棱柱展开图探索

棱柱展开图探索
几何画板及绘图内容加载中,请稍等……
2022-10-18 16:18
①本范例演示棱柱的展开图及其折叠过程;②涉及核心数学概念包括棱柱、线段、二次方程、不等式、百分比、泊松分布;③作图要点提炼自GeoGebra命令:PointIn, Polygon, Circle, Point, OrthogonalLine, Intersect, Segment, Prism, Net, SelectedIndex;④适合高中及以上学生及数学爱好者用于立体几何学习和探索。

GeoGebra 命令及参数

  1. PointIn(xOyPlane) → A
  2. PointIn(xOyPlane) → B
  3. Polygon(A, B, 4, xOyPlane) → squa, segmAB, g, h, i, C, D
  4. Circle(Midpoint[A, B], (0.5 * Segment[A, B]), xOyPlane) → c
  5. Point(c) → E
  6. Polygon(A, B, E) → rightTri, e, a_1, b
  7. OrthogonalLine(Midpoint[A, B], segmAB, xOyPlane) → f
  8. Point(f) → P
  9. Polygon(A, B, P) → isoTri, p, a_2, b_1
  10. PointIn(xOyPlane) → F
  11. OrthogonalLine(F, Segment[A, F], xOyPlane) → j
  12. Point(j) → G
  13. OrthogonalLine(G, j, xOyPlane) → k
  14. OrthogonalLine(A, Segment[A, F], xOyPlane) → l
  15. Intersect(k, l) → H
  16. Polygon(A, F, G, H) → rect, a_3, f_1, g_1, h_1
  17. OrthogonalLine(A, squa) → m
  18. Point(m) → I
  19. Segment(A, I) → hei
  20. Prism(squa, I) → squaPri, J, edgeBJ, edgeCK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, K, L, faceABJI, faceBCKJ, faceCDLK, faceADLI, faceIJKL, edgeAI_{1}
  21. Prism(rect, I) → rectPri, M, edgeFM, edgeGN, edgeHO, edgeIM, edgeMN, edgeNO, edgeIO, N, O, faceAFMI, faceFGNM, faceGHON, faceAHOI, faceIMNO, edgeAI_{2}
  22. Prism(isoTri, I) → isoPri, Q, edgeIQ, edgeQR, edgeIR, R, faceABQI, faceBPRQ, faceAIRP, faceIQR, edgeAI_{3}, edgeBQ, edgePR
  23. Prism(rightTri, I) → rightPri, S, edgeIS, edgeST, edgeIT, T, faceABSI, faceBETS, faceAETI, faceIST, edgeAI, edgeBS, edgeET
  24. Net(isoPri, open) → isoNet, U, F_1, faceUVW, face2, face4, face3, face1, edgeUV, edgeVW, edgeUW, edgeUZ, V, edge6, edge2, edge3, edge9, edge4, edge5, edge10, edge1, edge8, edge7, W, Z, A_1, B_1, C_1, D_1, E_1
  25. Net(rectPri, open) → rectNet, G_1, P_1, Q_1, R_1, S_1, T_1, face5, face6, face8, face9, face7, H_1, face10, edge11, edge15, edge18, edge12, edge13, edge23, edge16, edge17, edge26, I_1, edge19, edge20, edge27, edge21, edge22, edge28, edge14, edge25, edge29, edge24, J_1, K_1, L_1, M_1, N_1, O_1
  26. Net(rightPri, open) → rightNet, U_1, F_2, face11, face13, face15, face14, face12, edge30, edge34, edge31, edge32, V_1, edge39, edge35, edge36, edge42, edge37, edge38, edge43, edge33, edge41, edge40, W_1, Z_1, A_2, B_2, C_2, D_2, E_2
  27. Net(squaPri, open) → squaNet, G_2, P_2, Q_2, R_2, S_2, T_2, face16, face17, face19, face20, face18, H_2, face21, edge44, edge48, edge51, edge45, edge46, edge56, edge49, edge50, edge59, I_2, edge52, edge53, edge60, edge54, edge55, edge61, edge47, edge58, edge62, edge57, J_2, K_2, L_2, M_2, N_2, O_2
  28. SelectedIndex(baseMenu) → is

AI 绘图提示语参考

绘制一个正方形棱柱,包含底面正方形、侧面四个矩形面和两个底面。首先绘制一个正方形,然后从正方形的一个顶点向上绘制一条垂直线,这条线的长度将作为棱柱的高。接着,以这条线的端点为底,绘制四个矩形面,连接正方形的四个顶点和这条线的端点。最后,绘制两个正方形底面,分别位于棱柱的两端。
以上提示语为根据原始绘图命令整理而来,仅供参考。