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Perspective Tesseract Demonstration

Perspective Tesseract Demonstration
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2019-09-26 07:33
Solid GeometryMatrixParametric EquationGeometric Construction
This example provides an interactive demonstration of a tesseract, showcasing its projection in 3D space. It involves core mathematical concepts such as solid geometry, matrix transformations, parametric equations, and integral calculus. The construction utilizes GeoGebra commands like Ray, Point, Segment, and Intersect, along with objects like H_1, D, F_3, etc. It is suitable for high school and above students to visualize and understand higher-dimensional geometry and spatial transformations.

GeoGebra Commands & Parameters

  1. Ray(F_3, H_3) → r_7
  2. Point(r_7) → J_3
  3. Segment(E, G) → l
  4. Segment(G, F) → m
  5. Segment(F, E) → n
  6. Ray(E, H) → p
  7. Point(p) → I
  8. Segment(I, H) → q
  9. Ray(F, H) → r
  10. Point(r) → J
  11. Segment(H, J) → s
  12. Ray(G, H) → t
  13. Point(t) → K
  14. Segment(H, K) → a
  15. Ray(G, J) → b
  16. Ray(G, I) → c
  17. Ray(E, K) → d
  18. Ray(F, K) → e
  19. Intersect(b, e) → L
  20. Segment(L, K) → f_1
  21. Intersect(c, d) → M
  22. Segment(M, K) → g_1
  23. Segment(J, L) → h_1
  24. Segment(I, M) → i_1
  25. Ray(E, J) → j_1
  26. Ray(F, I) → k_1
  27. Intersect(j_1, k_1) → N
  28. Ray(G, N) → l_1
  29. Segment(N, J) → m_1
  30. Segment(N, I) → n_1
  31. Ray(E, L) → p_1
  32. Ray(F, M) → q_1
  33. Intersect(l_1, p_1) → O
  34. Segment(O, M) → r_1
  35. Segment(O, L) → s_1
  36. Segment(N, O) → t_1
  37. Ray(E_1, H_1) → p_2
  38. Point(p_2) → I_1
  39. Segment(I_1, H_1) → q_2
  40. Ray(F_1, H_1) → r_3
  41. Point(r_3) → J_1
  42. Segment(H_1, J_1) → s_2
  43. Ray(G_1, H_1) → t_3
  44. Point(t_3) → K_1
  45. Segment(H_1, K_1) → a_1
  46. Ray(G_1, J_1) → b_1
  47. Ray(G_1, I_1) → c_1
  48. Ray(E_1, K_1) → d_1
  49. Ray(F_1, K_1) → e_1
  50. Intersect(b_1, e_1) → L_1
  51. Segment(L_1, K_1) → f_2
  52. Intersect(c_1, d_1) → M_1
  53. Segment(M_1, K_1) → g_2
  54. Segment(J_1, L_1) → h_2
  55. Segment(I_1, M_1) → i_2
  56. Ray(E_1, J_1) → j_2
  57. Ray(F_1, I_1) → k_2
  58. Intersect(j_2, k_2) → N_1
  59. Ray(G_1, N_1) → l_3
  60. Segment(N_1, J_1) → m_3
  61. Segment(N_1, I_1) → n_3
  62. Ray(E_1, L_1) → p_3
  63. Ray(F_1, M_1) → q_3
  64. Intersect(l_3, p_3) → O_1
  65. Segment(O_1, M_1) → r_2
  66. Segment(O_1, L_1) → s_3
  67. Segment(N_1, O_1) → t_2
  68. Segment(F_2, E_2) → n_4
  69. Ray(E_2, H_2) → p_4
  70. Segment(I_2, H_2) → q_4
  71. Ray(F_2, H_2) → r_5
  72. Segment(H_2, J_2) → s_4
  73. Ray(G_2, H_2) → t_5
