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Dynamic Geometry Illustration by Tim Brzezinski (3)

Dynamic Geometry Illustration by Tim Brzezinski (3)
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2018-03-28 08:55
FunctionCalculusGeometric ConstructionSlider AnimationGraphing
This example dynamically demonstrates a geometric problem posted by Antonio Gutierrez, showcasing key concepts through interactive visuals. It involves exponential functions, hypothesis testing, tree diagrams, parabolas, and integral calculus. Construction highlights the use of commands like Line, Polygon, Segment, Angle, Rotate, Ray, Intersect, OrthogonalLine, Circle, Midpoint, Translate, Dilate, Vector, and Point. Ideal for high school students and educators exploring complex geometry and advanced mathematics applications.

GeoGebra Commands & Parameters

  1. Line(A, B) → r
  2. Polygon(A, B, C, D) → q1, a_3, b_2, c_3, d_2
  3. Polygon(A, C, D) → t1, d_1, a_1, c_1
  4. Polygon(A, B, C) → t2, c_2, a_2, b_1
  5. Segment(D, A) → a
  6. Segment(A, C) → g
  7. Segment(C, D) → b
  8. Segment(C, B) → c
  9. Segment(B, A) → d
  10. Angle(A, D, C) → α
  11. Angle(D, C, A) → β
  12. Angle(C, B, A) → γ
  13. Angle(B, A, C) → δ
  14. Rotate(A, α / 2, D) → A'
  15. Angle(A, D, A') → ε
  16. Rotate(D, β / 2, C) → D'
  17. Angle(D, C, D') → ζ
  18. Rotate(B, δ / 2, A) → B'
  19. Angle(B, A, B') → η
  20. Ray(A, B') → k
  21. Ray(D, A') → l
  22. Ray(C, D') → m
  23. Rotate(C, γ / 2, B) → C'
  24. Angle(C, B, C') → θ_1
  25. Ray(B, C') → n
  26. Intersect(l, m) → E
  27. Intersect(n, k) → F
  28. OrthogonalLine(E, g) → p
  29. OrthogonalLine(F, g) → q
  30. Intersect(g, p) → G
  31. Intersect(g, q) → H
  32. Circle(E, G) → e
  33. Circle(F, H) → f
  34. Midpoint(a) → I
  35. Midpoint(b) → J
  36. Midpoint(c) → K
  37. Midpoint(d) → L
  38. Segment(A, G) → h
  39. Segment(G, H) → i
  40. Segment(H, C) → j
  41. Translate(r, (0, (-o))) → r'
  42. OrthogonalLine(A, r') → s
  43. OrthogonalLine(L, r') → t
  44. Intersect(r', t) → M
  45. Circle(M, Distance[D, J]) → e_1
  46. Intersect(e_1, r') → N, O
  47. Translate(r, (0, (-2 * o))) → r'_1
  48. Intersect(r', s) → P
  49. OrthogonalLine(O, r'_1) → f_1
  50. Intersect(r'_1, f_1) → Q
  51. Circle(Q, Distance[B, K]) → g_1
  52. Intersect(g_1, r'_1) → R, S
  53. Circle(R, Distance[A, I]) → h_1
  54. Intersect(h_1, r'_1) → T, U
  55. Intersect(s, r'_1) → V
  56. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], L) → A'_1
  57. Segment(A, A'_1) → i_1
  58. Rotate(A, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], L) → A'_2
  59. Rotate(A'_1, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], L) → W
  60. Segment(A'_2, W) → j_1
  61. Dilate(D, If[3 < u ≤ 4, 4 - u, 0], J) → D'_1
  62. Segment(D, D'_1) → k_1
  63. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], P) → A'_3
  64. Vector(A, A'_3) → v
  65. Translate(A, v) → A'_4
  66. Translate(A'_1, v) → Z
  67. Segment(A'_4, Z) → l_1
  68. Vector(L, Z) → w
  69. Rotate(D, If[4 < u ≤ 5, ((u - 4) * π), π], J) → D'_2
  70. Rotate(D'_1, If[4 < u ≤ 5, ((u - 4) * π), π], J) → A_1
  71. Segment(D'_2, A_1) → m_1
  72. Ray(M, O) → n_1
  73. Circle(O, 2) → p_1
  74. Intersect(p_1, n_1, 2) → B_1
  75. Ray(O, B_1) → q_1
  76. Segment(M, O) → r_1
  77. Line(C, r'_1) → s_1
  78. Point(s_1) → C_1
