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梯形棱柱的截面 by nandrews (2)

梯形棱柱的截面 by nandrews (2)
几何画板及绘图内容加载中，请稍等……
2015-05-01 21:26
多边形向量立体几何矩阵几何作图
所属专题 Cross Sections of Prisms
①本范例演示了通过不同角度截取梯形棱柱所形成的截面图形；②涉及的核心数学概念包括立体几何、多边形、向量与矩阵运算；③作图要点——从下方『构造摘要』提炼用到了Intersect（相交）、Polygon（多边形）、Prism（棱柱）、LaTeX（公式显示）、Point（点）、OrthogonalLine（垂线）、Plane（平面）、IntersectPath（路径相交）等GeoGebra命令/对象；④适合高中及以上学生及数学爱好者用于理解空间几何与截面分析。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Prism(poly1, 5.170266100867449) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  4. LaTeX(e, true, true) → text1
  5. Point(edgeFG) → I
  6. OrthogonalLine(I, b, space) → f
  7. OrthogonalLine(I, edgeEH, space) → g
  8. Intersect(edgeEH, g) → J
  9. Intersect(f, b) → K
  10. OrthogonalLine(J, d, space) → h
  11. Intersect(d, h) → L
  12. Polygon(I, J, L, K) → poly2, i, j, l, k
  13. Point(edgeCG) → M
  14. OrthogonalLine(M, edgeBF, space) → n
  15. Intersect(edgeBF, n) → N
  16. OrthogonalLine(N, edgeAE, space) → p
  17. Intersect(edgeAE, p) → O
  18. OrthogonalLine(O, edgeDH, space) → q
  19. Intersect(edgeDH, q) → P
  20. Polygon(M, N, O, P) → poly3, m_1, n_1, o, p_1
  21. Point(edgeCG) → Q
  22. OrthogonalLine(Q, edgeBF, space) → s
  23. Intersect(edgeBF, s) → R
  24. Point(edgeDH) → S
  25. Plane(R, Q, S) → t
  26. IntersectPath(t, e) → poly4, T, U, V, W, a_1, b_1, c_1, d_1
  27. Point(edgeGH) → Z
  28. Point(edgeFG) → A_1
  29. Point(edgeCG) → B_1
  30. Plane(Z, A_1, B_1) → v
  31. IntersectPath(v, e) → poly5, C_1, D_1, E_1, e_1, f_1, g_1