Rotate(K, aa, E) → K'
  31. Rotate(E, aa, E) → E'
  32. Rotate(C, aa, E) → C'
  33. Polygon(K', E', C') → t2', c', k', e'
  34. Rotate(H, aa, H) → H'
  35. Rotate(J, aa, H) → J'
  36. Rotate(D, aa, H) → D'
  37. Polygon(H', J', D') → t1', d', h', j'
  38. Rotate(G, aa, G) → G'
  39. Rotate(M, aa, G) → M'
  40. Rotate(A, aa, G) → A'
  41. Polygon(G', M', A') → t4', a', g', m'

AI Drawing Prompt Reference

Draw a square and demonstrate its internal geometric division. Start by constructing a square, then find the midpoints of opposite sides and connect them to form a new quadrilateral. Further divide these quadrilaterals into smaller polygons, creating a complex geometric pattern. Ensure the symmetry and geometric accuracy of the design.
The prompt above was compiled from the original drawing commands and is for reference only.