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Rainbow - Giuseppe Condoluci

Rainbow - Giuseppe Condoluci
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2018-02-03 00:47
FunctionTrigonometryCoordinate GeometryOptimizationGeometric Construction
This example demonstrates the formation of a rainbow, illustrating the refraction and reflection of light in water droplets through dynamic geometry. Key math concepts include Linear Programming, Linear Optimization, Arithmetic, Linear Regression, Sine, and Step Functions. GeoGebra commands and objects used are Point, Polygon, Rotate, Textfield, and Translate. Suitable for high school and above students studying the intersection of physical optics and mathematical modeling.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, C) → t1, c, a, b
  4. Rotate(A, (-α), D) → A'
  5. Rotate(B, (-α), D) → B'
  6. Rotate(C, (-α), D) → C'
  7. Polygon(A', B', C') → t1', c', a', b'
  8. Textfield(α) → CampoInserimento1
  9. Translate(A', u) → A''
  10. Translate(B', u) → B''
  11. Translate(C', u) → C''
  12. Polygon(A'', B'', C'') → t1'', c'', a'', b''
  13. Translate(A', v) → A''_1
  14. Translate(B', v) → B''_1
  15. Translate(C', v) → C''_1
  16. Polygon(A''_1, B''_1, C''_1) → t1''_1, c''_1, a''_1, b''_1
  17. Translate(A', w) → A''_2
  18. Translate(B', w) → B''_2
  19. Translate(C', w) → C''_2
  20. Polygon(A''_2, B''_2, C''_2) → t1''_2, c''_2, a''_2, b''_2
  21. Translate(A''_1, d) → E
  22. Translate(B''_1, d) → F
  23. Translate(C''_1, d) → G
  24. Polygon(E, F, G) → t2, g, e, f
  25. Translate(A''_2, k) → K
  26. Translate(B''_2, k) → L
  27. Translate(C''_2, k) → M
  28. Polygon(K, L, M) → t4, m, k_1, l
  29. Translate(A''_2, n) → N
  30. Translate(B''_2, n) → O
  31. Translate(C''_2, n) → P
  32. Translate(A''_2, q) → Q
  33. Translate(B''_2, q) → R
  34. Translate(C''_2, q) → S
  35. Translate(A''_2, t) → T
  36. Translate(B''_2, t) → U
  37. Translate(C''_2, t) → V
  38. Translate(C''_2, w_1) → A_1
  39. Translate(A''_2, b_1) → B_1
  40. Translate(B''_2, b_1) → C_1
  41. Translate(C''_2, b_1) → D_1
  42. Polygon(B_1, C_1, D_1) → t9, d_1, b_2, c_1