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Find the Rolling Function

Find the Rolling Function
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2017-09-30 23:38
FunctionTrigonometryGeometric Construction
This example demonstrates how to use the sine function to simulate the rolling of an object. Key mathematical concepts include the properties of the sine function and its application in practical problems. Using GeoGebra commands such as Intersect, Segment, Polygon, etc., a dynamic graphical representation of the object's rolling can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → O
  2. Segment(O, E) → f
  3. Polygon((-4, -4, 0), (((2 * π) * r) + 4, -4, 0), (((2 * π) * r) + 4, h + 4, 0), (-4, h + 4, 0)) → v2, p, q, s, t
  4. Cylinder(M_1, M_2, r) → b, d, e_1, g
  5. Plane(M, N, P) → e
  6. Line(M_2, M_1) → j
  7. Sequence(Segment[Rotate[O, i°, j], Rotate[E, i°, j]], i, 0, 359) → Lm
  8. Sequence(Rotate[O, i°, j], i, 0, 359) → Lpu
  9. Polygon(M, N, P, Q) → v4, m_1, n_1, p_1, q_1
  10. Line((abw, 0, r), (abw, h, r)) → dre
  11. Rotate(J, o°, dre) → J'
  12. Circle(dre, J) → k
  13. Translate(g, Vector[J]) → g'
  14. Segment(K, J') → m
  15. Segment(O, J) → n
  16. Segment(J', R) → c
  17. Ray(((π * r / 2), 0), ((π * r / 2), 1)) → i_1
  18. Ray((((3 / 2 * π) * r), 0), (((3 * π) * r / 2), 1)) → h_1
  19. Textfield(af) → Eingabefeld1
  20. Textfield(bf) → Eingabefeld2
  21. Textfield(cf) → Eingabefeld3
  22. Textfield(df) → Eingabefeld4
  23. Sequence(Intersect[Element[Lm, i], v4], i, 1, 360) → L_1
  24. Sequence(Segment[Element[Lpu, i], Element[L_1, i]], i, 1, 360) → L_2
  25. Sequence(Rotate[J', i°, dre], i, 0, 359) → L_3
  26. Rotate(J, -1°, dre) → J'_1
  27. CircumcircleArc(J, J'_1, J') → c_1
  28. Cylinder(Mru, Mro, r) → u, d_1, k_1, v
  29. Sequence((((π * r / 180) * i), 0, 0), i, 0, 359) → Lx
  30. Sequence(Translate[Element[L_2, i], Vector[Element[L_1, i], Element[Lx, i]]], i, 1, o) → L_4
  31. Mirror(L_4, xAxis) → L_5
  32. Sequence(Rotate[J', i°, dre], i, 0, 359) → L_8
  33. Sequence(Translate[Element[L_2, i], Vector[Element[L_1, i], Element[L_8, i]]], i, 2, 360 - o) → L_7
  34. Mirror(L_7, w) → L_9
  35. Sequence((x(Element[L_8, i]), y(Element[L_1, i]), z(Element[L_1, i])), i, 360 - o, 360) → L_{10}
  36. Segment(J, J + (0, h, 0)) → l_1
  37. Textfield(r) → Eingabefeld5
  38. Sequence((x(Element[Lx, i]), y(Element[L_1, i]), 0), i, 1, o - 2) → L_6
  39. Sequence(π / 2 + ((i * 2) * π), i, 1, 100) → L_{11}
  40. Ray((((2 * π) * r), 0), (((2 * π) * r), 1)) → g_1
  41. Ray(S, S + (0, 1)) → r_1