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Rotation and Shrinking Demo

Rotation and Shrinking Demo
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2020-01-29 18:42
CircleTrigonometryGeometric Construction
This example demonstrates a dynamic effect of a shape rotating and shrinking simultaneously. It involves core mathematical concepts such as rotation, dilation, circle, and trigonometric functions. The construction utilizes commands like Mirror, Segment, CircleSector, Circle, Rotate, Dilate, Vector, and Translate from GeoGebra. It is suitable for high school students and teachers studying geometric transformations, function graphs, and dynamic geometry.

GeoGebra Commands & Parameters

  1. Mirror(U, f) → U'
  2. Mirror(V, f) → V'
  3. Mirror(T, f) → T'
  4. Mirror(S, f) → S'
  5. Mirror(R, f) → R'
  6. Mirror(Q, f) → Q'
  7. Mirror(P, f) → P'
  8. Segment(A, P) → g
  9. Segment(A, Q) → h
  10. Segment(R, A) → i
  11. Segment(S, A) → j
  12. Segment(A, T) → k
  13. Segment(U, A) → l
  14. Segment(A, V) → m
  15. Segment(C, A) → n
  16. Segment(A, D) → p
  17. Segment(A, E) → q
  18. Segment(A, F) → r
  19. Segment(A, G) → s
  20. Segment(A, V') → t
  21. Segment(U', A) → a
  22. Segment(A, T') → b
  23. Segment(S', A) → d
  24. Segment(A, R') → e
  25. Segment(Q', A) → f_1
  26. Segment(A, P') → g_1
  27. Segment(B, A) → h_1
  28. CircleSector(A, P, Q) → c_1
  29. CircleSector(A, Q, R) → d_1
  30. CircleSector(A, U', T') → e_1
  31. CircleSector(A, D, E) → k_1
  32. Segment(H, A) → i_1
  33. Segment(A, I) → j_1
  34. Segment(J, A) → l_1
  35. CircleSector(A, H, I) → p_1
  36. CircleSector(A, I, J) → q_1
  37. Segment(A, O) → m_1
  38. CircleSector(A, V, C) → r_1
  39. Circle(A, 5.019) → c
  40. Rotate(S, (-(D7°)), A) → S'_1
  41. Rotate(A, (-(D7°)), A) → A'
  42. Segment(S'_1, A') → j'
  43. Rotate(d_1, (-(D7°)), A) → s_1
  44. Rotate(e_1, (-(D7°)), A) → c_2
  45. Rotate(q_1, (-(D7°)), A) → d_2
  46. Rotate(k_1, (-(D7°)), A) → e_2
  47. Rotate(r_1, (-(D7°)), A) → f_2
  48. Rotate(A, (-(D7°)), A) → A'_1
  49. Rotate(P, (-(D7°)), A) → P'_1
  50. Segment(A'_1, P'_1) → g'
  51. Rotate(A, (-(D7°)), A) → A'_2
  52. Rotate(Q, (-(D7°)), A) → Q'_1
  53. Segment(A'_2, Q'_1) → h'
  54. Rotate(R, (-(D7°)), A) → R'_1
  55. Rotate(A, (-(D7°)), A) → A'_3
  56. Segment(R'_1, A'_3) → i'
  57. Rotate(A, (-(D7°)), A) → A'_4
  58. Rotate(T, (-(D7°)), A) → T'_1
  59. Segment(A'_4, T'_1) → k'
  60. Rotate(U, (-(D7°)), A) → U'_1
  61. Rotate(A, (-(D7°)), A) → A'_5
  62. Segment(U'_1, A'_5) → l'
  63. Rotate(A, (-(D7°)), A) → A'_6
  64. Rotate(V, (-(D7°)), A) → V'_1
  65. Segment(A'_6, V'_1) → m'
  66. Rotate(C, (-(D7°)), A) → C'
  67. Rotate(A, (-(D7°)), A) → A'_7
  68. Segment(C', A'_7) → n'
  69. Rotate(A, (-(D7°)), A) → A'_8
  70. Rotate(D, (-(D7°)), A) → D'
  71. Segment(A'_8, D') → p'
  72. Rotate(A, (-(D7°)), A) → A'_9
  73. Rotate(E, (-(D7°)), A) → E'
  74. Segment(A'_9, E') → q'
