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Means Demonstration

Means Demonstration
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2019-04-02 08:08
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the mean in a normal distribution, isosceles triangles, trigonometry, and piecewise functions. It involves core mathematical concepts such as normal distribution, isosceles triangles, trigonometric functions, piecewise functions, and geometric constructions. The construction uses commands like Intersect, Point, Segment, Midpoint, Circle, OrthogonalLine, and Distance. It is suitable for high school students and teachers for teaching demonstrations and explorations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → X
  3. Segment(A, X) → f
  4. Point(xAxis) → B
  5. Segment(X, B) → g
  6. Midpoint(A, B) → O
  7. Circle(O, B) → c
  8. OrthogonalLine(X, f) → i
  9. Intersect(c, i) → E, G
  10. Segment(G, O) → h
  11. Segment(G, X) → j
  12. OrthogonalLine(X, h) → k
  13. Intersect(h, k) → H
  14. Segment(X, H) → l
  15. Segment(H, G) → m
  16. Distance(O, G) → distanceOG
  17. Distance(H, G) → distanceHG
  18. Distance(X, G) → distanceXG
  19. Distance(A, X) → distanceAX
  20. Distance(X, B) → distanceXB
  21. OrthogonalLine(X, g) → n
  22. OrthogonalLine(B, g) → p
  23. OrthogonalLine(A, xAxis) → q
  24. OrthogonalLine(H, h) → r
  25. OrthogonalLine(G, h) → s
  26. Point(q) → C
  27. OrthogonalLine(C, q) → t
  28. Point(n) → D
  29. Segment(X, D) → a
  30. Intersect(p, t) → F
  31. Segment(F, B) → d
  32. Intersect(q, t) → I
  33. Segment(I, A) → f_1
  34. Circle(G, 1) → c_1
  35. Circle(H, 1) → d_1
  36. Intersect(c_1, s) → J, K
  37. Intersect(d_1, r) → L, M
  38. Segment(G, K) → g_1
  39. Segment(H, M) → h_1
  40. Segment(K, M) → i_1
  41. Intersect(n, t) → N
  42. Intersect(t, yAxis) → P
  43. Intersect(p, t) → Q
  44. Segment(B, Q) → j_1
  45. Segment(Q, N) → k_1
  46. Segment(N, P) → l_1
  47. Segment(P, A) → m_1
  48. Segment(N, X) → n_1
  49. Circle(G, 1.5) → e
  50. Circle(O, 1.5) → e_1
  51. OrthogonalLine(O, h) → b
  52. OrthogonalLine(G, h) → p_1
  53. Intersect(e, p_1) → R, S
  54. Intersect(e_1, b) → T, U
  55. Segment(G, S) → q_1
  56. Segment(S, U) → r_1
  57. Segment(U, O) → s_1