  79. Angle(D, C, C_1) → θ
  80. Dilate(J, If[5 < u ≤ 6, 6 - u, 0], M) → J'
  81. Vector(J, J') → u_1
  82. Translate(D'_2, u_1) → D_1
  83. Translate(A_1, u_1) → E_1
  84. Segment(D_1, E_1) → t_1
  85. Rotate(D_1, If[5 < u ≤ 6, ((u - 5) * θ), θ], J') → F_1
  86. Rotate(E_1, If[5 < u ≤ 6, ((u - 5) * θ), θ], J') → G_1
  87. Segment(F_1, G_1) → f_2
  88. OrthogonalLine(R, r'_1) → g_2
  89. OrthogonalLine(T, r'_1) → h_2
  90. Intersect(r', h_2) → H_1
  91. Intersect(g_2, r') → I_1
  92. Segment(P, H_1) → i_2
  93. Segment(H_1, I_1) → j_2
  94. Segment(I_1, O) → k_2
  95. Dilate(P, If[6 < u ≤ 7, 7 - u, 0], V) → P'
  96. Vector(P, P') → v_1
  97. Dilate(O, If[6 < u ≤ 7, 7 - u, 0], Q) → O'
  98. Vector(O, O') → w_1
  99. Translate(P, v_1) → P'_1
  100. Translate(H_1, v_1) → J_1
  101. Segment(P'_1, J_1) → l_2
  102. Translate(H_1, v_1) → K_1
  103. Translate(I_1, v_1) → L_1
  104. Segment(K_1, L_1) → m_2
  105. Translate(I_1, v_1) → M_1
  106. Translate(O, v_1) → O'_1
  107. Segment(M_1, O'_1) → n_2
  108. Dilate(C, If[7 < u ≤ 8, 8 - u, 0], K) → B'_1
  109. Rotate(B, If[8 < u ≤ 9, ((-(u - 8)) * π), (-π)], K) → B'_2
  110. Rotate(B'_1, If[8 < u ≤ 9, ((-(u - 8)) * π), (-π)], K) → N_1
  111. Segment(C, B'_1) → p_2
  112. Rotate(C, If[8 < u ≤ 9, ((u - 8) * π), π], K) → C'_1
  113. Rotate(B'_1, If[8 < u ≤ 9, ((u - 8) * π), π], K) → O_1
  114. Segment(C'_1, O_1) → q_2
  115. Dilate(B, If[9 < u ≤ 10, 10 - u, 0], O'_1) → B'_3
  116. Vector(B, B'_3) → u_2
  117. Translate(C'_1, u_2) → P_1
  118. Translate(O_1, u_2) → Q_1
  119. Segment(P_1, Q_1) → r_2
  120. Rotate(P_1, If[9 < u ≤ 10, ((u - 9) * γ), γ], P_1) → R_1
  121. Rotate(Q_1, If[9 < u ≤ 10, ((u - 9) * γ), γ], P_1) → S_1
  122. Segment(R_1, S_1) → s_2
  123. Dilate(D, If[10 < u ≤ 11, 11 - u, 0], I) → D'_3
  124. Segment(D, D'_3) → t_2
  125. Rotate(D, If[11 < u ≤ 12, ((-(u - 11)) * π), (-π)], I) → D'_4
  126. Rotate(D'_3, If[11 < u ≤ 12, ((-(u - 11)) * π), (-π)], I) → T_1
  127. Segment(D'_4, T_1) → e_2
  128. Angle(C, A, D) → λ
  129. Dilate(A, If[12 < u ≤ 13, 13 - u, 0], T) → A'_5
  130. Vector(A, A'_5) → v_2
  131. Translate(D'_4, v_2) → U_1
  132. Translate(T_1, v_2) → V_1
  133. Segment(U_1, V_1) → f_3
  134. Rotate(U_1, If[12 < u ≤ 13, ((-(u - 12)) * (λ + δ)), (-(λ + δ))], A'_5) → W_1
  135. Rotate(V_1, If[12 < u ≤ 13, ((-(u - 12)) * (λ + δ)), (-(λ + δ))], A'_5) → Z_1
  136. Segment(W_1, Z_1) → g_3
  137. Dilate(A, If[14 < u ≤ 15, 15 - u, 0], G) → A'_6
  138. Dilate(C, If[14 < u ≤ 15, 15 - u, 0], H) → C'_2
  139. Segment(A, A'_6) → h_3
  140. Segment(C, C'_2) → i_3
  141. Dilate(T, If[15 < u ≤ 16, 16 - u, 0], V) → T'
  142. Segment(T, T') → j_3
  143. Line(V, h_3) → k_3
  144. Point(k_3) → A_2
  145. Angle(T, V, A_2) → ρ
  146. Dilate(T, If[17 < u ≤ 18, 18 - u, 0], H) → T'_1
  147. Vector(T, T'_1) → w_2
  148. Translate(T, w_2) → T'_2
  149. Translate(T', w_2) → T''
  150. Segment(T'_2, T'') → l_3
  151. Rotate(T'_2, If[16 < u ≤ 17, ((-(u - 16)) * ((2 * π) - ρ)), ρ - (2 * π)], T'_2) → B_2
  152. Rotate(T'', If[16 < u ≤ 17, ((-(u - 16)) * ((2 * π) - ρ)), ρ - (2 * π)], T'_2) → T'''
  153. Rotate(T'_2, If[16 < u ≤ 17, ((u - 16) * ρ), ρ], T'_2) → C_2
  154. Rotate(T'_2, If[17 < u ≤ 18, ((u - 17) * ρ), ρ], T'_2) → D_2
  155. Rotate(T'', If[17 < u ≤ 18, ((u - 17) * ρ), ρ], T'_2) → T'''_1
  156. Segment(D_2, T'''_1) → m_3