MathPlotAI Logo MathPlotAI

Geometric Transformations Between Dodecagons

Geometric Transformations Between Dodecagons
Loading the math board and drawing, please wait…
2023-03-13 17:58
PolygonAngleVectorTransformationGeometric Construction
In collections geometriadinamica.es
This example demonstrates the arrangement and spatial relationships of multiple dodecagons on a plane. Key mathematical concepts include polygon properties, rotation transformations, translation transformations, and vector applications. Construction highlights: Using the Polygon command to draw dodecagons, the Rotate command for rotation around a point, Translate for translation, Vector to define vector relationships, Intersect to find intersection points, and Circle and Segment to complete the geometric figure. Suitable for senior high school students learning polygon properties and geometric transformations, as well as college freshmen studying preparatory geometry.

GeoGebra Commands & Parameters

  1. Rotate(B, 29.999999999999996°, A) → C
  2. Rotate(C, 29.999999999999996°, A) → D
  3. Rotate(D, 29.999999999999996°, A) → E
  4. Rotate(E, 29.999999999999996°, A) → F
  5. Rotate(F, 29.999999999999996°, A) → G
  6. Rotate(G, 29.999999999999996°, A) → H
  7. Rotate(H, 29.999999999999996°, A) → I
  8. Rotate(I, 29.999999999999996°, A) → J
  9. Rotate(J, 29.999999999999996°, A) → K
  10. Rotate(K, 29.999999999999996°, A) → L
  11. Rotate(L, 29.999999999999996°, A) → M
  12. Polygon(B, C, L, M, D, E, F, G, H, I, J, K) → P, b, k, l, m, c, d, e, f, g, h, i, j
  13. Segment(C, A) → a
  14. Circle(C, n) → p
  15. Intersect(p, a, 1) → N
  16. Rotate(C, 210°, N) → O
  17. Rotate(N, 210°, O) → Q
  18. Rotate(O, 210°, Q) → R
  19. Rotate(N, 329.99999999999994°, A) → S
  20. Polygon(B, C, N, O, Q, R, S) → T, b_1, c_1, n_1, o, q, r, s
  21. Rotate(S, 329.99999999999994°, A) → U
  22. Polygon(B, S, R, U, M) → V, b_2, s_1, r_1, u, m_1
  23. Rotate(R, 210°, Q) → W
  24. Rotate(Q, 210°, W) → Y
  25. Rotate(M, 210°, U) → Z
  26. Rotate(U, 119.99999999999999°, Z) → A_1
  27. Polygon(A, A_1, Z, U, R, Q, W, Y) → P_1, a_1, a_2, z, u_1, r_2, q_1, w, y
  28. Rotate(U, 210°, Z) → B_1
  29. Rotate(Z, 59.99999999999999°, B_1) → C_1
  30. Rotate(Y, 300.00000000000006°, A) → D_1
  31. Polygon(D_1, C_1, B_1, Z, A_1) → Q_1, d_1, c_2, b_3, z_1, a_3
  32. Rotate(B, (t * 210°), B) → B'
  33. Rotate(S, (t * 210°), B) → S'
  34. Rotate(R, (t * 210°), B) → R'
  35. Rotate(U, (t * 210°), B) → U'
  36. Rotate(M, (t * 210°), B) → M'
  37. Polygon(B', S', R', U', M') → V', b', s', r', u', m'
  38. Rotate(B', 59.99999999999999°, A) → B''
  39. Rotate(S', 59.99999999999999°, A) → S''
  40. Rotate(R', 59.99999999999999°, A) → R''
  41. Rotate(U', 59.99999999999999°, A) → U''
  42. Rotate(M', 59.99999999999999°, A) → M''
  43. Polygon(B'', S'', R'', U'', M'') → V'', b'', s'', r'', u'', m''
  44. Rotate(A, (t * 240°), U) → A'
  45. Rotate(A_1, (t * 240°), U) → A_1'
  46. Rotate(Z, (t * 240°), U) → Z'
  47. Rotate(U, (t * 240°), U) → U'_1
  48. Rotate(R, (t * 240°), U) → R'_1
  49. Rotate(Q, (t * 240°), U) → Q'
  50. Rotate(W, (t * 240°), U) → W'
  51. Rotate(Y, (t * 240°), U) → Y'
  52. Polygon(A', A_1', Z', U'_1, R'_1, Q', W', Y') → P_1', a', a_1', z', u'_1, r'_1, q', w', y'
  53. Vector(U'_1, R) → v
  54. Translate(A', v_1) → A''
