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Tetrahedron Construction and Calculation

Tetrahedron Construction and Calculation
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2017-05-13 01:25
Solid GeometryGeometric Construction
This example demonstrates the construction of a tetrahedron and its volume calculation. Core mathematical concepts include polygons, solid geometry, and volume formulas. GeoGebra commands used in construction are Sphere, Segment, Point, Tetrahedron, Volume, and Dilate. Suitable for high school solid geometry teaching and geometric construction practice.

GeoGebra Commands & Parameters

  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}