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Piano Keys

Piano Keys
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2019-04-10 23:06
VectorFunctionTrigonometryGeometric ConstructionGraphing
This example demonstrates the arrangement of piano keys through geometric visualization, involving core math concepts like Sine, Trigonometric Functions, Random Experiments, Step Functions, Polynomial Functions, Vectors 2D, and Linear Functions. It is constructed using GeoGebra commands such as Polygon, Vector, and Translate, making it suitable for high school mathematics education or exploration by math enthusiasts interested in the intersection of functions and geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E, F) → poly1, a, b, c, d, e, f
  2. Polygon(B, G, H, I, J, K, L, C) → poly2, b_1, g, h, i, j, k, l, c_1
  3. Polygon(G, M, N, O, P, H) → poly3, g_1, m, n, o, p, h_1
  4. Vector(Q, R) → u
  5. Translate(A, u) → A'
  6. Translate(B, u) → B'
  7. Translate(C, u) → C'
  8. Translate(D, u) → D'
  9. Translate(E, u) → E'
  10. Translate(F, u) → F'
  11. Polygon(A', B', C', D', E', F') → poly1', a', b', c', d', e', f'
  12. Translate(B, u) → B'_1
  13. Translate(G, u) → G'
  14. Translate(H, u) → H'
  15. Translate(I, u) → I'
  16. Translate(J, u) → J'
  17. Translate(K, u) → K'
  18. Translate(L, u) → L'
  19. Translate(C, u) → C'_1
  20. Polygon(B'_1, G', H', I', J', K', L', C'_1) → poly2', b'_1, g', h', i', j', k', l', c'_1
  21. Vector(S, T) → v
  22. Translate(B, v) → B'_2
  23. Translate(G, v) → G'_1
  24. Translate(H, v) → H'_1
  25. Translate(I, v) → I'_1
  26. Translate(J, v) → J'_1
  27. Translate(K, v) → K'_1
  28. Translate(L, v) → L'_1
  29. Translate(C, v) → C'_2
  30. Polygon(B'_2, G'_1, H'_1, I'_1, J'_1, K'_1, L'_1, C'_2) → poly2'_1, b'_2, g'_1, h'_1, i'_1, j'_1, k'_1, l'_1, c'_2
  31. Translate(G, v) → G'_2
  32. Translate(M, v) → M'
  33. Translate(N, v) → N'
  34. Translate(O, v) → O'
  35. Translate(P, v) → P'
  36. Translate(H, v) → H'_2
  37. Polygon(G'_2, M', N', O', P', H'_2) → poly3', g'_2, m', n', o', p', h'_2
  38. Translate(A', v) → A''
  39. Translate(B', v) → B''
  40. Translate(C', v) → C''
  41. Translate(D', v) → D''
  42. Translate(E', v) → E''
  43. Translate(F', v) → F''
  44. Polygon(D, E, K, L) → q1, d_1, e_1, k_1, l_1
  45. Polygon(I, J, O, P) → q2, i_1, j_1, o_1, p_1
  46. Translate(D, u) → D'_1
  47. Translate(E, u) → E'_1
  48. Translate(K, u) → K'_2
  49. Translate(L, u) → L'_2
  50. Polygon(D'_1, E'_1, K'_2, L'_2) → q1', d'_1, e'_1, k'_2, l'_2
  51. Translate(I, u) → I'_2
  52. Translate(J, u) → J'_2
  53. Translate(O, u) → O'_1
  54. Translate(P, u) → P'_1
  55. Polygon(I'_2, J'_2, O'_1, P'_1) → q2', i'_2, j'_2, o'_1, p'_1
  56. Translate(I, v) → I'_3
  57. Translate(J, v) → J'_3
  58. Translate(O, v) → O'_2
  59. Translate(P, v) → P'_2
  60. Polygon(I'_3, J'_3, O'_2, P'_2) → q2'_1, i'_3, j'_3, o'_2, p'_2