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Dynamic Geometric Construction Demo

Dynamic Geometric Construction Demo
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2018-01-15 09:47
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates a geometric problem involving geometric mean, unit circle, Pythagorean theorem, and function graphs. It visually showcases geometric relationships through operations like rotation, intersection, and dilation. The construction utilizes commands and objects such as Rotate, Ray, Line, Point, Intersect, Segment, Dilate, Angle, Circle, CircleSector, Vector, Translate, Polygon, Midpoint, CircleArc, Semicircle, OrthogonalLine, Distance. Suitable for high school mathematics education to understand the connection between complex geometric concepts and function graphs.

GeoGebra Commands & Parameters

  1. Rotate(D, a°, A) → B'
  2. Ray(A, B') → g
  3. Line(D, g) → h
  4. Point(g) → B
  5. Ray(A, D) → f
  6. Line(B, f) → i
  7. Intersect(h, i) → C
  8. Line(A, C) → t_1
  9. Line(C, D) → i_3
  10. Segment(A, D) → b_2
  11. Point(b_2) → E
  12. Line(B, E) → j_3
  13. Intersect(j_3, t_1) → F
  14. Dilate(F, If[7 < o ≤ 8, 8 - o, 0], E) → O'
  15. Segment(F, O') → r_1
  16. Intersect(i_3, j_3) → G
  17. Segment(E, G) → g_2
  18. Segment(B, C) → g_3
  19. Segment(A, B) → f_3
  20. Angle(D, A, B') → α
  21. Segment(B, C) → j
  22. Segment(A, D) → k
  23. Segment(D, C) → l
  24. Segment(A, B) → m
  25. Min(m, k) → b
  26. Circle(B, (0.2 * b)) → d
  27. Circle(A, (0.2 * b)) → e
  28. Circle(D, (0.2 * b)) → p
  29. Circle(C, (0.2 * b)) → c
  30. Intersect(e, k, 1) → E_1
  31. Intersect(e, m, 1) → F_1
  32. Intersect(p, k, 1) → G_1
  33. Intersect(p, l, 1) → H
  34. Intersect(d, g, 2) → I
  35. Ray(B, I) → q
  36. Intersect(c, h, 2) → J
  37. Ray(C, J) → r
  38. Intersect(c, i, 2) → K
  39. Ray(C, K) → s
  40. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  41. Segment(A, A') → t
  42. Rotate(E_1, If[1 < o ≤ 2, ((o - 1) * α), α], A) → E'
  43. CircleSector(A, E_1, E') → c_1
  44. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], B) → A'_1
  45. Vector(A, A'_1) → u
  46. Translate(c_1, u) → d_1
  47. Segment(A, A'_1) → f_1
  48. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], C) → C'
  49. Vector(B, C') → v
  50. Translate(d_1, v) → e_1
  51. Segment(B, C') → g_1
  52. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], D) → D'
  53. Segment(C, D') → h_1
  54. Polygon(A, D, C, B) → poly1, a_1, b_1, d_2, c_2
  55. Dilate(A, If[5.5 < o ≤ 6.5, 6.5 - o, 0], B) → A'_2
  56. Vector(A, A'_2) → w
  57. Translate(A, w) → A'_3
  58. Translate(A', w) → A''
  59. Dilate(A, If[6.5 < o ≤ 7.5, 7.5 - o, 0], D) → A'_4
  60. Vector(A, A'_4) → u_1
  61. Translate(A, u_1) → A'_5
  62. Translate(A'_1, u_1) → L
  63. Rotate(C, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → D'_2
  64. Rotate(D', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], D) → D''
  65. Rotate(B, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → C'_2
  66. Rotate(C', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], C) → C''