  55. Translate(A_1', v_1) → A_1''
  56. Translate(Z', v_1) → Z''
  57. Translate(U'_1, v_1) → U'_1'
  58. Translate(R'_1, v_1) → R'_1'
  59. Translate(Q', v_1) → Q''
  60. Translate(W', v_1) → W''
  61. Translate(Y', v_1) → Y''
  62. Polygon(A'', A_1'', Z'', U'_1', R'_1', Q'', W'', Y'') → P_1'', a'', a_1'', z'', u'_1', r'_1', q'', w'', y''
  63. Vector(B_1, S') → w_1
  64. Translate(D_1, e_1) → D_1'
  65. Translate(C_1, e_1) → C_1'
  66. Translate(B_1, e_1) → B_1'
  67. Translate(Z, e_1) → Z'_1
  68. Translate(A_1, e_1) → A_2
  69. Polygon(D_1', C_1', B_1', Z'_1, A_2) → Q_1', d_1', c_1', b_1', z'_1, a_4
  70. Rotate(B'', 59.99999999999999°, A) → B'''
  71. Rotate(S'', 59.99999999999999°, A) → S'''
  72. Rotate(R'', 59.99999999999999°, A) → R'''
  73. Rotate(U'', 59.99999999999999°, A) → U'''
  74. Rotate(M'', 59.99999999999999°, A) → M'''
  75. Polygon(B''', S''', R''', U''', M''') → V''', b''', s''', r''', u''', m'''
  76. Rotate(B''', 59.99999999999999°, A) → B''''
  77. Rotate(S''', 59.99999999999999°, A) → S''''
  78. Rotate(R''', 59.99999999999999°, A) → R''''
  79. Rotate(U''', 59.99999999999999°, A) → U''''
  80. Rotate(M''', 59.99999999999999°, A) → M''''
  81. Polygon(B'''', S'''', R'''', U'''', M'''') → V'''', b'''', s'''', r'''', u'''', m''''
  82. Rotate(B'''', 59.99999999999999°, A) → B'''''
  83. Rotate(S'''', 59.99999999999999°, A) → S'''''
  84. Rotate(R'''', 59.99999999999999°, A) → R'''''
  85. Rotate(U'''', 59.99999999999999°, A) → U'''''
  86. Rotate(M'''', 59.99999999999999°, A) → M'''''
  87. Polygon(B''''', S''''', R''''', U''''', M''''') → V''''', b''''', s''''', r''''', u''''', m'''''
  88. Rotate(B''''', 59.99999999999999°, A) → B''''''
  89. Rotate(S''''', 59.99999999999999°, A) → S''''''
  90. Rotate(R''''', 59.99999999999999°, A) → R''''''
  91. Rotate(U''''', 59.99999999999999°, A) → U''''''
  92. Rotate(M''''', 59.99999999999999°, A) → M''''''
  93. Polygon(B'''''', S'''''', R'''''', U'''''', M'''''') → V'''''', b'''''', s'''''', r'''''', u'''''', m''''''
  94. Rotate(B, 59.99999999999999°, A) → B'_1
  95. Rotate(C, 59.99999999999999°, A) → C'
  96. Rotate(N, 59.99999999999999°, A) → N'
  97. Rotate(O, 59.99999999999999°, A) → O'
  98. Rotate(Q, 59.99999999999999°, A) → Q'_1
  99. Rotate(R, 59.99999999999999°, A) → R'_2
  100. Rotate(S, 59.99999999999999°, A) → S'_1
  101. Polygon(B'_1, C', N', O', Q'_1, R'_2, S'_1) → T', b'_1, c', n', o', q'_1, r'_2, s'_1
  102. Rotate(B'_1, 59.99999999999999°, A) → B'_1'
  103. Rotate(C', 59.99999999999999°, A) → C''
  104. Rotate(N', 59.99999999999999°, A) → N''
  105. Rotate(O', 59.99999999999999°, A) → O''
  106. Rotate(Q'_1, 59.99999999999999°, A) → Q'_1'
  107. Rotate(R'_2, 59.99999999999999°, A) → R'_2'
  108. Rotate(S'_1, 59.99999999999999°, A) → S'_1'
  109. Polygon(B'_1', C'', N'', O'', Q'_1', R'_2', S'_1') → T'', b'_1', c'', n'', o'', q'_1', r'_2', s'_1'
  110. Rotate(B'_1', 59.99999999999999°, A) → B'_1''
  111. Rotate(C'', 59.99999999999999°, A) → C'''
  112. Rotate(N'', 59.99999999999999°, A) → N'''
  113. Rotate(O'', 59.99999999999999°, A) → O'''
  114. Rotate(Q'_1', 59.99999999999999°, A) → Q'_1''
  115. Rotate(R'_2', 59.99999999999999°, A) → R'_2''
  116. Rotate(S'_1', 59.99999999999999°, A) → S'_1''
