积极 AI Logo 积极 AI

立方和的几何表示

立方和的几何表示
几何画板及绘图内容加载中，请稍等……
2019-03-27 19:31
解析几何立体几何几何作图
这个范例展示了立方和的几何表示。核心数学概念包括立方、体积和几何构造。通过使用GeoGebra命令如Point、Cube、Prism和Translate，可以构造出立方体和棱柱。适合初中及以上学生学习立体几何和代数概念。

GeoGebra 命令及参数

  1. Point(Circle[(10, 0, 0), Distance[(0, 0, 0), (10, 0, 0)], Segment[(0, 0, 0), (10, 0, 0)]]) → A
  2. Cube((0, 0, 0), (10, 0, 0), A) → a, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  3. Point(edge1) → G
  4. Point(Circle[G, Distance[I, G], Segment[I, G]]) → K
  5. Cube(I, G, K) → b, L, faceKLPO, faceMNOP, edgeIL, edgeGI, edgeGK, edgeKL, edgeIM, edgeLP, edgeMP, edgeMN, M, edgeGN, edgeNO, edgeKO, edgeOP, N, O, P, faceGILK, faceILPM, faceGIMN, faceGKON
  6. Point(Circle[Q, Distance[O, Q], Segment[O, Q]]) → R
  7. Cube(O, Q, R) → c, S, faceRSWV, faceTUVW, edgeOS, edgeOQ, edgeQR, edgeRS, edgeOT, edgeSW, edgeTW, edgeTU, T, edgeQU, edgeUV, edgeRV, edgeVW, U, V, W, faceOQRS, faceOSWT, faceOQUT, faceQRVU
  8. Prism(faceOQUT, Z) → d, A_1, edge6, edge7, edge8, edge9, edge11, edge12, edge10, B_1, C_1, face5, face6, face8, face7, face9, edgeQZ
  9. Prism(faceOSWT, D_1) → e, E_1, edge13, edge14, edge16, edge17, edge19, edge20, edge18, F_1, G_1, face11, face10, face12, face13, face14, edge15
  10. Prism(faceOQRS, H_1) → f, I_1, edge21, edge22, edge23, edge25, edge27, edge28, edge26, J_1, K_1, face16, face15, face17, face18, face19, edge24
  11. Prism(faceGKON, J_1) → g, L_1, edge29, edge31, edge32, edge33, edge35, edge36, edge34, M_1, N_1, face20, face21, face23, face22, face24, edge30
  12. Prism(faceMNOP, C) → h, O_1, edge41, edge40, edge39, edge37, edge42, edge43, edge38, P_1, Q_1, face26, face29, face28, face25, face27, edgeCM
  13. Prism(faceKLPO, B) → i, R_1, edge46, edge47, edge48, edge44, edge49, edge50, edge45, S_1, T_1, face30, face33, face34, face31, face32, edgeBL
  14. Translate(c, Vector[(explode, explode, explode)]) → c'
  15. Translate(d, Vector[(explode, 0, explode)]) → d'
  16. Translate(e, Vector[(0, explode, explode)]) → e'
  17. Translate(f, Vector[(explode, explode, 0)]) → f'
  18. Translate(g, Vector[(explode, 0, 0)]) → g'
  19. Translate(h, Vector[(0, 0, explode)]) → h'
  20. Translate(i, Vector[(0, explode, 0)]) → i'
  21. Point(Circle[G, Distance[(0, 0, 0), G], Segment[(0, 0, 0), G]]) → U_1
  22. Cube((0, 0, 0), G, U_1) → j, V_1, face39, face40, edge54, edge51, edge52, edge56, edge55, edge58, edge60, edge59, W_1, edge53, edge61, edge57, edge62, Z_1, A_2, B_2, face35, face38, face36, face37

AI 绘图提示语参考

画一个立方体和一个棱柱，立方体底面在x轴上，棱柱底面与立方体侧面重合，再分别向上和向侧面延伸，最后将三个棱柱分别沿三个坐标轴方向平移，展示立方体体积与三个小立方体体积之和的几何关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。