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Fraction Associations: Interactive Random Circles and Geometric Probability

Fraction Associations: Interactive Random Circles and Geometric Probability
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2020-04-01 17:22
CircleProbability & StatisticsInequalityGeometric Construction
① This GeoGebra example demonstrates the association between fractions, inequalities, and geometric probability through randomly generated points and circles, incorporating circumcircles and area concepts. ② Core mathematical concepts include fraction representation, differential equations (as a background tag), inequalities, area calculation, circumscribed circles, and random experiments; the inclusion of random points in circles links fractions to probability visually. ③ Construction highlights: using GeoGebra commands Random, Shuffle, Element, If, and Circle to generate random point sets and circles, with multiple objects (a, e, d, b, bb, dd, f, aa, ff, ee, ar, br, c, cc, cr, dr, er, fr, lijst) and a button Bouton1 that triggers random shuffling to dynamically update fraction associations. ④ Suitable for middle school mathematics, this tool aids teaching fraction concepts, geometric probability, inequalities, and circle properties, and serves as an interactive exploration of random experiments and area relationships.

GeoGebra Commands & Parameters

  1. Random(1, 12) → a
  2. Random(1, 12) → e
  3. Random(1, 12) → d
  4. Random(1, 12) → b
  5. Random(1, 12) → bb
  6. Random(1, 12) → dd
  7. Random(1, 12) → f
  8. Random(1, 12) → aa
  9. Random(1, 12) → ff
  10. Random(1, 12) → ee
  11. Random(1, 12) → c
  12. Random(1, 12) → cc
  13. Shuffle({(-10, 3.5), (0, 3.5), (10, 3.5), (-10, -3), (0, -3), (10, -3)}) → lijst, {(-10, -3), (0, 3.5), (10, 3.5), (10, -3), (-10, 3.5), (0, -3)}
  14. Element(lijst, 1) → A
  15. Element(lijst, 2) → B
  16. Element(lijst, 3) → C
  17. Element(lijst, 4) → D
  18. Element(lijst, 5) → E
  19. Element(lijst, 6) → F
  20. If(Distance[A, AA] < 0.5, ar, If[Distance[A, BB] < 0.5, br, If[Distance[A, CC] < 0.5, cr, If[Distance[A, DD] < 0.5, dr, If[Distance[A, EE] < 0.5, er, If[Distance[A, FF] < 0.5, fr, 0]]]]]) → anta
  21. If(Distance[B, AA] < 0.5, ar, If[Distance[B, BB] < 0.5, br, If[Distance[B, CC] < 0.5, cr, If[Distance[B, DD] < 0.5, dr, If[Distance[B, EE] < 0.5, er, If[Distance[B, FF] < 0.5, fr, 0]]]]]) → antb
  22. If(Distance[C, AA] < 0.5, ar, If[Distance[C, BB] < 0.5, br, If[Distance[C, CC] < 0.5, cr, If[Distance[C, DD] < 0.5, dr, If[Distance[C, EE] < 0.5, er, If[Distance[C, FF] < 0.5, fr, 0]]]]]) → antc
  23. If(Distance[D, AA] < 0.5, ar, If[Distance[D, BB] < 0.5, br, If[Distance[D, CC] < 0.5, cr, If[Distance[D, DD] < 0.5, dr, If[Distance[D, EE] < 0.5, er, If[Distance[D, FF] < 0.5, fr, 0]]]]]) → antd
  24. If(Distance[E, AA] < 0.5, ar, If[Distance[E, BB] < 0.5, br, If[Distance[E, CC] < 0.5, cr, If[Distance[E, DD] < 0.5, dr, If[Distance[E, EE] < 0.5, er, If[Distance[E, FF] < 0.5, fr, 0]]]]]) → ante
  25. If(Distance[F, AA] < 0.5, ar, If[Distance[F, BB] < 0.5, br, If[Distance[F, CC] < 0.5, cr, If[Distance[F, DD] < 0.5, dr, If[Distance[F, EE] < 0.5, er, If[Distance[F, FF] < 0.5, fr, 0]]]]]) → antf
  26. Random(2, 4) → faca
  27. Random(2, 4) → facb
  28. Random(2, 4) → facc
  29. Random(2, 4) → facd
  30. Random(2, 4) → face
  31. Random(2, 4) → facf
  32. Circle(A, 1.5) → g
  33. Circle(C, 1.5) → g_2
  34. Circle(D, 1.5) → g_3
  35. Circle(E, 1.5) → g_4
  36. Circle(F, 1.5) → g_5
  37. Circle(B, 1.5) → g_1
  38. Circle(AA, 1.5) → h
  39. Circle(BB, 1.5) → k
  40. Circle(CC, 1.5) → p
  41. Circle(DD, 1.5) → q
  42. Circle(EE, 1.5) → r
  43. Circle(FF, 1.5) → s
  44. Circle(AA, 1.5) → t
  45. Circle(BB, 1.5) → c_1
  46. Circle(CC, 1.5) → d_1
  47. Circle(DD, 1.5) → e_1
  48. Circle(EE, 1.5) → f_1
  49. Circle(FF, 1.5) → h_1