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Polygon Rotation and Construction Demo

Polygon Rotation and Construction Demo
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2014-04-06 11:04
PolygonTrigonometryGeometric ConstructionGraphing
In collections Phebe Tanner Tessellation Rotation
This example demonstrates how to construct new shapes by rotating polygons and observing their transformation patterns. Key math concepts include polygons, rotation, volume calculation, function graphing, trigonometric applications, and percentage change analysis. The construction highlights the use of GeoGebra commands like Polygon, Segment, and Rotate, as detailed in the summary. Suitable for high school mathematics education, integrating geometric construction, function graphs, and transformation concepts for visual learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, b, c, C
  2. Segment(B, D) → d
  3. Segment(D, E) → e
  4. Segment(E, F) → f
  5. Segment(F, G) → g
  6. Segment(G, H) → h
  7. Segment(H, I) → i
  8. Segment(I, J) → j
  9. Segment(J, K) → k
  10. Segment(K, L) → l
  11. Segment(L, M) → m
  12. Segment(M, N) → n
  13. Segment(N, O) → p
  14. Segment(O, P) → q
  15. Segment(P, Q) → r
  16. Segment(Q, R) → s
  17. Segment(R, S) → t
  18. Segment(S, T) → a_1
  19. Segment(T, U) → b_1
  20. Segment(U, V) → c_1
  21. Segment(V, W) → d_1
  22. Segment(W, Z) → e_1
  23. Segment(Z, A_1) → f_1
  24. Segment(A_1, B_1) → g_1
  25. Segment(B_1, C) → h_1
  26. Rotate(B, 60*°, B) → B'
  27. Rotate(D, 60*°, B) → D'
  28. Segment(B', D') → d'
  29. Rotate(D, 60*°, B) → D'_1
  30. Rotate(E, 60*°, B) → E'
  31. Segment(D'_1, E') → e'
  32. Rotate(E, 60*°, B) → E'_1
  33. Rotate(F, 60*°, B) → F'
  34. Segment(E'_1, F') → f'
  35. Rotate(F, 60*°, B) → F'_1
  36. Rotate(G, 60*°, B) → G'
  37. Segment(F'_1, G') → g'
  38. Rotate(G, 60*°, B) → G'_1
  39. Rotate(H, 60*°, B) → H'
  40. Segment(G'_1, H') → h'
  41. Rotate(H, 60*°, B) → H'_1
  42. Rotate(I, 60*°, B) → I'
  43. Segment(H'_1, I') → i'
  44. Rotate(I, 60*°, B) → I'_1
  45. Rotate(J, 60*°, B) → J'
  46. Segment(I'_1, J') → j'
  47. Rotate(J, 60*°, B) → J'_1
  48. Rotate(K, 60*°, B) → K'
  49. Segment(J'_1, K') → k'
  50. Rotate(K, 60*°, B) → K'_1
  51. Rotate(L, 60*°, B) → L'
  52. Segment(K'_1, L') → l'
  53. Rotate(L, 60*°, B) → L'_1
  54. Rotate(M, 60*°, B) → M'
  55. Segment(L'_1, M') → m'
  56. Rotate(M, 60*°, B) → M'_1
  57. Rotate(N, 60*°, B) → N'
  58. Segment(M'_1, N') → n'
  59. Rotate(N, 60*°, B) → N'_1
  60. Rotate(O, 60*°, B) → O'
  61. Segment(N'_1, O') → p'
  62. Rotate(O, 60*°, B) → O'_1
  63. Rotate(P, 60*°, B) → P'
  64. Segment(O'_1, P') → q'
  65. Rotate(P, 60*°, B) → P'_1
  66. Rotate(Q, 60*°, B) → Q'
  67. Segment(P'_1, Q') → r'
  68. Rotate(Q, 60*°, B) → Q'_1
  69. Rotate(R, 60*°, B) → R'
  70. Segment(Q'_1, R') → s'
  71. Rotate(R, 60*°, B) → R'_1
  72. Rotate(S, 60*°, B) → S'
  73. Segment(R'_1, S') → t'
  74. Rotate(S, 60*°, B) → S'_1
  75. Rotate(T, 60*°, B) → T'
  76. Segment(S'_1, T') → i_1
  77. Rotate(T, 60*°, B) → T'_1
  78. Rotate(U, 60*°, B) → U'
  79. Segment(T'_1, U') → j_1
  80. Rotate(U, 60*°, B) → U'_1
  81. Rotate(V, 60*°, B) → V'
