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Multi-stage Animation Geometric Construction Example

Multi-stage Animation Geometric Construction Example
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2015-06-26 03:11
Solid GeometryGeometric ConstructionSlider Animation
This example demonstrates a multi-stage animation showing geometric transformations. Key mathematical concepts include prisms, volume calculations, quadratic functions, Pythagorean theorem, and logarithms. Construction involves GeoGebra commands like If, Vector, Translate, Line, Point, OrthogonalLine, Segment, Polygon, and Circle. Suitable for middle school students and above to understand geometric transformations and function graphs.

GeoGebra Commands & Parameters

  1. If(o < 1, o, 1) → o1
  2. Vector(A, E) → q
  3. If(o1 < 0.2, Vector[(0 * q)], Vector[If[o1 < 0.8, Vector[(((5 / 3 * o1) - 1 / 3) * q)], q]]) → q1
  4. Translate(A, q1) → A'
  5. Vector(A', A) → m
  6. If(k1 < 1, Vector[(k1 * m)], Vector[If[k1 < 4, m, Vector[((5 - k1) * m)]]]) → m1
  7. Translate(A', m1) → A''
  8. Line(A, B_1) → a
  9. Point(a) → B
  10. Vector(A, C) → u
  11. OrthogonalLine(A, a) → b
  12. Point(b) → D
  13. Vector(A, B) → v
  14. Vector(A, D) → w
  15. Translate(C, w) → C'
  16. Vector(C, C') → c
  17. Translate(B, w) → B'
  18. Vector(B, B') → d
  19. Segment(C, B) → e
  20. Segment(C', B') → f
  21. Segment(D, B') → g
  22. Segment(D, C') → h
  23. Segment(A, C) → i
  24. Segment(D, A) → j
  25. Segment(C', C) → k_2
  26. Segment(B', B) → l_2
  27. Segment(C', A) → m_2
  28. Segment(A, B') → n_2
  29. Segment(B', C) → p_2
  30. Vector(A, G) → s
  31. If(o < 1, 0, o - 1) → o2
  32. If(o2 < 0.2, Vector[(0 * s)], Vector[If[o2 < 0.8, Vector[(((5 / 3 * o2) - 1 / 3) * s)], s]]) → s1
  33. Translate(D, q1) → D'
  34. Translate(C', q1) → C''
  35. Translate(B', q1) → B''
  36. Segment(C'', B'') → t
  37. Segment(B'', D') → a_1
  38. Segment(A', B'') → b_1
  39. Segment(C'', A') → c_1
  40. Segment(A', D') → d_1
  41. Segment(D', C'') → e_1
  42. Translate(A, s1) → A'_1
  43. Translate(C, s1) → C'_1
  44. Translate(B, s1) → B'_1
  45. Translate(B', s1) → B''_1
  46. Segment(A'_1, B'_1) → r
  47. Segment(B'_1, C'_1) → f_1
  48. Segment(C'_1, A'_1) → g_1
  49. Segment(B''_1, B'_1) → h_1
  50. Segment(B''_1, C'_1) → i_1
  51. Segment(B''_1, A'_1) → j_1
  52. Segment(C', D) → k_1
  53. Segment(D, A) → l_1
  54. Segment(D, B') → m_1
  55. Segment(B, A) → n_1
  56. Segment(B, B') → p_1
  57. Segment(B, C) → q_1
  58. Vector(A'_1, A) → n
  59. Point(n) → F
  60. Vector(F, A') → p
  61. If(k2 < 1, Vector[(k2 * n)], Vector[If[k2 < 4, n, Vector[((5 - k2) * n)]]]) → n1
  62. If(k3 < 1, Vector[(k3 * p)], Vector[If[k3 < 4, p, Vector[((5 - k3) * p)]]]) → p1
  63. Polygon(C'', D', H) → poly1, h_2, c'', d'
  64. Polygon(C', A, C) → poly2, c_2, c', a_2
  65. Translate(C'', m1) → C'''
  66. Translate(D', m1) → D''
  67. Translate(H, m1) → H'
  68. Polygon(C''', D'', H') → poly1', h', c''', d''
  69. Translate(C'', m1) → C'''_1
  70. Translate(B'', m1) → B'''
  71. Segment(C'''_1, B''') → t'
  72. Translate(B'', m1) → B'''_1
  73. Translate(D', m1) → D''_1
  74. Segment(B'''_1, D''_1) → k
  75. Translate(B'', m1) → B'''_2
  76. Segment(A'', B'''_2) → l
  77. Translate(C'', m1) → C'''_2
  78. Translate(A', m1) → A''_1
  79. Segment(C'''_2, A''_1) → r_1
  80. Translate(A', m1) → A''_2
  81. Translate(D', m1) → D''_2
  82. Segment(A''_2, D''_2) → s_1
  83. Translate(D', m1) → D''_3
