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Fraction Circles on Number Line

Fraction Circles on Number Line
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2020-03-21 22:35
CircleCoordinate GeometryGeometric Construction
This example demonstrates how to visualize fraction sizes on a number line by drawing circles corresponding to each fraction. It involves core mathematical concepts like fraction representation, number line, circle geometry, and geometric transformations (rotation, reflection). Key GeoGebra commands/objects used include Intersect, Circle, Line, Rotate, Mirror, Parabola, Midpoint, Center, CircleArc, Point, OrthogonalLine, etc. Suitable for middle school and above students to enhance understanding of fractions, geometric transformations, and number line representation.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, f) → B
  2. Circle(B, 1 / 2) → c
  3. Intersect(c, xAxis, 1) → E
  4. Line(T, xAxis) → m
  5. Circle(T, 1 / 4) → t
  6. Rotate(m, (π * ((2 * num)) / (num + denom)), T) → xAxis'_1
  7. Intersect(t, m) → O, Q
  8. Mirror(O, xAxis'_1) → O'
  9. Intersect(t, xAxis'_1, 2) → R
  10. Intersect(eq1, xAxis) → A
  11. Intersect(g, eq1) → C
  12. Circle(C, A) → d
  13. Intersect(c, f, 1) → D
  14. Intersect(eq2, h) → F
  15. Intersect(eq2, xAxis) → G
  16. Circle(F, G) → e
  17. Intersect(r, yAxis) → L
  18. Mirror(r, xAxis) → r'
  19. Parabola(L, r') → s
  20. Intersect(s, vgl1) → M,
  21. Intersect(yAxis, f_1) → H
  22. Intersect(f_1, eq2) → I
  23. Midpoint(H, I) → J
  24. Circle(J, G, E) → k
  25. Center(k) → K
  26. Line(K, M) → i
  27. Intersect(k, i, 2) → N
  28. CircleArc(K, N, E) → p
  29. CircleArc(K, G, N) → q
  30. Mirror(N, eq3) → N'
  31. Intersect(f, eq3) → P
  32. Mirror(d, yAxis) → d'_1
  33. Mirror(e, yAxis) → e'_1
  34. Line(D, yAxis) → l
  35. Intersect(l, xAxis) → C_1
  36. Rotate(xAxis, 45°, C_1) → xAxis'
  37. Mirror(d, xAxis) → d'_2
  38. Mirror(e, xAxis) → e'_2
  39. Mirror(e'_2, yAxis) → p_1
  40. Mirror(d'_2, yAxis) → q_1
  41. Mirror(d'_1, xAxis') → r_1
  42. Mirror(q_1, xAxis') → s_1
  43. Mirror(e'_1, xAxis') → t_1
  44. Mirror(p_1, xAxis') → c_2
  45. Mirror(q_1, l) → d_2
  46. Mirror(e'_1, l) → e_2
  47. Mirror(c_2, xAxis) → f_2
  48. Mirror(t_1, xAxis) → g_2
  49. Intersect(eq4, xAxis) → G_1
  50. Midpoint(G_1, A) → I_1
  51. Circle(I_1, G_1) → q_2
  52. Mirror(q_2, yAxis) → r_2
  53. Mirror(r_2, l) → s_2
  54. Mirror(s_2, xAxis') → t_2
  55. Mirror(r_2, xAxis') → c_3
  56. Mirror(O', R) → O''
  57. Line(R, O'') → j
  58. Circle(O'', Distance[F, G]) → c_1
  59. Intersect(c_1, j, 2) → S
  60. Mirror(S, O'') → S'
  61. Circle(S, O'') → d_1
  62. Circle(S', O'') → e_1
  63. Intersect(s, m, 1) → V
  64. Intersect(s, m, 1) → W
  65. Point(m) → Z
  66. Circle(Z, O) → g_1
  67. Mirror(F, G) → F'
  68. OrthogonalLine(F', eq2) → a
  69. Parabola(F, a) → h_1