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Finding Perimeter

Finding Perimeter
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2016-04-02 08:31
PolygonVectorOptimizationGeometric Construction
This example demonstrates how to calculate and visualize the perimeter of polygons using GeoGebra. Core mathematical concepts include perimeter calculation, vector operations, and geometric transformations. Key construction elements involve commands and objects like UnitOrthogonalVector, Point, Ray, Segment, Length, Intersect, Rotate, Polygon. Suitable for high school mathematics education, helping students understand and apply methods for calculating polygon perimeters.

GeoGebra Commands & Parameters

  1. UnitOrthogonalVector(xAxis) → v
  2. Point(xAxis) → E
  3. If(i > 0, i, 0) → α
  4. If(i ≤ 0, i, 0) → tr
  5. Ray(L, K) → n
  6. Point(n) → B
  7. UnitVector(Segment[B, O]) → u
  8. Translate(B, Vector[(((tr + 1) * u) * Distance[B, O])]) → B'
  9. Ray(L, J) → l
  10. Point(l) → A
  11. Translate(A, Vector[(((tr + 1) * u) * Distance[B, O])]) → A'
  12. OrthogonalLine(A, l) → b
  13. Point(b) → C
  14. Translate(C, Vector[(((tr + 1) * u) * Distance[B, O])]) → C'
  15. Segment(A, C) → c
  16. OrthogonalLine(C, c) → d
  17. Length(Vector[A, C]) → h
  18. Segment(A, B) → a
  19. OrthogonalLine(B, a) → e
  20. Intersect(d, e) → D
  21. Translate(D, Vector[(((tr + 1) * u) * Distance[B, O])]) → D'
  22. Angle(E, O, D') → β
  23. If(α < β, 1, Div[α - β, 1.5708] + 2) → m
  24. If(m ≟ 1, α, α - β - ((m - 2) * 3.141592653589793 / 2)) → AngR
  25. Length(Vector[A, B]) → t
  26. Max(h, t) → long
  27. Sequence((Element[list1, k], 0), k, 1, 5) → list2
  28. If(m ≟ 1, D', If[Distance[Element[list2, m - 1], Element[list2, m]] ≟ h, Element[list2, m] + (v * t), Element[list2, m] + (v * h)]) → D_1
  29. If(m ≟ 1, C', If[Distance[Element[list2, m - 1], Element[list2, m]] ≟ h, Element[list2, m - 1] + (v * t), Element[list2, m - 1] + (v * h)]) → C_1
  30. If(m ≟ 1, B', Element[list2, m]) → B_1
  31. If(m ≟ 1, A', Element[list2, m - 1]) → A_1
  32. Element(list2, m) → cent
  33. Rotate(C_1, (-AngR), cent) → I
  34. Rotate(D_1, (-AngR), cent) → H
  35. Rotate(B_1, (-AngR), cent) → G
  36. Rotate(A_1, (-AngR), cent) → F
  37. Polygon(F, G, H, I) → poly3', f_1, g_1, h_1, i_1
  38. Line(A, B) → a11
  39. Polygon(A, B, D, C) → poly1, a_1, b_1, d_1, c_1
  40. Polygon(A', B', D', C') → poly1', a', b', d', c'
  41. Append(A', list2) → list3
  42. Polygon(A_1, B_1, D_1, C_1) → poly3, a_2, b_2, d_2, c_2
  43. Sequence(Segment[Element[list2, k], Element[list2, k + 1]], k, 1, 4) → list4
  44. Element(list4, 1) → side1
  45. Element(list4, 2) → side2
  46. Element(list4, 3) → side3
  47. If(f_1 ≟ long, 1, 0) → colorf
  48. Element(list4, 4) → side4
  49. If(h_1 ≟ long, 1, 0) → colorh
  50. If(g_1 ≟ long, 1, 0) → colorg
  51. If(i_1 ≟ long, 1, 0) → colori
  52. Point(A, Vector[UnitVector[l]]) → M
  53. Point((x(C), y(C) + 0.5), Vector[UnitVector[c]]) → N
  54. If(side1 ≟ long, 1, 0) → co1
  55. If(side2 ≟ long, 1, 0) → co2
  56. If(side3 ≟ long, 1, 0) → co3
  57. If(side4 ≟ long, 1, 0) → co4
  58. Vector((x(A) - 0.5, y(A)), (x(M) - 0.5, y(A) + 1.3)) → f
  59. Vector((x(A) - 0.5, y(A)), (x(M) - 0.5, y(A) - 1.3)) → z
  60. Vector((x(C) - 0.5, y(C) + 0.5), (x(N) + 0.5, y(N))) → g
  61. Vector((x(C) + 0.5, y(C) + 0.5), (x(N) - 2.5, y(N))) → w

AI Drawing Prompt Reference

Visualize the perimeter calculation of a polygon using vector operations and geometric transformations. Start with a base line, construct polygon vertices with orthogonal vectors and rays, then adjust vertex positions through rotations and translations to form a closed polygon. Highlight the sides and key points of the polygon in different colors, and label the perimeter length to intuitively demonstrate the calculation process.
The prompt above was compiled from the original drawing commands and is for reference only.