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Intersection of a Hypercube by Matthew Kennedy (Dr. K)

Intersection of a Hypercube by Matthew Kennedy (Dr. K)
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2018-04-27 12:38
VectorSolid GeometryGeometric Construction
This example demonstrates the intersection of a three-dimensional space while moving through a four-dimensional hypercube. It involves core mathematical concepts such as hypercube, dimensions, intersection, and geometric visualization. The construction utilizes GeoGebra commands and objects like ellipse, point, angle, conditional statements, join, segment, vector, intersect, circle, line, conic, dilation, and maximum. It is suitable for high school students and math enthusiasts to understand high-dimensional geometry and spatial relationships, serving as a teaching aid for solid geometry and analytical geometry.

GeoGebra Commands & Parameters

  1. Ellipse(O_r - (0, 0.95), O_r + (0, 0.95), 1) → mira2
  2. Point(mira2) → B
  3. Angle(M_3, O_r, B) → θ
  4. Ellipse(O_r - (0.95, 0), O_r + (0.95, 0), 1) → mira1
  5. Point(mira1) → A
  6. Angle(U_1, O_r, A) → φ
  7. If(t > 2, t - 2, t) → tt
  8. If(tt < 1, tt, 1) → tt1
  9. If(tt ≥ 1, tt - 1, 0) → tt2
  10. Angle(U_1, O_r, AM) → φ2
  11. Angle(M_3, O_r, BM) → θ2
  12. Join({{x0, y0, z0}} * MM') → M
  13. If(iguales, 1, 0.5 + cos(φ)^(2)) → hh
  14. If(iguales, hh, 2 - hh) → gg
  15. Join({{1, 1, -1} * hh} * MM) → MV1
  16. Join({{-1, -1, -1} * hh} * MM) → MV8
  17. Join({{-1, -1, 1} * hh} * MM) → MV7
  18. Join({{-1, 1, -1} * hh} * MM) → MV6
  19. Join({{-1, 1, 1} * hh} * MM) → MV5
  20. Join({{1, -1, -1} * hh} * MM) → MV4
  21. Join({{1, 1, 1} * hh} * MM) → MV2
  22. Join({{1, -1, 1} * hh} * MM) → MV3
  23. Segment(CV7, CV6) → r_{13}
  24. Vector(O_r, O) → u
  25. Intersect(mira1, mira2) → Mira1, Mira2, Mira3, Mira4
  26. Circle(O, Scale) → c
  27. Line(O, yAxis) → b
  28. Segment(Mira3, Mira2) → k_{13}
  29. Segment((-1, 0), U_1) → l
  30. Segment((0, -1), M_3) → m
  31. Angle(V3, V2, V4) → cub1Ang
  32. Angle(V6, V2, V5) → cub3Ang
  33. Angle(V5, V7, V6) → cub5Ang
  34. Angle(V4, V7, V3) → cub6Ang
  35. Angle(V5, V2, V7) → cub2Ang
  36. Angle(V4, V1, V8) → cub4Ang
  37. Segment(V1, V2) → cubo1A1
  38. Segment(V2, V3) → cubo1A2
  39. Segment(V3, V4) → cubo1A3
  40. Segment(V4, V1) → cubo1A4
  41. Segment(V1, V6) → cubo1A5
  42. Segment(V6, V8) → cubo1A6
  43. Segment(V8, V4) → cubo1A7
  44. Segment(V2, V5) → cubo1A8
  45. Segment(V5, V7) → cubo1A9
  46. Segment(V7, V3) → cubo1A10
  47. Segment(V6, V5) → cubo1A11
  48. Segment(V7, V8) → cubo1A12
  49. Segment(P, CV3) → rayo3
  50. Segment(P, CV2) → rayo2
  51. Segment(P, CV5) → rayo5
  52. Segment(P, CV7) → rayo7
  53. Segment(P, CV4) → rayo4
  54. Segment(P, CV8) → rayo8
  55. Segment(P, CV6) → rayo6
  56. Segment(P, CV1) → rayo1
  57. Segment(CV3, CV5) → f
  58. Segment(CV7, CV2) → h1
  59. Segment(CV3, CV8) → d_{13}
  60. Segment(CV7, CV4) → i_{13}
