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Quarters of a Square

Quarters of a Square
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2019-01-17 06:37
TriangleOptimizationGeometric Construction
This example demonstrates how to divide a square into four similar triangles. Core math concepts include similar triangles, geometric construction, and vector operations. It uses commands like Point, Polygon, Segment, Midpoint, Centroid, Circle, Intersect, Vector, Translate in GeoGebra. Suitable for high school mathematics teaching, explaining properties of similar triangles and optimization problems.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  4. Polygon(E, F, 4) → poly2, j, k, l, m, G, H
  5. Segment(H, F) → n
  6. Segment(E, G) → p
  7. Midpoint(i) → I
  8. Midpoint(m) → J
  9. Midpoint(l) → K
  10. Midpoint(k) → L
  11. Midpoint(j) → M
  12. Midpoint(n) → N
  13. Midpoint(h) → O
  14. Midpoint(g) → P
  15. Centroid(poly1) → Q
  16. Centroid(poly1) → R
  17. Midpoint(f) → S
  18. Polygon(D, I, J, E, N, H, K, O) → poly3, d, i_1, j_1, e, n_1, h_1, k_1, o
  19. Polygon(O, K, H, N, G, L, P, C) → poly4, o_1, k_2, h_2, n_2, g_1, l_1, p_1, c
  20. Polygon(L, G, N, F, M, S, B, P) → poly5, l_2, g_2, n_3, f_1, m_1, s, b, p_2
  21. Polygon(I, A, S, M, F, N, E, J) → poly6, i_2, a, s_1, m_2, f_2, n_4, e_1, j_2
  22. Circle(N, r) → q
  23. Intersect(q, h_2) → T,
  24. Intersect(q, g_2) → U,
  25. Vector(N, T) → u
  26. Vector(N, U) → v
  27. Translate(O, v) → O'
  28. Translate(K, v) → K'
  29. Translate(H, v) → H'
  30. Translate(N, v) → N'
  31. Translate(G, v) → G'
  32. Translate(L, v) → L'
  33. Translate(P, v) → P'
  34. Translate(C, v) → C'
  35. Polygon(O', K', H', N', G', L', P', C') → poly4', o', k', h', n', g', l', p', c'
  36. Translate(D, u) → D'
  37. Translate(I, u) → I'
  38. Translate(J, u) → J'
  39. Translate(E, u) → E'
  40. Translate(N, u) → N'_1
  41. Translate(H, u) → H'_1
  42. Translate(K, u) → K'_1
  43. Translate(O, u) → O'_1
  44. Polygon(D', I', J', E', N'_1, H'_1, K'_1, O'_1) → poly3', d', i', j', e', n'_1, h'_1, k'_1, o'_1
  45. Translate(I, Vector[(-v)]) → I'_1
  46. Translate(A, Vector[(-v)]) → A'
  47. Translate(S, Vector[(-v)]) → S'
  48. Translate(M, Vector[(-v)]) → M'
  49. Translate(F, Vector[(-v)]) → F'
  50. Translate(N, Vector[(-v)]) → N'_2
  51. Translate(E, Vector[(-v)]) → E'_1
  52. Translate(J, Vector[(-v)]) → J'_1
  53. Polygon(I'_1, A', S', M', F', N'_2, E'_1, J'_1) → poly6', i'_1, a', s', m', f', n'_2, e'_1, j'_1
  54. Translate(L, Vector[(-u)]) → L'_1
  55. Translate(G, Vector[(-u)]) → G'_1
  56. Translate(N, Vector[(-u)]) → N'_3
  57. Translate(F, Vector[(-u)]) → F'_1
  58. Translate(M, Vector[(-u)]) → M'_1
  59. Translate(S, Vector[(-u)]) → S'_1
  60. Translate(B, Vector[(-u)]) → B'
  61. Translate(P, Vector[(-u)]) → P'_1
  62. Polygon(L'_1, G'_1, N'_3, F'_1, M'_1, S'_1, B', P'_1) → poly5', l'_1, g'_1, n'_3, f'_1, m'_1, s'_1, b', p'_1

AI Drawing Prompt Reference

Draw a square and divide it into four similar triangles by connecting midpoints of opposite sides, forming intersecting lines. Mark the intersection points and draw new polygons using these points. Draw a circle centered at the square's center that intersects the lines. Translate some points along the vector direction from the center and connect them to form nested polygons.
The prompt above was compiled from the original drawing commands and is for reference only.