积极 AI Logo 积极 AI

四边形金字塔及其展开图

四边形金字塔及其展开图
几何画板及绘图内容加载中，请稍等……
2015-01-10 03:12
多边形立体几何几何作图函数图像
①本范例演示了四边形金字塔的3D视图及其展开图；②涉及的核心数学概念包括立体几何、多边形面积、表面积与体积计算；③作图要点提炼自构造摘要，使用了PointIn, Ray, Point, Polygon, Pyramid, Circle, Intersect, Segment等GeoGebra命令与对象；④适合高中阶段学生学习和理解三维图形的构造与性质，也可用于相关数学概念的教学演示。

GeoGebra 命令及参数

  1. PointIn(a) → A
  2. PointIn(a) → B
  3. PointIn(a) → C
  4. PointIn(a) → D
  5. PointIn(a) → E
  6. Ray(E, E + (0, 0, 1)) → b
  7. Point(b) → F
  8. Polygon(A, B, C, D) → poly1, a_1, b_1, c, d
  9. Pyramid(poly1, F) → e, faceABF, faceBCF, faceCDF, faceADF, edgeAF, edgeBF, edgeCF, edgeDF
  10. Circle(A, Distance[F, A], xOyPlane) → f
  11. Circle(B, Distance[F, B], xOyPlane) → g
  12. Intersect
  13. Intersect(f, g, 1) → G
  14. Polygon(B, G, A) → poly2, a_2, b_2, g_1
  15. Circle(C, Distance[F, C], xOyPlane) → h
  16. Intersect
  17. Intersect(g, h, 1) → H
  18. Polygon(H, B, C) → poly3, c_1, h_1, b_3
  19. Circle(D, Distance[F, D], xOyPlane) → k
  20. Intersect
  21. Intersect(h, k, 1) → I
  22. Polygon(I, C, D) → poly4, d_1, i, c_2
  23. Intersect
  24. Intersect(f, k, 2) → J
  25. Polygon(D, J, A) → poly5, a_3, d_2, j
  26. Segment(E, F) → l