  61. Segment(CV2, CV6) → n
  62. Segment(CV5, CV1) → p
  63. Segment(CV8, CV5) → q_2
  64. Segment(CV3, CV1) → k_1
  65. Segment(CV4, CV2) → l_1
  66. Segment(CV8, CV1) → m_1
  67. Segment(CV6, CV4) → n_1
  68. Segment(E11, E12) → a_9
  69. Segment(E12, E14) → b_9
  70. Segment(E14, E13) → c_9
  71. Segment(E11, E13) → d_9
  72. Segment(E15, E17) → e_9
  73. Segment(E17, E18) → f_9
  74. Segment(E16, E18) → g_9
  75. Segment(E16, E15) → h_9
  76. Segment(E11, E15) → i_9
  77. Segment(E12, E16) → j_9
  78. Segment(E18, E14) → k_9
  79. Segment(E17, E13) → l_9
  80. Conic(C1, C2, C3, C4, C5) → luz
  81. Line(O, j) → a
  82. Line(O, i) → g
  83. Line(O, k) → j_{13}
  84. Dilate(luz, 0.05, P) → luz1
  85. Dilate(luz, 0.045, P) → luz2
  86. Dilate(luz, 0.04, P) → luz3
  87. Dilate(luz, 0.035, P) → luz4
  88. Dilate(luz, 0.03, P) → luz5
  89. Dilate(luz, 0.025, P) → luz6
  90. Dilate(luz, 0.02, P) → luz7
  91. Dilate(luz, 0.015, P) → luz8
  92. Dilate(luz, 0.01, P) → luz9
  93. Dilate(luz, 0.005, P) → luz10
  94. Segment(CV7, CV3) → linea29
  95. Segment(CV7, CV5) → linea05
  96. Segment(CV5, CV2) → linea14
  97. Segment(CV3, CV2) → linea16
  98. Segment(CV7, CV8) → linea31
  99. Segment(CV3, CV4) → linea0304
  100. Segment(CV5, CV6) → linea0506
  101. Segment(CV2, CV1) → linea08
  102. Segment(CV8, CV6) → linea10
  103. Segment(CV6, CV1) → linea12
  104. Segment(CV1, CV4) → linea18
  105. Segment(CV8, CV4) → linea19
  106. Segment(B_2, C_2) → n_{14}
  107. Segment(D_2, E_2) → p_{14}
  108. Segment(F_2, G_2) → q_{14}
  109. Segment(H_2, I_2) → r_{14}
  110. Segment(C_2, D_2) → s_{14}
  111. Segment(E_2, F_2) → t_{14}
  112. Segment(G_2, H_2) → a_{15}
  113. Segment(I_2, J_2) → b_{15}
  114. Segment(V9, V10) → cubo2A13
  115. Segment(V15, V11) → cubo2A22
  116. Segment(V14, V13) → cubo2A23
  117. Segment(V15, V16) → cubo2A24
  118. Segment(V10, V11) → cubo2A14
  119. Segment(V11, V12) → cubo2A15
  120. Segment(V12, V9) → cubo2A16
  121. Segment(V9, V14) → cubo2A17
  122. Segment(V14, V16) → cubo2A18
  123. Segment(V16, V12) → cubo2A19
  124. Segment(V10, V13) → cubo2A20
  125. Segment(V13, V15) → cubo2A21
  126. Segment(V1, V9) → cubo3A25
  127. Segment(V2, V10) → cubo3A26
  128. Segment(V3, V11) → cubo3A27
  129. Segment(V4, V12) → cubo3A28
  130. Segment(V6, V14) → cubo4A30
  131. Segment(V5, V13) → cubo4A29
  132. Segment(V7, V15) → cubo4A31
  133. Segment(V8, V16) → cubo4A32
  134. Join({{1 + h3i, 1 + h3j, 1 + h3k} * gg} * MM) → MV10
  135. Join({{1 + h3i, 1 + h3j, -1 + h3k} * gg} * MM) → MV9
  136. Join({{1 + h3i, -1 + h3j, 1 + h3k} * gg} * MM) → MV11
  137. Join({{1 + h3i, -1 + h3j, -1 + h3k} * gg} * MM) → MV12
  138. Join({{-1 + h3i, 1 + h3j, 1 + h3k} * gg} * MM) → MV13
  139. Join({{-1 + h3i, 1 + h3j, -1 + h3k} * gg} * MM) → MV14
  140. Join({{-1 + h3i, -1 + h3j, 1 + h3k} * gg} * MM) → MV15
  141. Join({{-1 + h3i, -1 + h3j, -1 + h3k} * gg} * MM) → MV16
  142. Segment(P, CV9) → rayo9
  143. Segment(P, CV12) → rayo12
