MathPlotAI Logo MathPlotAI

Additional Fractions per Unit (Part 2)

Additional Fractions per Unit (Part 2)
Loading the math board and drawing, please wait…
2020-04-01 17:59
VectorProbability & StatisticsGeometric Construction
This example demonstrates the geometric construction and visualization of additional fractions per unit using GeoGebra, involving core concepts like fractions, binomial distribution, vectors, random experiments, spheres, and exponential functions. Key GeoGebra commands and objects used in the construction include Sequence, Rotate, CircleSector, GCD, Circle, Vector, Translate, Segment, Point, Midpoint, Mirror, and CircleArc. It is suitable for high school and advanced learners to explore complex mathematical ideas through dynamic geometry representations.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[B, ((i * 360) * ° / denom), A], i, 1, denom) → liste1
  2. Sequence(Segment[A, Element[liste1, i]], i, 1, denom) → liste3
  3. Rotate(B, ((num * 360) * ° / denom), A) → B'_1
  4. CircleSector(A, B, B'_1) → d
  5. GCD(num, denom) → PGCD
  6. Circle(A, B) → e
  7. Circle(A, B) → c
  8. Sequence(Segment[A, Element[liste1, i]], i, 1, denom) → liste2
  9. Circle(A, B) → h
  10. Vector(A, C) → u
  11. Translate(h, u) → h'
  12. Translate(B, u) → D
  13. Rotate(D, ((num * 360) * ° / denom), C) → D'
  14. Sequence(Rotate[D, (((PGCD * i) * 360) * ° / denom), C], i, 1, denom / PGCD) → liste4
  15. CircleSector(C, D, D') → k
  16. Sequence(Segment[C, Element[liste4, i]], i, 1, denom / PGCD) → liste5
  17. CircleSector(C, D, D') → f
  18. Segment(E, F) → i
  19. Segment(G, H) → j
  20. Circle(I, R) → p
  21. Point(p) → J
  22. Rotate(J, ((num * 360) * ° / denom), I) → J'
  23. CircleSector(I, J, J') → q
  24. Sequence(Rotate[J, ((i * 360) * ° / denom), I], i, 1, num) → liste1b
  25. Sequence(Segment[I, Element[liste1b, i]], i, 1, num) → liste2b
  26. CircleSector(I, J, J') → r
  27. Circle(K, R) → s
  28. Point(s) → L
  29. Rotate(L, ((num * 360) * ° / denom), K) → L'
  30. CircleSector(K, L', L) → t
  31. Sequence(Rotate[L', ((i * 360) * ° / denom), K], i, 1, denom) → liste1c
  32. Sequence(Segment[K, Element[liste1c, i]], i, 1, denom - num) → liste2c
  33. CircleSector(K, L', L) → c_1
  34. Midpoint(I, J) → N
  35. Rotate(N, (((0.5 * num) * 360) * ° / denom), I) → N'
  36. Midpoint(K, L) → O
  37. Rotate(O, (((0.5 * num) * 360) * ° / denom), K) → L'_1
  38. Mirror(L'_1, K) → P
  39. Circle(M, R) → d_1
  40. Point(d_1) → Q
  41. Rotate(Q, ((num * 360) * ° / denom), M) → Q'
  42. CircleSector(M, Q, Q') → e_1
  43. CircleSector(M, Q, Q') → f_1
  44. Sequence(Rotate[Q, (((PGCD * i) * 360) * ° / denom), M], i, 1, num2) → liste4b
  45. Sequence(Segment[M, Element[liste4b, i]], i, 1, num / PGCD) → liste5b
  46. Segment(M, Q) → l
  47. Segment(M, Q') → m
  48. CircleArc(M, Q, Q') → g_1
  49. Circle(R_1, R) → h_1
  50. Point(h_1) → S
  51. Rotate(S, ((num * 360) * ° / denom), R_1) → S'
  52. CircleSector(R_1, S', S) → k_1
  53. CircleSector(R_1, S', S) → p_1
  54. Sequence(Rotate[S', ((i * 360) * ° / denom2), R_1], i, 1, denom2 - num2) → liste4c
  55. Sequence(Segment[R_1, Element[liste4c, i]], i, 1, denom - num) → liste5c
  56. Midpoint(M, Q) → T
  57. Rotate(T, (((0.5 * num) * 360) * ° / denom), M) → T'
  58. Midpoint(R_1, S) → U
  59. Rotate(U, (((0.5 * num) * 360) * ° / denom), R_1) → U'
  60. Mirror(U', R_1) → U''