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Geogebra Demonstration of Transformations and Integrals

Geogebra Demonstration of Transformations and Integrals
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2017-03-29 07:36
FunctionTrigonometryCoordinate GeometryIntegralGeometric Construction
In collections Tessellations
This example dynamically demonstrates function graphs, vector transformations, and integral calculations using GeoGebra. It involves core concepts like cosine functions, coordinate geometry, definite integrals, and arithmetic-geometric mean. Construction highlights include commands like Segment, OrthogonalLine, Point, Intersect, Vector, Translate, Polygon, Circle, and Semicircle. Suitable for high school and above, helping students understand function transformations, integral applications, and geometric constructions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. Point(g) → C
  5. OrthogonalLine(C, g) → i
  6. Intersect(h, i) → D
  7. Segment(A, B) → j
  8. Segment(A, C) → k
  9. Segment(C, D) → l
  10. Segment(B, D) → m
  11. Segment(A, E) → n
  12. Segment(F, E) → p
  13. Segment(F, G) → q
  14. Segment(H, G) → r
  15. Segment(H, B) → s
  16. Vector(A, C) → u
  17. Translate(A, u) → A'
  18. Translate(E, u) → E'
  19. Segment(A', E') → n'
  20. Translate(F, u) → F'
  21. Translate(E, u) → E'_1
  22. Segment(F', E'_1) → p'
  23. Translate(F, u) → F'_1
  24. Translate(G, u) → G'
  25. Segment(F'_1, G') → q'
  26. Translate(H, u) → H'
  27. Translate(G, u) → G'_1
  28. Segment(H', G'_1) → r'
  29. Translate(H, u) → H'_1
  30. Translate(B, u) → B'
  31. Segment(H'_1, B') → s'
  32. Segment(A, I) → t
  33. Segment(I, J) → a
  34. Segment(J, K) → b
  35. Segment(K, L) → c
  36. Segment(L, M) → d
  37. Segment(N, O) → e
  38. Segment(P, C) → f_1
  39. Vector(A, B) → v
  40. Translate(A, v) → A'_1
  41. Translate(I, v) → I'
  42. Segment(A'_1, I') → t'
  43. Translate(I, v) → I'_1
  44. Translate(J, v) → J'
  45. Segment(I'_1, J') → a'
  46. Translate(J, v) → J'_1
  47. Translate(K, v) → K'
  48. Segment(J'_1, K') → b'
  49. Translate(K, v) → K'_1
  50. Translate(L, v) → L'
  51. Segment(K'_1, L') → c'
  52. Translate(L, v) → L'_1
  53. Translate(M, v) → M'
  54. Segment(L'_1, M') → d'
  55. Translate(N, v) → N'
  56. Translate(O, v) → O'
  57. Segment(N', O') → e'
  58. Translate(P, v) → P'
  59. Translate(C, v) → C'
  60. Segment(P', C') → g_1
  61. Segment(M, N) → h_1
  62. Segment(M, N) → i_1
  63. Segment(O, P) → j_1
  64. Segment(M, N) → k_1
  65. Segment(M', N') → l_1
  66. Segment(P', O') → m_1
  67. Polygon(F, E, P, C, E', F', G', H', D, P', O', N', A, M', L', K', J', I', B, H, G, I, J, K, L, M, N, O) → poly1, f_2, o, p_1, c_1, e'_1, f', g', h', d_1, p'_1, o', e_1, n'_1, m', l', k', j', i', b_1, h_2, g_2, a_1, i_2, j_2, k_2, l_2, m_2, n_1
  68. Circle(Q, S) → q_1
  69. Circle(R, T) → r_1
  70. Semicircle(U, V) → s_1
  71. Segment(V, U) → t_1
  72. Segment(V, U) → n_{2}
  73. Vector(A, B) → w
  74. Translate(F, w) → F'_2
  75. Translate(E, w) → E'_2
  76. Translate(A, w) → A'_2
  77. Translate(I, w) → I'_2
  78. Translate(J, w) → J'_2
  79. Translate(K, w) → K'_2
  80. Translate(L, w) → L'_2
  81. Translate(M, w) → M'_1
  82. Translate(N, w) → N'_1
  83. Translate(O, w) → O'_1
  84. Translate(P, w) → P'_1
  85. Translate(C, w) → C'_1
  86. Translate(E', w) → E''
  87. Translate(F', w) → F''
  88. Translate(G', w) → G''
  89. Translate(H', w) → H''
  90. Translate(D, w) → D'
  91. Translate(P', w) → P''
  92. Translate(O', w) → O''
  93. Translate(N', w) → N''
  94. Translate(M', w) → M''
  95. Translate(L', w) → L''
  96. Translate(K', w) → K''
  97. Translate(J', w) → J''
  98. Translate(I', w) → I''
  99. Translate(B, w) → B'_1
  100. Translate(H, w) → H'_2
  101. Translate(G, w) → G'_2
