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长方体的截面 by cbannon

长方体的截面 by cbannon
几何画板及绘图内容加载中，请稍等……
2017-03-01 00:58
立体几何变换几何作图
这个范例演示了长方体的截面。它涉及立体几何中的截面概念，通过使用GeoGebra中的Polygon, PointIn, Translate, Rotate, Prism等命令，可以动态展示长方体在不同平面截取下的截面形状。适合初中及以上学生学习立体几何。

GeoGebra 命令及参数

  1. Polygon(B + (-2, -2), B + (2, -2), B + (2, 2), B + (-2, 2)) → poly3, e, f, g, i
  2. PointIn(poly3) → C
  3. Translate((0, 0, 0), Vector[B, C]) → A
  4. Polygon(A + (-4, -4), A + (4, -4), A + (4, 4), A + (-4, 4)) → poly1, a, b, c, d
  5. Rotate(Rotate[Translate[poly1, Vector[A, A + (0, 0, h)]], (90° * s), A + (0, 0, h), yAxis], (90° * t), A, zAxis) → poly2
  6. Rotate(D, 120°, (0, 0, 0)) → E
  7. Prism(Polygon[(-1.5, -1.25, 0), (1.5, -1.25, 0), (1.5, 1.25, 0), (-1.5, 1.25, 0)], (-1.5, -1.25, 4)) → m, M, edge2, edge3, edge4, edge5, edge6, edge7, edge8, N, Q, face1, face2, face3, face4, face5, edge1
  8. Polygon(D, E, 3, xOyPlane) → poly4, j, k, l, F
  9. PointIn(poly2) → G
  10. PointIn(poly2) → H
  11. PointIn(poly2) → I
  12. Plane(G, I, H) → n
  13. IntersectPath(n, m) → poly6, poly5, r, a_1, b_1, c_1, K, L_1, O, P, J, L, p, q
  14. Rotate(m, 0, zAxis) → m'
  15. Rotate(m, 0, zAxis) → m'_1
  16. OrthogonalLine(A, n) → d_1