  144. Segment(P, CV14) → rayo14
  145. Segment(P, CV15) → rayo15
  146. Segment(P, CV11) → rayo11
  147. Segment(P, CV13) → rayo13
  148. Segment(P, CV10) → rayo10
  149. Segment(P, CV16) → rayo16
  150. Segment(CV15, CV13) → linea06
  151. Segment(CV13, CV14) → linea09
  152. Segment(CV16, CV15) → linea11
  153. Segment(CV16, CV14) → linea13
  154. Segment(CV15, CV7) → linea15
  155. Segment(CV13, CV5) → linea17
  156. Segment(CV6, CV14) → linea20
  157. Segment(CV8, CV16) → linea21
  158. Segment(CV12, CV9) → linea22
  159. Segment(CV9, CV10) → linea23
  160. Segment(CV11, CV10) → linea24
  161. Segment(CV11, CV12) → linea25
  162. Segment(CV10, CV2) → linea26
  163. Segment(CV11, CV3) → linea27
  164. Segment(CV4, CV12) → linea28
  165. Segment(CV1, CV9) → linea30
  166. Segment(CV14, CV9) → linea32
  167. Segment(CV10, CV13) → linea1013
  168. Segment(CV11, CV15) → linea04
  169. Segment(CV16, CV12) → linea07
  170. If(t < 1, t, 1) → t1
  171. If((t ≥ 1) ∧ (t ≤ 2), t - 1, If[t < 1, 0, 1]) → t2
  172. Segment(N1103, N1110) → n1
  173. Segment(N1110, N1112) → n2
  174. Segment(N1103, N1112) → n3
  175. Segment(N1103, N1115) → n4
  176. Segment(N1115, N1112) → n5
  177. Segment(N1115, N1110) → n6
  178. If((t ≥ 2) ∧ (t ≤ 3), t - 2, If[t < 2, 0, 1]) → t3
  179. If((t ≥ 3) ∧ (t ≤ 4), t - 3, If[t < 3, 0, 1]) → t4
  180. If((t ≥ 4) ∧ (t ≤ 5), t - 4, If[t < 4, 0, 1]) → t5
  181. Segment(N1516, N1513) → n7
  182. Segment(N1513, N1507) → n8
  183. Segment(N1507, N1516) → n9
  184. Segment(N0302, N0304) → n10
  185. Segment(N0304, N0307) → n11
  186. Segment(N0307, N0302) → n12
  187. Segment(N1013, N1002) → n13
  188. Segment(N1013, N1009) → n14
  189. Segment(N1002, N1009) → n15
  190. Segment(N1216, N1209) → n16
  191. Segment(N1204, N1216) → n17
  192. Segment(N1204, N1209) → n18
  193. Segment(N1209, N1009) → n22
  194. Segment(N1513, N1013) → n23
  195. Segment(N1507, N0307) → n24
  196. Segment(N1516, N1216) → n19
  197. Segment(N0302, N1002) → n21
  198. Angle(N1110, N1112, N1103) → angPoli1
  199. Angle(N1110, N1103, N1115) → angPoli4
  200. Angle(N1115, N1112, N1110) → angPoli3
  201. Angle(N1103, N1112, N1115) → angPoli2
  202. Angle(N1216, N1209, N1513) → angPoli11
  203. Angle(N1013, N1009, N1002) → angPoli6
  204. Angle(N1013, N1002, N1507) → angPoli9
  205. Angle(N1204, N1209, N1216) → angPoli7
  206. Angle(N1204, N1216, N1507) → angPoli12
  207. Angle(N1209, N1204, N0302) → angPoli10
  208. Angle(N0302, N0304, N0307) → angPoli5
  209. Angle(N1513, N1507, N1516) → angPoli8
  210. Segment(V6, V11) → diagonalPrincipal
  211. Vector((N1103 + N1110 + N1112) / 3, (N1103 + N1110 + N1112 + Element[tetraL1, 1] * i + Element[tetraL1, 2] * j + Element[tetraL1, 3] * k) / 3) → zzVectorTetra1
  212. Vector((N1103 + N1115 + N1112) / 3, (N1103 + N1115 + N1112 + Element[tetraL2, 2] * i + Element[tetraL2, 2] * j + Element[tetraL2, 3] * k) / 3) → zzVectorTetra2
