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镂空金字塔的构造

镂空金字塔的构造
几何画板及绘图内容加载中，请稍等……
2016-07-09 01:08
立体几何几何作图
所属专题 surface 3D surface 3D
①本范例演示了一个镂空金字塔的几何构造与表面展示；②涉及的核心数学概念包括立体几何、表面构造、四边形、面积计算、平移变换和坐标系；③作图要点提炼自构造摘要，使用了点(Point)、样条曲线(Spline)、表面(Surface)、线段(Segment)、镜像(Mirror)等GeoGebra命令与对象；④适合高中阶段学习立体几何、空间想象和几何作图的学生使用。

GeoGebra 命令及参数

  1. Point(x = y) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → H
  4. Spline({D, E, F, G, H}, 3) → a
  5. Surface(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → c
  6. Surface(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → e
  7. Surface((-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → f
  8. Surface((-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → g
  9. Surface((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → h
  10. Surface((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))), (-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → i
  11. Surface((-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → j
  12. Surface((-((y(a(u)) * (1 - v)) + (v * ((y(A) * (1 - u)) + (u * y(B)))))), (-(x(A) + (cos((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))))), (sin((d * p)) * ((-x(A)) + (x(a(u)) * (1 - v)) + (v * ((x(A) * (1 - u)) + (u * x(B)))))), u, 0, 1, v, 0, 1) → k
  13. Surface((x(A) * u), (x(A) * v), 0, u, -1, 1, v, -1, 1) → b
  14. Segment(A, B) → l
  15. Surface(((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), y(a(u)), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → m
  16. Surface(((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), (-y(a(u))), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → n
  17. Surface(y(a(u)), ((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → o
  18. Surface((-y(a(u))), ((x(A) + (cos(d) * (x(a(u)) - x(A)))) * (1 - v)) + (v * ((-x(A)) + (cos(π - d) * (x(a(u)) - x(A))))), (sin(d) * (x(a(u)) - x(A))), u, 0, 1, v, 0, 1) → r
  19. Mirror(a, xAxis) → a'
  20. Mirror(A, xAxis) → A'
  21. Mirror(B, xAxis) → B'
  22. Segment(A', B') → l'
  23. Segment(A, A') → q

AI 绘图提示语参考

画一个空心的金字塔，底部由五边形构成，顶部为点。金字塔的侧面由多个三角形组成，每个侧面通过四边形连接底部和顶部。金字塔的底部和侧面使用不同的颜色和材质表示，以便区分。金字塔的底部和侧面都使用网格线进行装饰，以便更好地展示其几何结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。