  84. Translate(C'', m1) → C'''_3
  85. Segment(D''_3, C'''_3) → t_1
  86. Polygon(C', C, B') → poly3, b', c'_1, c_3
  87. Polygon(C'_1, B'_1, B''_1) → poly4, b''_1, c'_2, b'_1
  88. Translate(C'_1, n1) → I
  89. Translate(B'_1, n1) → J
  90. Translate(B''_1, n1) → K
  91. Polygon(I, J, K) → poly4', k_3, i_2, j_2
  92. Translate(A'_1, n1) → L
  93. Translate(B'_1, n1) → M
  94. Segment(L, M) → r'
  95. Translate(B'_1, n1) → N
  96. Translate(C'_1, n1) → O
  97. Segment(N, O) → b_2
  98. Translate(C'_1, n1) → P
  99. Translate(A'_1, n1) → Q
  100. Segment(P, Q) → d_2
  101. Translate(B''_1, n1) → R
  102. Translate(B'_1, n1) → S
  103. Segment(R, S) → e_2
  104. Translate(B''_1, n1) → T
  105. Translate(C'_1, n1) → U
  106. Segment(T, U) → f_2
  107. Translate(B''_1, n1) → V
  108. Translate(A'_1, n1) → W
  109. Segment(V, W) → g_2
  110. Translate(F, n1) → F'
  111. Polygon(C''', D'', B''') → poly5, b''', c'''_1, d''_1
  112. Polygon(I, F, J) → poly6, j_3, i_3, f_3
  113. Translate(I, p1) → I'
  114. Translate(F, p1) → F'_1
  115. Translate(J, p1) → J'
  116. Polygon(I', F'_1, J') → poly6', j', i', f'_1
  117. Translate(A'_1, p1) → Z
  118. Translate(B'_1, p1) → A_1
  119. Segment(Z, A_1) → r'_1
  120. Translate(B'_1, p1) → C_1
  121. Translate(C'_1, p1) → D_1
  122. Segment(C_1, D_1) → q_2
  123. Translate(C'_1, p1) → E_1
  124. Translate(A'_1, p1) → F_1
  125. Segment(E_1, F_1) → r_2
  126. Translate(B''_1, p1) → G_1
  127. Translate(B'_1, p1) → H_1
  128. Segment(G_1, H_1) → s_2
  129. Translate(B''_1, p1) → I_1
  130. Translate(C'_1, p1) → J_1
  131. Segment(I_1, J_1) → t_2
  132. Translate(B''_1, p1) → K_1
  133. Translate(A'_1, p1) → L_1
  134. Segment(K_1, L_1) → a_3
  135. Translate(K, p1) → K'
  136. Translate(I, p1) → I'_1
  137. Segment(K', I'_1) → b_3
  138. Translate(J, p1) → J'_1
  139. Translate(K, p1) → K'_1
  140. Segment(J'_1, K'_1) → d_3
  141. Translate(L, p1) → L'
  142. Translate(M, p1) → M'
  143. Segment(L', M') → r''
  144. Translate(N, p1) → N'
  145. Translate(O, p1) → O'
  146. Segment(N', O') → e_3
  147. Translate(P, p1) → P'
  148. Translate(Q, p1) → Q'
  149. Segment(P', Q') → g_3
  150. Translate(R, p1) → R'
  151. Translate(S, p1) → S'
  152. Segment(R', S') → h_3
  153. Translate(T, p1) → T'
  154. Translate(U, p1) → U'
  155. Segment(T', U') → l_3
  156. Translate(V, p1) → V'
  157. Translate(W, p1) → W'
  158. Segment(V', W') → m_3
  159. Translate(F', p1) → F''
  160. Segment(G_1, J') → n_3
  161. Segment(D'', H) → p_3
  162. Polygon(H, B''', C''') → poly7, c'''_2, h_4, b'''_1
  163. Polygon(F, K, C') → poly8, c'_3, f_4, k_4
  164. Polygon(F, K, I) → poly9, i_4, f_5, k_5
  165. Polygon(A, B', C) → poly10, c_4, a_4, b'_2
  166. Segment(I', F'_1) → q_3
  167. Segment(I', J') → r_3
  168. Segment(G_1, J') → s_3
  169. Segment(G_1, I') → t_3
  170. Circle(B''', 0.3) → d_4
  171. Circle(A, 0.3) → e_4

AI Drawing Prompt Reference

Draw a multi‑stage animated triangular prism: start with a base triangle, translate it along a vector to create a top triangle and connect corresponding vertices to form the lateral edges. Add two sliders; the first drives a gradual translation of the whole prism along one direction, the second drives a piecewise translation along another direction, so the prism expands and then retracts in two successive phases, illustrating volume change, Pythagorean relations, and a quadratic trajectory.
The prompt above was compiled from the original drawing commands and is for reference only.