  74. Segment(H_2, K_2) → a_2
  75. Ray(G_2, J_2) → b_2
  76. Ray(G_2, I_2) → c_2
  77. Ray(E_2, K_2) → d_2
  78. Ray(F_2, K_2) → e_2
  79. Intersect(b_2, e_2) → L_2
  80. Segment(L_2, K_2) → f_3
  81. Intersect(c_2, d_2) → M_2
  82. Segment(M_2, K_2) → g_3
  83. Segment(J_2, L_2) → h_3
  84. Segment(I_2, M_2) → i_3
  85. Ray(E_2, J_2) → j_3
  86. Ray(F_2, I_2) → k_3
  87. Intersect(j_3, k_3) → N_2
  88. Ray(G_2, N_2) → l_5
  89. Segment(N_2, J_2) → m_5
  90. Segment(N_2, I_2) → n_5
  91. Ray(E_2, L_2) → p_5
  92. Ray(F_2, M_2) → q_5
  93. Intersect(l_5, p_5) → O_2
  94. Segment(O_2, M_2) → r_4
  95. Segment(O_2, L_2) → s_5
  96. Segment(N_2, O_2) → t_4
  97. Segment(E_3, G_3) → l_6
  98. Segment(G_3, F_3) → m_6
  99. Ray(E_3, H_3) → p_6
  100. Segment(I_3, H_3) → q_6
  101. Segment(H_3, J_3) → s_6
  102. Ray(G_3, H_3) → t_7
  103. Segment(H_3, K_3) → a_3
  104. Ray(G_3, J_3) → b_3
  105. Ray(G_3, I_3) → c_3
  106. Ray(E_3, K_3) → d_3
  107. Ray(F_3, K_3) → e_3
  108. Intersect(b_3, e_3) → L_3
  109. Segment(L_3, K_3) → f_4
  110. Intersect(c_3, d_3) → M_3
  111. Segment(M_3, K_3) → g_4
  112. Segment(J_3, L_3) → h_4
  113. Segment(I_3, M_3) → i_4
  114. Ray(E_3, J_3) → j_4
  115. Ray(F_3, I_3) → k_4
  116. Intersect(j_4, k_4) → N_3
  117. Ray(G_3, N_3) → l_7
  118. Segment(N_3, J_3) → m_7
  119. Segment(N_3, I_3) → n_7
  120. Ray(E_3, L_3) → p_7
  121. Ray(F_3, M_3) → q_7
  122. Intersect(l_7, p_7) → O_3
  123. Segment(O_3, M_3) → r_6
  124. Segment(O_3, L_3) → s_7
  125. Segment(N_3, O_3) → t_6
  126. Segment(E_4, G_4) → l_8
  127. Segment(G_4, F_4) → m_8
  128. Segment(F_4, E_4) → n_8
  129. Ray(E_4, H_4) → p_8
  130. Segment(I_4, H_4) → q_8
  131. Ray(F_4, H_4) → r_9
  132. Segment(H_4, J_4) → s_8
  133. Ray(G_4, H_4) → t_9
  134. Segment(H_4, K_4) → a_4
  135. Ray(G_4, J_4) → b_4
  136. Ray(G_4, I_4) → c_4
  137. Ray(E_4, K_4) → d_4
  138. Ray(F_4, K_4) → e_4
  139. Intersect(b_4, e_4) → L_4
  140. Segment(L_4, K_4) → f_5
  141. Intersect(c_4, d_4) → M_4
  142. Segment(M_4, K_4) → g_5
  143. Segment(J_4, L_4) → h_5
  144. Segment(I_4, M_4) → i_5
  145. Ray(E_4, J_4) → j_5
  146. Ray(F_4, I_4) → k_5
  147. Intersect(j_5, k_5) → N_4
  148. Ray(G_4, N_4) → l_9
  149. Segment(N_4, J_4) → m_9
  150. Segment(N_4, I_4) → n_9
  151. Ray(E_4, L_4) → p_9
  152. Ray(F_4, M_4) → q_9
  153. Intersect(l_9, p_9) → O_4
  154. Segment(O_4, M_4) → r_8
  155. Segment(O_4, L_4) → s_9
  156. Segment(N_4, O_4) → t_8
  157. Ray(E_1, O_2) → a_5
  158. Ray(F_1, O_3) → b_5
  159. Ray(D, O_1) → c_5
  160. Intersect(a_5, b_5) → P
  161. Segment(P, O_3) → d_5
  162. Segment(O_2, P) → e_5
  163. Segment(O_1, P) → f_6
  164. Ray(G_1, P) → g_6
  165. Segment(O_4, P) → h_6