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三角锥截面演示

三角锥截面演示
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2020-03-04 22:21
解析几何立体几何几何作图
所属专题 Cross Sections
①本范例演示三角锥被平面截切后的截面形状；②涉及核心数学概念包括立体几何、截面几何、平面与立体的交线；③作图要点提炼自构造摘要，使用了Point, Polygon, Pyramid, Plane, Circle, Line, Intersect, OrthogonalLine, CircleArc, Segment, OrthogonalPlane, IntersectPath等GeoGebra命令与对象；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问题。

GeoGebra 命令及参数

  1. Point(xAxis) → V
  2. Polygon(U, V, W) → t1, w, u, v
  3. Pyramid(t1, m) → ThePyra, P, facePUV, facePVW, facePUW, edgePU, edgePV, edgePW
  4. Point(xAxis) → A
  5. Point(zAxis) → O
  6. Point(xAxis) → K
  7. Point(yAxis) → J
  8. Point(xAxis) → I
  9. Plane(I, K, O) → b
  10. Plane(I, J, K) → p
  11. PointIn(b) → CenterOfNormalAngle
  12. Circle(CenterOfNormalAngle, 0.25, b) → d
  13. Line(CenterOfNormalAngle, xAxis) → g
  14. Point(yAxis) → B
  15. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  16. Intersect(xAxis, yAxis) → M
  17. OrthogonalLine(CenterOfNormalAngle, g, b) → h
  18. Intersect(g, d) → i_1, i_2
  19. CircleArc(CenterOfNormalAngle, i_1, i_2, b) → ArcForPlaneAngle
  20. Point(ArcForPlaneAngle) → NormalAngleHandle
  21. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  22. PointIn(ThePyra) → SliceChooser
  23. OrthogonalPlane(SliceChooser, NormalSeg) → PerPenPlane
  24. IntersectPath(PerPenPlane, ThePyra) → poly1, D, E, F, R, f, i, j, r