  102. Polygon(F'_2, E'_2, P'_1, C'_1, E'', F'', G'', H'', D', P'', O'', N'', A'_2, M'', L'', K'', J'', I'', B'_1, H'_2, G'_2, I'_2, J'_2, K'_2, L'_2, M'_1, N'_1, O'_1) → poly1', f'_2, o'_1, p'_2, c'_1, e'', f'', g'', h'', d'_1, p'', o'', e'_2, n'', m'', l'', k'', j'', i'', b'_1, h'_2, g'_2, a'_2, i'_2, j'_2, k'_2, l'_2, m'_1, n'_2
  103. Translate(q_1, w) → c_2
  104. Translate(r_1, w) → d_2
  105. Translate(s_1, w) → e_2
  106. Translate(A, w) → A'_3
  107. Translate(E, w) → E'_3
  108. Segment(A'_3, E'_3) → n'_3
  109. Translate(F, w) → F'_3
  110. Translate(E, w) → E'_4
  111. Segment(F'_3, E'_4) → p'_3
  112. Translate(F, w) → F'_4
  113. Translate(G, w) → G'_3
  114. Segment(F'_4, G'_3) → q'_1
  115. Translate(H, w) → H'_3
  116. Translate(G, w) → G'_4
  117. Segment(H'_3, G'_4) → r'_1
  118. Translate(H, w) → H'_4
  119. Translate(B, w) → B'_2
  120. Segment(H'_4, B'_2) → s'_1
  121. Translate(A', w) → A''
  122. Translate(E', w) → E''_1
  123. Segment(A'', E''_1) → n''_1
  124. Translate(F', w) → F''_1
  125. Translate(E'_1, w) → W
  126. Segment(F''_1, W) → p''_1
  127. Translate(F'_1, w) → Z
  128. Translate(G', w) → G''_1
  129. Segment(Z, G''_1) → q''
  130. Translate(H', w) → H''_1
  131. Translate(G'_1, w) → A_1
  132. Segment(H''_1, A_1) → r''
  133. Translate(H'_1, w) → B_1
  134. Translate(B', w) → B''
  135. Segment(B_1, B'') → s''
  136. Translate(A, w) → A'_4
  137. Translate(I, w) → I'_3
  138. Segment(A'_4, I'_3) → t'_1
  139. Translate(I, w) → I'_4
  140. Translate(J, w) → J'_3
  141. Segment(I'_4, J'_3) → a'_1
  142. Translate(J, w) → J'_4
  143. Translate(K, w) → K'_3
  144. Segment(J'_4, K'_3) → b'_2
  145. Translate(K, w) → K'_4
  146. Translate(L, w) → L'_3
  147. Segment(K'_4, L'_3) → c'_2
  148. Translate(L, w) → L'_4
  149. Translate(M, w) → M'_2
  150. Segment(L'_4, M'_2) → d'_2
  151. Translate(N, w) → N'_2
  152. Translate(O, w) → O'_2
  153. Segment(N'_2, O'_2) → e'_3
  154. Translate(P, w) → P'_2
  155. Translate(C, w) → C'_2
  156. Segment(P'_2, C'_2) → n_2
  157. Translate(A'_1, w) → C_1
  158. Translate(I', w) → I''_1
  159. Segment(C_1, I''_1) → t''
  160. Translate(I'_1, w) → D_1
  161. Translate(J', w) → J''_1
  162. Segment(D_1, J''_1) → a''
  163. Translate(J'_1, w) → E_1
  164. Translate(K', w) → K''_1
  165. Segment(E_1, K''_1) → b''
  166. Translate(K'_1, w) → F_1
  167. Translate(L', w) → L''_1
  168. Segment(F_1, L''_1) → c''
  169. Translate(L'_1, w) → G_1
  170. Translate(M', w) → M''_1
  171. Segment(G_1, M''_1) → d''
  172. Translate(N', w) → N''_1
  173. Translate(O', w) → O''_1
  174. Segment(N''_1, O''_1) → e''_1
  175. Translate(P', w) → P''_1
  176. Translate(C', w) → C''
  177. Segment(P''_1, C'') → p_2
  178. Translate(M, w) → M'_3
  179. Translate(N, w) → N'_3
  180. Segment(M'_3, N'_3) → q_2
  181. Translate(M, w) → M'_4
  182. Translate(N, w) → N'_4
  183. Segment(M'_4, N'_4) → r_2
  184. Translate(O, w) → O'_3
  185. Translate(P, w) → P'_3
  186. Segment(O'_3, P'_3) → s_2
  187. Translate(M, w) → M'_5
  188. Translate(N, w) → N'_5
  189. Segment(M'_5, N'_5) → t_2
  190. Translate(M', w) → M''_2
  191. Translate(N', w) → N''_2
  192. Segment(M''_2, N''_2) → a_2
  193. Translate(P', w) → P''_2
  194. Translate(O', w) → O''_2
  195. Segment(P''_2, O''_2) → b_2
  196. Translate(V, w) → V'
  197. Translate(U, w) → U'
  198. Segment(V', U') → f_3
  199. Translate(A, Vector[(0, -0.027146446191190776)]) → A'_5

AI Drawing Prompt Reference

Draw a dynamic illustration showing function graphs, vector transformations, and integral calculations. Start by drawing a line segment and perpendicular lines from its endpoints, connecting the intersections to form a new shape. Then, use the segment as a vector to translate the line and shape, demonstrating transformation effects. Finally, add multiple segments connecting the translated points to create a complex geometric structure, highlighting applications of coordinate geometry and integrals.
The prompt above was compiled from the original drawing commands and is for reference only.