  82. Segment(U'_1, V') → k_1
  83. Rotate(V, 60*°, B) → V'_1
  84. Rotate(W, 60*°, B) → W'
  85. Segment(V'_1, W') → l_1
  86. Rotate(W, 60*°, B) → W'_1
  87. Rotate(Z, 60*°, B) → Z'
  88. Segment(W'_1, Z') → m_1
  89. Rotate(Z, 60*°, B) → Z'_1
  90. Rotate(A_1, 60*°, B) → C_1
  91. Segment(Z'_1, C_1) → n_1
  92. Rotate(A_1, 60*°, B) → D_1
  93. Rotate(B_1, 60*°, B) → E_1
  94. Segment(D_1, E_1) → p_1
  95. Rotate(B_1, 60*°, B) → F_1
  96. Rotate(C, 60*°, B) → C'
  97. Segment(F_1, C') → q_1
  98. Rotate(B', 60*°, A) → B''
  99. Rotate(D', 60*°, A) → D''
  100. Segment(B'', D'') → d''
  101. Rotate(D'_1, 60*°, A) → G_1
  102. Rotate(E', 60*°, A) → E''
  103. Segment(G_1, E'') → e''
  104. Rotate(E'_1, 60*°, A) → H_1
  105. Rotate(F', 60*°, A) → F''
  106. Segment(H_1, F'') → f''
  107. Rotate(F'_1, 60*°, A) → I_1
  108. Rotate(G', 60*°, A) → G''
  109. Segment(I_1, G'') → g''
  110. Rotate(G'_1, 60*°, A) → J_1
  111. Rotate(H', 60*°, A) → H''
  112. Segment(J_1, H'') → h''
  113. Rotate(H'_1, 60*°, A) → K_1
  114. Rotate(I', 60*°, A) → I''
  115. Segment(K_1, I'') → i''
  116. Rotate(I'_1, 60*°, A) → L_1
  117. Rotate(J', 60*°, A) → J''
  118. Segment(L_1, J'') → j''
  119. Rotate(J'_1, 60*°, A) → M_1
  120. Rotate(K', 60*°, A) → K''
  121. Segment(M_1, K'') → k''
  122. Rotate(K'_1, 60*°, A) → N_1
  123. Rotate(L', 60*°, A) → L''
  124. Segment(N_1, L'') → l''
  125. Rotate(L'_1, 60*°, A) → O_1
  126. Rotate(M', 60*°, A) → M''
  127. Segment(O_1, M'') → m''
  128. Rotate(M'_1, 60*°, A) → P_1
  129. Rotate(N', 60*°, A) → N''
  130. Segment(P_1, N'') → n''
  131. Rotate(N'_1, 60*°, A) → Q_1
  132. Rotate(O', 60*°, A) → O''
  133. Segment(Q_1, O'') → p''
  134. Rotate(O'_1, 60*°, A) → R_1
  135. Rotate(P', 60*°, A) → P''
  136. Segment(R_1, P'') → q''
  137. Rotate(P'_1, 60*°, A) → S_1
  138. Rotate(Q', 60*°, A) → Q''
  139. Segment(S_1, Q'') → r''
  140. Rotate(Q'_1, 60*°, A) → T_1
  141. Rotate(R', 60*°, A) → R''
  142. Segment(T_1, R'') → s''
  143. Rotate(R'_1, 60*°, A) → U_1
  144. Rotate(S', 60*°, A) → S''
  145. Segment(U_1, S'') → t''
  146. Rotate(S'_1, 60*°, A) → V_1
  147. Rotate(T', 60*°, A) → T''
  148. Segment(V_1, T'') → r_1
  149. Rotate(T'_1, 60*°, A) → W_1
  150. Rotate(U', 60*°, A) → U''
  151. Segment(W_1, U'') → s_1
  152. Rotate(U'_1, 60*°, A) → Z_1
  153. Rotate(V', 60*°, A) → V''
  154. Segment(Z_1, V'') → t_1
  155. Rotate(V'_1, 60*°, A) → A_2
  156. Rotate(W', 60*°, A) → W''
  157. Segment(A_2, W'') → a_2
  158. Rotate(W'_1, 60*°, A) → B_2
  159. Rotate(Z', 60*°, A) → Z''
  160. Segment(B_2, Z'') → b_2
  161. Rotate(Z'_1, 60*°, A) → C_2
  162. Rotate(C_1, 60*°, A) → D_2
  163. Segment(C_2, D_2) → c_2
  164. Rotate(D_1, 60*°, A) → E_2
  165. Rotate(E_1, 60*°, A) → F_2
  166. Segment(E_2, F_2) → d_2
  167. Rotate(F_1, 60*°, A) → G_2
  168. Rotate(C', 60*°, A) → C''
  169. Segment(G_2, C'') → e_2
  170. Rotate(B, 60*°, A) → B'_1

AI Drawing Prompt Reference

Draw a regular polygon with multiple sides, then rotate it around one vertex by 60 degrees to create multiple rotated copies, showing the transformation pattern.
The prompt above was compiled from the original drawing commands and is for reference only.