  213. Vector((N1112 + N1110 + N1115) / 3, (N1112 + N1110 + N1115 + Element[tetraL3, 1] * i + Element[tetraL3, 2] * j + Element[tetraL3, 3] * k) / 3) → zzVectorTetra3
  214. Segment(N0901, N0914) → n42
  215. Segment(N1608, N1614) → n27
  216. Segment(N1305, N1314) → n33
  217. Segment(N0705, N0708) → n34
  218. Segment(N0205, N0201) → n36
  219. Segment(N0408, N0401) → n38
  220. Segment(N0205, N1305) → n32
  221. Segment(N0705, N1305) → n29
  222. Segment(N0705, N0205) → n31
  223. Segment(N1314, N1614) → n30
  224. Segment(N1314, N0914) → n37
  225. Segment(N1614, N0914) → n28
  226. Segment(N0201, N0401) → n39
  227. Segment(N0401, N0901) → n41
  228. Segment(N0201, N0901) → n40
  229. Segment(N0408, N1608) → n26
  230. Segment(N0708, N1608) → n25
  231. Segment(N0708, N0408) → n35
  232. Segment(N1406, N0506) → n45
  233. Segment(N0506, N0106) → n44
  234. Segment(N0106, N1406) → n48
  235. Segment(N0506, N0806) → n43
  236. Segment(N0806, N0106) → n47
  237. Segment(N0806, N1406) → n46
  238. Angle(N0708, N0408, N1608) → angPoli16
  239. Angle(N0705, N1305, N0205) → angPoli13
  240. Angle(N0201, N0901, N0401) → angPoli14
  241. Angle(N0914, N1314, N1614) → angPoli15
  242. Vector(O, O + (Element[tetraL5, 1] * i + Element[tetraL5, 2] * j + Element[tetraL5, 3] * k) / 3) → zzVectorTetra5
  243. Segment(N1103', N1110') → n1'
  244. Segment(N0302', N0304') → n10'
  245. Segment(N0304', N0307') → n11'
  246. Segment(N0307', N0302') → n12'
  247. Segment(N1013', N1002') → n13'
  248. Segment(N1013', N1009') → n14'
  249. Segment(N1002', N1009') → n15'
  250. Segment(N1216', N1209') → n16'
  251. Segment(N1204', N1216') → n17'
  252. Segment(N1204', N1209') → n18'
  253. Segment(N1516', N1216') → n19'
  254. Segment(N1110', N1112') → n2'
  255. Segment(N0304, N1204) → n20
  256. Segment(N0304', N1204') → n20'
  257. Segment(N0302', N1002') → n21'
  258. Segment(N1209', N1009') → n22'
  259. Segment(N1513', N1013') → n23'
  260. Segment(N1507', N0307') → n24'
  261. Segment(N0708', N1608') → n25'
  262. Segment(N0408', N1608') → n26'
  263. Segment(N1608', N1614') → n27'
  264. Segment(N1614', N0914') → n28'
  265. Segment(N0705', N1305') → n29'
  266. Segment(N1103', N1112') → n3'
  267. Segment(N1314', N1614') → n30'
  268. Segment(N0705', N0205') → n31'
  269. Segment(N0205', N1305') → n32'
  270. Segment(N1305', N1314') → n33'
  271. Segment(N0705', N0708') → n34'
  272. Segment(N0708', N0408') → n35'
  273. Segment(N0205', N0201') → n36'
  274. Segment(N1314', N0914') → n37'
  275. Segment(N0408', N0401') → n38'
  276. Segment(N0201', N0401') → n39'
  277. Segment(N1103', N1115') → n4'
  278. Segment(N0201', N0901') → n40'
  279. Segment(N0401', N0901') → n41'
  280. Segment(N0901', N0914') → n42'
  281. Segment(N0506', N0806') → n43'
  282. Segment(N0506', N0106') → n44'
  283. Segment(N1406', N0506') → n45'
  284. Segment(N0806', N1406') → n46'
  285. Segment(N0806', N0106') → n47'
  286. Segment(N0106', N1406') → n48'
  287. Segment(N1115', N1112') → n5'