  117. Polygon(B'_1'', C''', N''', O''', Q'_1'', R'_2'', S'_1'') → T''', b'_1'', c''', n''', o''', q'_1'', r'_2'', s'_1''
  118. Rotate(B'_1'', 59.99999999999999°, A) → B'_1'''
  119. Rotate(C''', 59.99999999999999°, A) → C''''
  120. Rotate(N''', 59.99999999999999°, A) → N''''
  121. Rotate(O''', 59.99999999999999°, A) → O''''
  122. Rotate(Q'_1'', 59.99999999999999°, A) → Q'_1'''
  123. Rotate(R'_2'', 59.99999999999999°, A) → R'_2'''
  124. Rotate(S'_1'', 59.99999999999999°, A) → S'_1'''
  125. Polygon(B'_1''', C'''', N'''', O'''', Q'_1''', R'_2''', S'_1''') → T'''', b'_1''', c'''', n'''', o'''', q'_1''', r'_2''', s'_1'''
  126. Rotate(B'_1''', 59.99999999999999°, A) → B'_1''''
  127. Rotate(C'''', 59.99999999999999°, A) → C'''''
  128. Rotate(N'''', 59.99999999999999°, A) → N'''''
  129. Rotate(O'''', 59.99999999999999°, A) → O'''''
  130. Rotate(Q'_1''', 59.99999999999999°, A) → Q'_1''''
  131. Rotate(R'_2''', 59.99999999999999°, A) → R'_2''''
  132. Rotate(S'_1''', 59.99999999999999°, A) → S'_1''''
  133. Polygon(B'_1'''', C''''', N''''', O''''', Q'_1'''', R'_2'''', S'_1'''') → T''''', b'_1'''', c''''', n''''', o''''', q'_1'''', r'_2'''', s'_1''''
  134. Rotate(A'', 59.99999999999999°, A) → A'''
  135. Rotate(A_1'', 59.99999999999999°, A) → A_1'''
  136. Rotate(Z'', 59.99999999999999°, A) → Z'''
  137. Rotate(U'_1', 59.99999999999999°, A) → U'_1''
  138. Rotate(R'_1', 59.99999999999999°, A) → R'_1''
  139. Rotate(Q'', 59.99999999999999°, A) → Q'''
  140. Rotate(W'', 59.99999999999999°, A) → W'''
  141. Rotate(Y'', 59.99999999999999°, A) → Y'''
  142. Polygon(A''', A_1''', Z''', U'_1'', R'_1'', Q''', W''', Y''') → P_1''', a''', a_1''', z''', u'_1'', r'_1'', q''', w''', y'''
  143. Rotate(A''', 59.99999999999999°, A) → A''''
  144. Rotate(A_1''', 59.99999999999999°, A) → A_1''''
  145. Rotate(Z''', 59.99999999999999°, A) → Z''''
  146. Rotate(U'_1'', 59.99999999999999°, A) → U'_1'''
  147. Rotate(R'_1'', 59.99999999999999°, A) → R'_1'''
  148. Rotate(Q''', 59.99999999999999°, A) → Q''''
  149. Rotate(W''', 59.99999999999999°, A) → W''''
  150. Rotate(Y''', 59.99999999999999°, A) → Y''''
  151. Polygon(A'''', A_1'''', Z'''', U'_1''', R'_1''', Q'''', W'''', Y'''') → P_1'''', a'''', a_1'''', z'''', u'_1''', r'_1''', q'''', w'''', y''''
  152. Rotate(A'''', 59.99999999999999°, A) → A'''''
  153. Rotate(A_1'''', 59.99999999999999°, A) → A_1'''''
  154. Rotate(Z'''', 59.99999999999999°, A) → Z'''''
  155. Rotate(U'_1''', 59.99999999999999°, A) → U'_1''''
  156. Rotate(R'_1''', 59.99999999999999°, A) → R'_1''''
  157. Rotate(Q'''', 59.99999999999999°, A) → Q'''''
  158. Rotate(W'''', 59.99999999999999°, A) → W'''''
  159. Rotate(Y'''', 59.99999999999999°, A) → Y'''''
  160. Polygon(A''''', A_1''''', Z''''', U'_1'''', R'_1'''', Q''''', W''''', Y''''') → P_1''''', a''''', a_1''''', z''''', u'_1'''', r'_1'''', q''''', w''''', y'''''
  161. Rotate(A''''', 59.99999999999999°, A) → A''''''
  162. Rotate(A_1''''', 59.99999999999999°, A) → A_1''''''
  163. Rotate(Z''''', 59.99999999999999°, A) → Z''''''
  164. Rotate(U'_1'''', 59.99999999999999°, A) → U'_1'''''
  165. Rotate(R'_1'''', 59.99999999999999°, A) → R'_1'''''
  166. Rotate(Q''''', 59.99999999999999°, A) → Q''''''
  167. Rotate(W''''', 59.99999999999999°, A) → W''''''
  168. Rotate(Y''''', 59.99999999999999°, A) → Y''''''
