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三棱柱的截面探究 by nandrews

三棱柱的截面探究 by nandrews
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2016-05-10 19:03
多边形立体几何几何作图
①This example dynamically cuts a triangular prism with a plane to visually explore how the cross-section shape changes with different positions and angles, helping students understand the relationship between planes and solids in 3D geometry. ②Core mathematical concepts include the structure of a triangular prism, cross-section polygons formed by plane-solid intersection, and applications of parallelism and perpendicularity in space. ③Construction highlights: the Prism command builds the triangular prism, a Plane and OrthogonalLine define the cutting plane, IntersectPath computes the intersection lines with each face, and Point, Polygon objects allow dynamic adjustment of the cutting position to generate the final cross-section. ④It is suitable for high school or early college students learning solid geometry, and for teachers to demonstrate in class to enhance spatial visualization and geometric intuition.

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 3) → poly1, a, b, c, C
  4. Prism(poly1, 3.586878522587578) → d, D, edgeCF, edgeDE, edgeEF, edgeDF, E, F, faceABED, faceBCFE, faceACFD, faceDEF, edgeAD, edgeBE
  5. Point(edgeCF) → G
  6. OrthogonalLine(G, edgeBE, space) → e
  7. OrthogonalLine(G, edgeAD, space) → f
  8. Intersect(edgeBE, e) → H
  9. Intersect(edgeAD, f) → I
  10. Plane(H, G, I) → g
  11. IntersectPath(g, d) → poly2, J, K, L, h, i, j
  12. Point(edgeDE) → M
  13. Point(edgeDF) → N
  14. OrthogonalLine(M, a, space) → l
  15. Point(l) → O
  16. Plane(M, N, O) → m
  17. IntersectPath(m, d) → poly3, P, Q, R, S, n, p, q, r
  18. Point(edgeEF) → T
  19. Point(edgeDE) → U
  20. Point(edgeBE) → V
  21. Plane(U, T, V) → s
  22. IntersectPath(s, d) → poly4, W, Z, A_1, t, a_1, b_1
  23. Point(edgeBE) → B_1
  24. Point(edgeAD) → C_1
  25. Point(edgeCF) → D_1
  26. Plane(B_1, C_1, D_1) → v
  27. IntersectPath(v, d) → poly5, E_1, F_1, G_1, c_1, d_1, e_1

AI 绘图提示语参考

绘制一个三角柱，并用一个平面切割它，观察不同位置和角度下形成的截面形状变化。首先使用Polygon命令创建一个三角形，然后用Prism命令构建三角柱。接着定义一个切割平面，通过计算平面与三角柱各面的交线来生成截面。最后通过调整切割位置，动态生成不同的截面形状。
以上提示语为根据原始绘图命令整理而来，仅供参考。