  288. Segment(N1115', N1110') → n6'
  289. Segment(N1516', N1513') → n7'
  290. Segment(N1513', N1507') → n8'
  291. Segment(N1507', N1516') → n9'
  292. Segment(CV6, CV11) → diagonal'
  293. Segment(G, J) → e
  294. Segment(K, L) → q
  295. Segment(K, N) → s
  296. Segment(N, Q) → a_1
  297. Segment(Q, L) → b_1
  298. Segment(K, R) → c_1
  299. Segment(R, S) → d_1
  300. Segment(S, N) → e_1
  301. Segment(S, U) → f_1
  302. Segment(U, Q) → g_1
  303. Segment(R, V) → h_1
  304. Segment(V, L) → i_1
  305. Segment(V, U) → j_1
  306. Segment(W, Z) → p_1
  307. Segment(W, A_1) → q_1
  308. Segment(A_1, B_1) → r_1
  309. Segment(Z, B_1) → s_1
  310. Segment(W, D_1) → t_1
  311. Segment(D_1, E_1) → a_2
  312. Segment(E_1, A_1) → b_2
  313. Segment(E_1, F_1) → c_2
  314. Segment(F_1, B_1) → d_2
  315. Segment(D_1, G_1) → e_2
  316. Segment(G_1, F_1) → f_2
  317. Segment(G_1, Z) → g_2
  318. Segment(N, A_1) → h_2
  319. Segment(S, E_1) → i_2
  320. Segment(W, K) → j_2
  321. Segment(D_1, R) → k_2
  322. Segment(G_1, V) → l_2
  323. Segment(Z, L) → m_2
  324. Segment(F_1, U) → n_2
  325. Segment(B_1, Q) → p_2
  326. Segment(J, H_1) → r_2
  327. Segment(H_1, I_1) → s_2
  328. Segment(I_1, J_1) → t_2
  329. Segment(J_1, K_1) → a_3
  330. Segment(K_1, L_1) → b_3
  331. Segment(L_1, M_1) → c_3
  332. Segment(M_1, N_1) → d_3
  333. Segment(N_1, O_1) → e_3
  334. Segment(O_1, P_1) → f_3
  335. Segment(P_1, Q_1) → g_3
  336. Segment(Q_1, R_1) → h_3
  337. Segment(R_1, S_1) → i_3
  338. Segment(S_1, T_1) → j_3
  339. Segment(T_1, V_1) → k_3
  340. Segment(V_1, W_1) → l_3
  341. Segment(W_1, Z_1) → m_3
  342. Segment(Z_1, A_2) → n_3
  343. Segment(A_2, K_2) → p_3
  344. Segment(L_2, K_2) → q_3
  345. Segment(L_2, M_2) → r_3
  346. Segment(M_2, N_2) → s_3
  347. Segment(N_2, O_2) → t_3
  348. Segment(O_2, P_2) → a_4
  349. Segment(P_2, Q_2) → b_4
  350. Segment(Q_2, R_2) → c_4
  351. Segment(R_2, S_2) → d_4
  352. Segment(S_2, T_2) → e_4
  353. Segment(T_2, U_2) → f_4
  354. Segment(U_2, V_2) → g_4
  355. Segment(V_2, W_2) → h_4
  356. Segment(W_2, Z_2) → i_4
  357. Segment(A_3, B_3) → j_4
  358. Segment(C_3, D_3) → k_4
  359. Segment(B_3, E_3) → l_4
  360. Segment(E_3, F_3) → m_4
  361. Segment(F_3, G_3) → n_4
  362. Segment(C_3, I_3) → q_4
  363. Segment(I_3, J_3) → r_4
  364. Segment(J_3, D_3) → s_4
  365. Segment(H_3, K_3) → p_4
  366. Segment(L_3, N_3) → t_4
  367. Angle(W3, W2, W4) → w1Ang
  368. Angle(W5, W2, W7) → w2Ang
  369. Angle(W6, W2, W5) → w3Ang
  370. Angle(W4, W1, W8) → w4Ang
  371. Angle(W5, W7, W6) → w5Ang
  372. Angle(W4, W7, W3) → w6Ang
  373. Segment(W1, W2) → w1A1
  374. Segment(W7, W3) → w1A10
  375. Segment(W6, W5) → w1A11
  376. Segment(W7, W8) → w1A12
  377. Segment(W2, W3) → w1A2
  378. Segment(W3, W4) → w1A3
  379. Segment(W4, W1) → w1A4
  380. Segment(W1, W6) → w1A5
  381. Segment(W6, W8) → w1A6
  382. Segment(W8, W4) → w1A7
  383. Segment(W2, W5) → w1A8
  384. Segment(W5, W7) → w1A9
  385. Join({{1, 1, -1}} * MM) → MW1
