Area of Equal Composition Figures

Area of Equal Composition Figures
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2016-02-02 04:47
This example demonstrates three problems on the area of equal composition figures. Key mathematical concepts include geometric construction, transformation, and coordinate geometry. Using GeoGebra commands such as RotateText, Point, Translate, Segment, and Polygon, students can visually understand the properties of equal composition figures. Suitable for middle school and above students.

GeoGebra Commands & Parameters

  1. RotateText("uStas\;\&\;Т.С.", 90*°) → надпись01
  2. Point(Arc[Circle[B, 0.5], 0, 3]) → C
  3. Point(Segment[A, B]) → M
  4. Translate(M, Vector[B, C]) → N
  5. Segment(M, N) → e
  6. Polygon(A, M, D) → s1, d, a, m
  7. Polygon(N, D, M) → s2, m_1, n, d_1
  8. Polygon(M, B, C) → s3, b, f, g
  9. Polygon(C, N, M) → s4, c, h, i
  10. Polygon(A, B, C, D) → s5, a_4, b_5, c_5, d_6
  11. Polygon(C, M, D) → s6, d_7, c_6, m_{10}
  12. Point(Arc[Circle[B_2, 0.5], 0, 3]) → C_2
  13. Polygon(A_2, B_2, C_2, D_2) → s7, a_2, b_2, c_2, d_2
  14. Polygon(A_2 + (0.01, 0.01), B_2 + (-0.01, 0.01), C_2 + (-0.01, -0.01), D_2 + (0.01, -0.01)) → s8, l, p, q, r
  15. PointIn(s8) → M_2
  16. Line(M_2, Line[A_2, D_2]) → j
  17. Intersect(j, a_2) → N_1
  18. Intersect(j, c_2) → N_2
  19. Segment(N_1, N_2) → h_1
  20. Line(M_2, Line[A_2, B_2]) → k
  21. Intersect(d_2, k) → L_1
  22. Intersect(k, b_2) → L_2
  23. Segment(L_1, L_2) → i_1
  24. Polygon(A_2, N_1, M_2) → t1, s, t, a_1
  25. Polygon(M_2, L_1, A_2) → t2, e_1, f_1, g_1
  26. Polygon(B_2, M_2, N_1) → t3, n_6, b_1, m_3
  27. Polygon(M_2, B_2, L_2) → t4, l_3, m_4, b_3
  28. Polygon(C_2, M_2, L_2) → t5, l_4, c_1, m_5
  29. Polygon(M_2, C_2, N_2) → t6, n_4, m_6, c_3
  30. Polygon(D_2, L_1, M_2) → t7, m_7, d_3, l_5
  31. Polygon(M_2, N_2, D_2) → t8, d_4, m_8, n_5
  32. Polygon(A_2, B_2, M_2) → t9, m_2, a_3, b_4
  33. Polygon(C_2, M_2, D_2) → t91, d_5, c_4, m_9
  34. Point(Arc[Circle[B_3, 0.5], 0, 3]) → C_3
  35. Point(Ray[Translate[A_3, Vector[0.9 * Vector[B_3, A_3]]], B_3]) → A'
  36. Translate(A', Vector[A_3, B_3]) → B'
  37. Polygon(A_3, B_3, C_3, D_3) → p1, a_5, b_6, c_7, d_8
  38. Polygon(A', B', C_3, D_3) → p2, a', b', c_8, d_9
  39. Polygon(A_3, A', D_3) → p3, d_{10}, a_6, a'_1
  40. Polygon(B_3, B', C_3) → p4, c_9, b_7, b'_1
  41. Polygon(A_3, B', C_3, D_3) → p5, a_7, b'_2, c_{10}, d_{11}

AI Drawing Prompt Reference

Draw a complex geometric figure with multiple polygons and points, demonstrating equal area compositions. Include a central rotating text label and four main polygons interconnected by points and line segments, forming intricate relationships. Start with the central text and basic polygon framework, then add connecting points and lines, and finally fill the polygons to highlight the equal area constructions.
The prompt above was compiled from the original drawing commands and is for reference only.