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Splitting into Equal Shapes

Splitting into Equal Shapes
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2018-11-03 20:51
CirclePolygonProbability & StatisticsGeometric Construction
This example demonstrates how to split shapes into equal parts. It involves core mathematical concepts like area, geometry, logic, and probability & statistics. Construction highlights include using GeoGebra commands such as Circle, Point, Polygon, Intersect, Line with objects like C_1, poly1, a_1. Suitable for middle school and above students to learn geometric constructions and spatial reasoning.

GeoGebra Commands & Parameters

  1. Circle(C_1, 3) → c_{1Ar3}
  2. Point(c_{1Ar3}) → R_1
  3. Polygon(C_1, R_1, 3) → poly1, a_1, g, h, C
  4. Circle(C_1, 2) → c_{1Ar2}
  5. Circle(C_1, 1) → c_{1Ar1}
  6. Circle(R_1, 2) → c_{1Br2}
  7. Circle(R_1, 1) → c_{1Br1}
  8. Intersect(c_{1Ar2}, h, 1) → A_1
  9. Intersect(c_{1Ar1}, h, 1) → B_1
  10. Intersect(c_{1Br1}, g, 1) → D_1
  11. Intersect(c_{1Br2}, g, 1) → E_1
  12. Line(A_1, g) → i_1
  13. Line(E_1, h) → j_1
  14. Intersect(i_1, j_1) → F_1
  15. Polygon(C_1, A_1, F_1, D_1, R_1) → poly1_A, c_1, g_1, l_1, e_1, r_1
  16. Polygon(C_1, R_1, E_1, F_1, B_1) → poly1_B, b_1, m_1, f_1, h_1, d_1
  17. Circle(C_2, 3) → c_{2Ar3}
  18. Point(c_{2Ar3}) → R_2
  19. Polygon(C_2, R_2, 3) → poly2, b_2, i, j, A
  20. Circle(C_2, 2) → c_{2Ar2}
  21. Circle(C_2, 1) → c_{2Ar1}
  22. Circle(R_2, 2) → c_{2Br2}
  23. Intersect(c_{2Br2}, i, 1) → D_2
  24. Intersect(c_{2Ar2}, j, 1) → E_2
  25. Intersect(c_{2Ar1}, j, 1) → F_2
  26. Line(E_2, i) → i_2
  27. Line(F_2, b_2) → j_2
  28. Intersect(i, j_2) → B_2
  29. Intersect(i_2, j_2) → A_2
  30. Polygon(R_2, C_2, E_2, A_2, B_2) → poly2_A, r_2, c_2, e_2, g_2, h_2
  31. Polygon(C_2, R_2, D_2, A_2, F_2) → poly2_B, a_2, m_2, d_2, l_2, f_2
  32. Circle(C_3, 3) → c_{3Ar3}
  33. Point(c_{3Ar3}) → R_3
  34. Polygon(C_3, R_3, 3) → poly3, b_3, k, l, B
  35. Circle(C_3, 2) → c_{3Ar2}
  36. Circle(C_3, 1) → c_{3Ar1}
  37. Circle(R_3, 2) → c_{3Br2}
  38. Intersect(c_{3Ar1}, l, 1) → D_3
  39. Intersect(c_{3Ar2}, l, 1) → E_3
  40. Intersect(c_{3Br2}, k, 1) → F_3
  41. Line(D_3, b_3) → j_3
  42. Line(F_3, l) → i_3
  43. Intersect(j_3, i_3) → A_3
  44. Intersect(j_3, k) → B_3
  45. Polygon(C_3, E_3, A_3, B_3, R_3) → poly3_A, c_3, e_3, g_3, h_3, r_3
  46. Polygon(R_3, F_3, A_3, D_3, C_3) → poly3_B, m_3, f_3, l_3, d_3, a_3
  47. Circle(C_4, 3) → c_{4Ar3}
  48. Point(c_{4Ar3}) → R_4
  49. Polygon(C_4, R_4, 3) → poly4, r_4, m, n, D
  50. Circle(C_4, 1) → c_{4Ar1}
  51. Circle(C_4, 2) → c_{4Ar2}
  52. Circle(R_4, 2) → c_{4Br2}
  53. Intersect(c_{4Ar1}, n, 1) → E_4
  54. Intersect(c_{4Ar2}, n, 1) → F_4
  55. Intersect(c_{4Br2}, m, 1) → A_4
  56. Line(A_4, n) → j_4
  57. Line(E_4, r_4) → i_4
  58. Intersect(j_4, i_4) → D_4
  59. Intersect(i_4, m) → B_4
  60. Polygon(F_4, C_4, R_4, B_4, D_4) → poly4_A, c_4, b_4, f_4, d_4, h_4
  61. Polygon(A_4, D_4, E_4, C_4, R_4) → poly4_B, g_4, l_4, e_4, a_4, m_4
  62. Point(xAxis) → E_{frame}
  63. Circle(E_{frame}, 6) → c_{frame6}
  64. Intersect(c_{frame6}, xAxis, 2) → F_{frame}
  65. Polygon(E_{frame}, F_{frame}, 3) → poly5, f, p, q, G
  66. Circle(F_{frame}, 4) → c_{frame4}
  67. Intersect(c_{frame4}, p, 1) → H_{frame}
  68. Circle(E_{frame}, 2) → c_{frame2}
  69. Intersect(c_{frame2}, q, 1) → I_{frame}
  70. Line(H_{frame}, q) → j_6
  71. Line(I_{frame}, f) → i_6
  72. Intersect(j_6, i_6) → J_{frame}
  73. Polygon(E_{frame}, F_{frame}, H_{frame}, J_{frame}, I_{frame}) → poly6, e_{frame}, f_{frame}, h_{frame}, j_{frame}, i_{frame}