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Geometric Demonstration of Square Fractions

Geometric Demonstration of Square Fractions
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2017-09-09 02:26
PolygonFunctionGeometric Construction
This example dynamically demonstrates dividing a square into fourths, visually illustrating the geometric meaning of fractions. Core math concepts include fractions, geometric partitioning, and square properties. Construction highlights the use of commands/objects like Polygon, Segment, Midpoint, Point, and Intersect in GeoGebra. Suitable for middle school and above mathematics education, focusing on the integration of fractions and geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. Polygon(A, B, D) → poly2, d, a, b
  3. Segment(B, D) → j
  4. Midpoint(a) → E
  5. Polygon(B, E, C) → poly3, c, b_1, e
  6. Segment(E, C) → k
  7. Segment(E, D) → l
  8. Midpoint(E, D) → G
  9. Midpoint(D, C) → H
  10. Polygon(D, G, H) → poly5, h_2, d_1, g_2
  11. Point(a) → I
  12. Segment(E, I) → q
  13. Segment(E, B) → r
  14. Intersect(g, b_1) → K
  15. Segment(B, K) → s
  16. Intersect(h, i) → L
  17. Intersect(f, i) → M
  18. Segment(L, M) → j_1
  19. Segment(M, B) → k_1
  20. Segment(I, L) → l_1
  21. Segment(E, M) → m
  22. Segment(L, K) → n
  23. Intersect(h, d_1) → F
  24. Polygon(E, F, I) → t1, i_1, e_1, f_1
  25. Midpoint(E, K) → J
  26. Midpoint(E, B) → N
  27. Midpoint(B, K) → O
  28. Polygon(E, J, F) → t2, f_2, e_2, j_2
  29. Polygon(J, K, F) → t3, f_3, j_3, k_2
  30. Polygon(B, O, N) → t4, n_1, b_2, o
  31. Polygon(N, J, E) → t5, e_3, n_2, j_4
  32. Polygon(N, O, J) → t6, j_5, n_3, o_1
  33. Polygon(O, K, J) → t7, j_6, o_2, k_3
  34. Segment(M, K) → p
  35. Segment(O, F) → t
  36. Segment(I, F) → g_1
  37. Segment(N, J) → h_1
  38. Segment(N, O) → m_1
  39. Segment(E, F) → p_1
  40. Segment(B, E) → q_1