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四面体构造与计算

四面体构造与计算
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2017-05-13 01:25
立体几何几何作图
所属专题 surface 3D /3D-Oberflächen 1 surface 3D /3D-Oberflächen 1
①本范例演示四面体的构造与体积计算；②涉及核心数学概念包括多边形、立体几何、体积公式；③构造中使用了球体(Sphere)、线段(Segment)、点(Point)、四面体(Tetrahedron)、体积(Volume)、缩放(Dilate)等GeoGebra命令；④适合高中立体几何教学与几何作图练习。

GeoGebra 命令及参数

  1. Sphere(M_1, r) → a
  2. Sphere(M_2, r) → b
  3. Sphere(M_3, r) → c
  4. Sphere(M_4, r) → d
  5. Segment(S, K_1) → f
  6. Point(Circle[Midpoint[K_1, K_3], (Distance[K_1, K_3] * sqrt(3) / 2), Segment[K_1, K_3]]) → A
  7. Tetrahedron(K_1, K_3, A) → g, B, KanteAB, Kante5, Fläche1, Fläche3, Fläche2, Fläche4, Kante2, Kante1, Kante4, Kante3
  8. Volume(a) → V_k
  9. Sphere(Z, (sqrt(6) / 12 * k)) → i
  10. Tetrahedron(K_1, K_3, A) → T_{u}, C, edgeAC, edge5, face1, face3, face2, face4, edge2, edge1, edge4, edge3
  11. Tetrahedron(M_3, M_2, M_1) → T_{I}, D, edge8, edge10, face5, face7, face8, face6, edge7, edge9, edge6, edge11
  12. Dilate(T_{I}, dilf, Z) → T_{dilate}