  67. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → A'_7
  68. Rotate(A'_1, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], B) → M
  69. Rotate(A, If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A'_8
  70. Rotate(A', If[6 < o ≤ 7, ((-(o - 6)) * π / 3), ((-π)) / 3], A) → A''_1
  71. Rotate(C, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → D'_3
  72. Rotate(D', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], C) → D''_1
  73. Rotate(B, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → C'_3
  74. Rotate(C', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], B) → C''_1
  75. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → A'_9
  76. Rotate(A'_1, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], A) → N
  77. Rotate(A, If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → A'_{10}
  78. Rotate(A', If[7 < o ≤ 8, ((o - 7) * π / 3), π / 3], D) → A''_2
  79. Line(A, C) → s_2
  80. Midpoint(A, C) → Q
  81. Rotate(A, If[16 < o ≤ 17, ((o - 16) * π), π], Q) → A'_{11}
  82. Line(A, C) → h_3
  83. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], C) → A'_6
  84. Segment(A, A'_6) → i_1
  85. Circle(G, r_1) → k_1
  86. Segment(F, E) → j_1
  87. Intersect(k_1, j_3, 2) → P
  88. Circle(P, 1) → p_1
  89. Intersect(p_1, j_3, 2) → R
  90. Segment(G, P) → l_1
  91. Ray(P, R) → m_1
  92. Intersect(k_1, i_3) → U, V
  93. Ray(G, V) → n_1
  94. Dilate(B, If[6 < o ≤ 7, 7 - o, 0], F) → C'_1
  95. Segment(B, C'_1) → q_1
  96. Dilate(E, If[8 < o ≤ 9, 9 - o, 0], G) → S'
  97. Dilate(D, If[8 < o ≤ 9, 9 - o, 0], G) → B'_1
  98. Segment(D, B'_1) → s_1
  99. Segment(E, S') → f_2
  100. Rotate(E, If[10 < o ≤ 11, ((o - 10) * π), π], G) → S'_1
  101. Rotate(S', If[10 < o ≤ 11, ((o - 10) * π), π], G) → S''
  102. Rotate(P, If[11 < o ≤ 13, ((o - 11) * π / 2), π], Midpoint[F, P]) → P'
  103. Midpoint(F, P) → W
  104. CircleArc(W, P, P') → e_2
  105. Semicircle(F, P) → k_2
  106. OrthogonalLine(E, m_1) → i_2
  107. Distance(B, F) → distanceCO
  108. OrthogonalLine(G, m_1) → j_2
  109. Intersect(k_2, j_2) → A_1,
  110. Distance(A_1, G) → distanceA1T
  111. Distance(A_1, G) → distanceA1G
  112. Distance(B, F) → distanceBF
  113. Rotate(F, If[10 < o ≤ 11, ((o - 10) * π), π], Midpoint[F, P]) → F'
  114. Rotate(O', If[10 < o ≤ 11, ((o - 10) * π), π], Midpoint[F, P]) → O''
  115. Segment(F', O'') → h_2
  116. Angle(A_1, G, F) → β
  117. Dilate(G, If[13 < o ≤ 14, 14 - o, 0], A_1) → G'
  118. Segment(G, G') → l_2
  119. Angle(B, F, A) → γ
  120. Rotate(B, If[14 < o ≤ 15, ((o - 14) * γ / 2), γ / 2], F) → B'_2
  121. Rotate(C'_1, If[14 < o ≤ 15, ((o - 14) * γ / 2), γ / 2], F) → O
  122. Segment(B'_2, O) → m_2
  123. Dilate(F, If[15 < o ≤ 16, 16 - o, 0], G) → F'_1
  124. Vector(F, F'_1) → v_1
  125. Translate(B'_2, v_1) → S
  126. Translate(O, v_1) → O'_1
  127. Segment(S, O'_1) → n_2
  128. Rotate(S, If[16 < o ≤ 17, ((-(o - 16)) * (γ / 2 + π / 2)), (-(γ / 2 + π / 2))], G) → S'_2
  129. Rotate(O'_1, If[16 < o ≤ 17, ((-(o - 16)) * (γ / 2 + π / 2)), (-(γ / 2 + π / 2))], G) → T
  130. Segment(S'_2, T) → p_2