  75. Rotate(A, (-(D7°)), A) → A'_{10}
  76. Rotate(F, (-(D7°)), A) → F'
  77. Segment(A'_{10}, F') → r'
  78. Rotate(A, (-(D7°)), A) → A'_{11}
  79. Rotate(V', (-(D7°)), A) → V''
  80. Segment(A'_{11}, V'') → t'
  81. Rotate(U', (-(D7°)), A) → U''
  82. Rotate(A, (-(D7°)), A) → A'_{12}
  83. Segment(U'', A'_{12}) → a'
  84. Rotate(A, (-(D7°)), A) → A'_{13}
  85. Rotate(T', (-(D7°)), A) → T''
  86. Segment(A'_{13}, T'') → b'
  87. Rotate(S', (-(D7°)), A) → S''
  88. Rotate(A, (-(D7°)), A) → A'_{14}
  89. Segment(S'', A'_{14}) → d'
  90. Rotate(A, (-(D7°)), A) → A'_{15}
  91. Rotate(R', (-(D7°)), A) → R''
  92. Segment(A'_{15}, R'') → e'
  93. Rotate(Q', (-(D7°)), A) → Q''
  94. Rotate(A, (-(D7°)), A) → A'_{16}
  95. Segment(Q'', A'_{16}) → n_1
  96. Rotate(A, (-(D7°)), A) → A'_{17}
  97. Rotate(P', (-(D7°)), A) → P''
  98. Segment(A'_{17}, P'') → a_1
  99. Rotate(B, (-(D7°)), A) → B'
  100. Rotate(A, (-(D7°)), A) → A'_{18}
  101. Segment(B', A'_{18}) → b_1
  102. Rotate(H, (-(D7°)), A) → H'
  103. Rotate(A, (-(D7°)), A) → A'_{19}
  104. Segment(H', A'_{19}) → h_2
  105. Rotate(A, (-(D7°)), A) → A'_{20}
  106. Rotate(I, (-(D7°)), A) → I'
  107. Segment(A'_{20}, I') → i_2
  108. Rotate(J, (-(D7°)), A) → J'
  109. Rotate(A, (-(D7°)), A) → A'_{21}
  110. Segment(J', A'_{21}) → j_2
  111. Rotate(A, (-(D7°)), A) → A'_{22}
  112. Rotate(O, (-(D7°)), A) → O'
  113. Segment(A'_{22}, O') → k_2
  114. Rotate(c_1, (-(D7°)), A) → t_1
  115. Rotate(L, (-(D7°)), A) → L'
  116. Circle(W, 3) → g_2
  117. Segment(Z, W) → l_2
  118. Rotate(Z, D7°, W) → Z'
  119. Rotate(W, D7°, W) → W'
  120. Segment(Z', W') → m_2
  121. Rotate(Z, (-(((2 * D7))°)), W) → Z'_1
  122. Rotate(W, (-(((2 * D7))°)), W) → W'_1
  123. Segment(Z'_1, W'_1) → n_2
  124. Dilate(Z, D7, W) → Z'_2
  125. Dilate(W, D7, W) → W'_2
  126. Dilate(W'_2, D7 / 100, W) → B_1
  127. Circle(W, Z') → r_2
  128. Dilate(g_2, D7 / 200, W) → p_2
  129. Dilate(g_2, D7 / 190, W) → q_2
  130. Dilate(r_2, (30 * 1 / D7), W) → s_2
  131. Vector((0, 0), (11, 0)) → v
  132. Translate(s_2, v) → t_2
  133. Dilate(t_2, 2, A) → c_3
  134. Dilate(t_2, 3, A) → d_3
  135. Dilate(t_2, 4, A) → e_3
  136. Dilate(t_2, 5, A) → f_3
  137. Dilate(t_2, 6, A) → g_3
  138. Dilate(t_2, 7, A) → h_3
  139. Dilate(t_2, 8, A) → k_3
  140. Dilate(t_2, 9, A) → p_3

AI Drawing Prompt Reference

Create a dynamic illustration showing a shape rotating and shrinking simultaneously. The figure consists of multiple circles, sectors, and segments, generated through transformations like mirroring, rotation, and dilation. Start by placing a central point, then draw several circles and sectors around it. Apply mirroring and rotation to create symmetrical shapes, and combine all elements into a cohesive dynamic whole that demonstrates geometric transformations and trigonometric principles.
The prompt above was compiled from the original drawing commands and is for reference only.