  169. Polygon(A'''''', A_1'''''', Z'''''', U'_1''''', R'_1''''', Q'''''', W'''''', Y'''''') → P_1'''''', a'''''', a_1'''''', z'''''', u'_1''''', r'_1''''', q'''''', w'''''', y''''''
  170. Rotate(A'''''', 59.99999999999999°, A) → A'''''''
  171. Rotate(A_1'''''', 59.99999999999999°, A) → A_1'''''''
  172. Rotate(Z'''''', 59.99999999999999°, A) → Z'''''''
  173. Rotate(U'_1''''', 59.99999999999999°, A) → U'_1''''''
  174. Rotate(R'_1''''', 59.99999999999999°, A) → R'_1''''''
  175. Rotate(Q'''''', 59.99999999999999°, A) → Q'''''''
  176. Rotate(W'''''', 59.99999999999999°, A) → W'''''''
  177. Rotate(Y'''''', 59.99999999999999°, A) → Y'''''''
  178. Polygon(A''''''', A_1''''''', Z''''''', U'_1'''''', R'_1'''''', Q''''''', W''''''', Y''''''') → P_1''''''', a''''''', a_1''''''', z''''''', u'_1'''''', r'_1'''''', q''''''', w''''''', y'''''''
  179. Rotate(D_1', 59.99999999999999°, A) → D_1''
  180. Rotate(C_1', 59.99999999999999°, A) → C_1''
  181. Rotate(B_1', 59.99999999999999°, A) → B_1''
  182. Rotate(Z'_1, 59.99999999999999°, A) → Z'_1'
  183. Rotate(A_2, 59.99999999999999°, A) → A_2'
  184. Polygon(D_1'', C_1'', B_1'', Z'_1', A_2') → Q_1'', d_1'', c_1'', b_1'', z'_1', a_2'
  185. Rotate(D_1'', 59.99999999999999°, A) → D_1'''
  186. Rotate(C_1'', 59.99999999999999°, A) → C_1'''
  187. Rotate(B_1'', 59.99999999999999°, A) → B_1'''
  188. Rotate(Z'_1', 59.99999999999999°, A) → Z'_1''
  189. Rotate(A_2', 59.99999999999999°, A) → A_2''
  190. Polygon(D_1''', C_1''', B_1''', Z'_1'', A_2'') → Q_1''', d_1''', c_1''', b_1''', z'_1'', a_2''
  191. Rotate(D_1''', 59.99999999999999°, A) → D_1''''
  192. Rotate(C_1''', 59.99999999999999°, A) → C_1''''
  193. Rotate(B_1''', 59.99999999999999°, A) → B_1''''
  194. Rotate(Z'_1'', 59.99999999999999°, A) → Z'_1'''
  195. Rotate(A_2'', 59.99999999999999°, A) → A_2'''
  196. Polygon(D_1'''', C_1'''', B_1'''', Z'_1''', A_2''') → Q_1'''', d_1'''', c_1'''', b_1'''', z'_1''', a_2'''
  197. Rotate(D_1'''', 59.99999999999999°, A) → D_1'''''
  198. Rotate(C_1'''', 59.99999999999999°, A) → C_1'''''
  199. Rotate(B_1'''', 59.99999999999999°, A) → B_1'''''
  200. Rotate(Z'_1''', 59.99999999999999°, A) → Z'_1''''
  201. Rotate(A_2''', 59.99999999999999°, A) → A_2''''
  202. Polygon(D_1''''', C_1''''', B_1''''', Z'_1'''', A_2'''') → Q_1''''', d_1''''', c_1''''', b_1''''', z'_1'''', a_2''''
  203. Rotate(D_1''''', 59.99999999999999°, A) → D_1''''''
  204. Rotate(C_1''''', 59.99999999999999°, A) → C_1''''''
  205. Rotate(B_1''''', 59.99999999999999°, A) → B_1''''''
  206. Rotate(Z'_1'''', 59.99999999999999°, A) → Z'_1'''''
  207. Rotate(A_2'''', 59.99999999999999°, A) → A_2'''''
  208. Polygon(D_1'''''', C_1'''''', B_1'''''', Z'_1''''', A_2''''') → Q_1'''''', d_1'''''', c_1'''''', b_1'''''', z'_1''''', a_2'''''

AI Drawing Prompt Reference

Draw a geometric figure consisting of multiple dodecagons with rotational and translational relationships between them. The figure includes multiple dodecagons, circles, line segments, and intersection points. First, draw a dodecagon, then replicate it multiple times through rotation and translation to form a complex figure. Finally, draw the connecting line segments and circles, including intersection points and circle centers.
The prompt above was compiled from the original drawing commands and is for reference only.