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Connecting Perimeters by John Ulbright

Connecting Perimeters by John Ulbright
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2018-04-11 20:16
PolygonFunctionCoordinate GeometryGeometric Construction
This example demonstrates how to connect perimeters of polygons using GeoGebra, analyzing changes through transformations like dilation and coordinate geometry. Core concepts include perimeter calculation, polynomial functions, and geometric constructions. It utilizes commands such as Sequence, Polygon, Point, OrthogonalLine, Intersect, Perimeter, Segment, and Text. Suitable for high school mathematics education to understand the relationship between geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. Sequence(Sequence[Point[{i, j}], i, ((-length)) / 2, length / 2, 1], j, ((-width)) / 2, width / 2, 1) → list1
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Point(list1) → E
  4. Point(list1) → F
  5. Point(list1) → G
  6. Point(list1) → H
  7. OrthogonalLine(E, d) → e
  8. OrthogonalLine(E, a) → f
  9. OrthogonalLine(F, a) → g
  10. OrthogonalLine(F, b) → h
  11. OrthogonalLine(H, c) → i
  12. OrthogonalLine(H, d) → j
  13. OrthogonalLine(G, c) → k
  14. OrthogonalLine(G, b) → l
  15. Intersect(c, i) → I
  16. Intersect(j, d) → J
  17. Intersect(b, l) → K
  18. Intersect(g, a) → L
  19. Intersect(h, b) → M
  20. Intersect(k, c) → N
  21. Intersect(f, a) → P
  22. Intersect(e, d) → R
  23. Polygon(H, I, R, J, N, G, K, M, F, L, P, E) → poly2, h_1, e_1, r, j_1, i_1, n, g_1, k_1, m, f_1, l_1, p
  24. Perimeter(poly1) → o
  25. Perimeter(poly2) → q
  26. Sequence(Segment[list1(i, 1), list1(i, length + 1)], i, 1, width + 1) → list2
  27. Sequence(Segment[list1(1, i), list1(width + 1, i)], i, 1, length + 1) → list3
  28. Segment((D * (1 - vertMove)) + (I * vertMove), (J * (1 - vertMove)) + (H * vertMove)) → topLeftVert
  29. Segment((C * (1 - horMove)) + (K * horMove), (N * (1 - horMove)) + (G * horMove)) → topRightHor
  30. Segment((C * (1 - vertMove)) + (N * vertMove), (K * (1 - vertMove)) + (G * vertMove)) → topRightVert
  31. Segment((B * (1 - vertMove)) + (L * vertMove), (M * (1 - vertMove)) + (F * vertMove)) → bottomRightVert
  32. Segment((A * (1 - vertMove)) + (P * vertMove), (R * (1 - vertMove)) + (E * vertMove)) → bottomLeftVert
  33. Segment((D * (1 - horMove)) + (J * horMove), (I * (1 - horMove)) + (H * horMove)) → topLeftHor
  34. Segment((A * (1 - horMove)) + (R * horMove), (P * (1 - horMove)) + (E * horMove)) → bottomLeftHor
  35. Segment((B * (1 - horMove)) + (M * horMove), (L * (1 - horMove)) + (F * horMove)) → bottomRightHor
  36. Segment(D, D + (Min[length, perimeterTimer], 0)) → top
  37. Segment(C, C - (0, ((perimeterTimer > length) * Min[width, perimeterTimer - length]))) → right
  38. Segment(B, B - (((perimeterTimer > length + width) * Min[length, perimeterTimer - width - length]), 0)) → bottom
  39. Segment(A, A + (0, ((perimeterTimer > (2 * length) + width) * Min[width, perimeterTimer - (2 * length) - width]))) → left
  40. Text(d, Midpoint[d] + (-1, 0)) → leftWidthText
  41. Text(a, Midpoint[a] + (0, -1)) → bottomLengthText
  42. Text(Distance[R, L], Midpoint[R, L] - (0, 1)) → text1
  43. Text(Distance[P, M], Midpoint[P, M] - (0, 1)) → text2
  44. Text(Distance[I, K], Midpoint[I, K] + (0, 0.5)) → text3
  45. Text(Distance[J, N], Midpoint[J, N] + (0, 0.5)) → text4
  46. Text(topRightHor, Midpoint[topRightHor] + (0, 1 / 2)) → TRHtext
  47. Text(topLeftHor, Midpoint[topLeftHor] + (0, 1 / 2)) → TLHtext
  48. Text(bottomLeftHor, Midpoint[bottomLeftHor] + (0, -1)) → BLHtext
  49. Text(Distance[P, L], Midpoint[P, L] + (0, -1)) → BMHtext
  50. Text(bottomRightHor, Midpoint[bottomRightHor] + (0, -1)) → BRHtext
  51. Text(Distance[R, D], Midpoint[R, D] + (-0.8, 0)) → text8
  52. Text(Distance[J, P], Midpoint[J, P] + (-0.8, 0)) → text6
  53. Text(Distance[J, R], Midpoint[J, R] + (-0.8, 0)) → text9
  54. Text(Distance[I, N], Midpoint[I, N] + (0, 1 / 2)) → topText
  55. Text(c, Midpoint[c] + (0, 1 / 2)) → topLengthText
  56. Text(Distance[K, M], Midpoint[K, M] + (1 / 2, 0)) → text10
  57. Text(Distance[K, B], Midpoint[K, B] + (1 / 2, 0)) → text13
  58. Text(Distance[M, C], Midpoint[M, C] + (1 / 2, 0)) → text14
  59. Text(b, Midpoint[b] + (1 / 2, 0)) → rightWidthText
  60. Text(Distance[N, G], Midpoint[topRightVert] + (1 / 2, 0)) → text11
  61. Text(Distance[I, H], Midpoint[topLeftVert] + (-0.8, 0)) → text5
  62. Text(Distance[F, L], Midpoint[bottomRightVert] + (1 / 2, 0)) → text12
  63. Text(Distance[E, P], Midpoint[bottomLeftVert] + (-0.8, 0)) → text7
  64. Segment(J, J + (Min[Distance[H, J], perimeterTimer], 0)) → p1
  65. Segment(H, H + (0, ((perimeterTimer > Distance[H, J]) * Min[Distance[I, H], perimeterTimer - Distance[H, J]]))) → p2
  66. Segment(I, I + (Min[Distance[I, N], perimeterTimer - p1 - p2], 0)) → p3
  67. Segment(N, N - (0, Min[Distance[G, N], perimeterTimer - p1 - p2 - p3])) → p4
  68. Segment(G, G + (Min[Distance[G, K], perimeterTimer - p1 - p2 - p3 - p4], 0)) → p5
  69. Segment(K, K + (0, (-Min[Distance[M, K], perimeterTimer - p1 - p2 - p3 - p4 - p5]))) → p6
  70. Segment(M, M + ((-Min[Distance[M, F], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6]), 0)) → p7
  71. Segment(F, F + (0, (-Min[Distance[F, L], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7]))) → p8
  72. Segment(L, L + ((-Min[Distance[L, P], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8]), 0)) → p9
  73. Segment(P, P + (0, Min[Distance[P, E], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8 - p9])) → p10
  74. Segment(E, E + ((-Min[Distance[E, R], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8 - p9 - p10]), 0)) → p11
  75. Segment(R, R + (0, Min[Distance[R, J], perimeterTimer - p1 - p2 - p3 - p4 - p5 - p6 - p7 - p8 - p9 - p10 - p11])) → p12
  76. Text(length, Midpoint[A, B] + (0, -1)) → bottomText
  77. Polygon(O, Q, S, T) → q1, o_1, q_1, s_1, t_1