  386. Join({{1, 1, 1}} * MM) → MW2
  387. Join({{1, -1, 1}} * MM) → MW3
  388. Join({{1, -1, -1}} * MM) → MW4
  389. Join({{-1, 1, 1}} * MM) → MW5
  390. Join({{-1, 1, -1}} * MM) → MW6
  391. Join({{-1, -1, 1}} * MM) → MW7
  392. Join({{-1, -1, -1}} * MM) → MW8
  393. Segment(P, CW1) → wrayo1
  394. Segment(P, CW2) → wrayo2
  395. Segment(P, CW3) → wrayo3
  396. Segment(P, CW4) → wrayo4
  397. Segment(P, CW5) → wrayo5
  398. Segment(P, CW6) → wrayo6
  399. Segment(P, CW7) → wrayo7
  400. Segment(P, CW8) → wrayo8
  401. Segment(CW3, CW4) → a_5
  402. Segment(CW7, CW8) → b_5
  403. Segment(CW2, CW1) → c_5
  404. Segment(CW5, CW6) → d_5
  405. Segment(CW3, CW7) → e_5
  406. Segment(CW7, CW5) → f_5
  407. Segment(CW5, CW2) → g_5
  408. Segment(CW3, CW2) → h_5
  409. Segment(CW8, CW4) → i_5
  410. Segment(CW4, CW1) → j_5
  411. Segment(CW1, CW6) → k_5
  412. Segment(CW6, CW8) → l_5
  413. Segment(NW0304', NW0302') → n_5
  414. Segment(NW0307', NW0302') → p_5
  415. Segment(NW0307', NW0304') → q_5
  416. Segment(NW0307, NW0302) → r_5
  417. Segment(NW0302, NW0304) → s_5
  418. Segment(NW0307, NW0304) → t_5
  419. Max(tetraMW0, 1 - tetraMW0) → tetraMW
  420. Angle(NW0302, NW0304, NW0307) → angWPoli1
  421. Segment(NW0408, NW0401) → m_5
  422. Segment(NW0201, NW0205) → b_6
  423. Segment(NW0705, NW0708) → d_6
  424. Segment(NW0705', NW0708') → f_6
  425. Segment(NW0708', NW0408') → g_6
  426. Segment(NW0408', NW0401') → h_6
  427. Segment(NW0401', NW0201') → i_6
  428. Segment(NW0201', NW0205') → j_6
  429. Segment(NW0205', NW0705') → k_6
  430. Segment(NW0806, NW0506) → l_6
  431. Segment(NW0506, NW0106) → m_6
  432. Segment(NW0806, NW0106) → n_6
  433. Segment(NW0806', NW0506') → p_6
  434. Segment(NW0506', NW0106') → q_6
  435. Segment(NW0806', NW0106') → r_6
  436. Segment(W3, W6) → s_6
  437. Segment(NW0705, NW0205) → a_6
  438. Segment(NW0708, NW0408) → c_6
  439. Segment(NW0201, NW0401) → e_6
  440. Segment(CW3, CW6) → b_7
  441. Max(tetraM1, 1 - tetraM1) → tetraM
  442. Segment(NZ0302, NZ0304) → t_6
  443. Segment(NZ0302', NZ0304') → a_7
  444. Segment(NZ0401, NZ0201) → c_7
  445. Segment(NZ0401', NZ0201') → d_7
  446. Segment(W3, W1) → e_7
  447. Segment(CW3, CW1) → f_7
  448. Segment(NY0304', P) → g_7
  449. Segment(J_2, Q_3) → h_7
  450. Segment(Q_3, R_3) → i_7
  451. Segment(R_3, S_3) → j_7
  452. Segment(S_3, T_3) → k_7

AI Drawing Prompt Reference

Visualize the intersection of a four-dimensional hypercube with a three-dimensional space. Start by drawing two perpendicular ellipses and identifying their intersection points. Then, construct multiple three-dimensional shapes like cubes and triangles using these points and vectors, distinguishing them with different colors and transparency. Finally, combine these shapes into a complex structure to intuitively demonstrate high-dimensional geometric concepts.
The prompt above was compiled from the original drawing commands and is for reference only.