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Equations of Planes and Tetrahedron Construction

Equations of Planes and Tetrahedron Construction
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2016-07-29 08:55
VectorCoordinate GeometrySolid GeometryGeometric ConstructionGraphing
① This example demonstrates how four plane equations define a tetrahedron, showing intersections, edges, and vertices in 3D space. ② Core math concepts include plane equations, spatial geometry, vector operations, centroid, and intersection of planes. ③ Construction uses GeoGebra commands: IntersectPath for plane intersections, Intersect for points, Pyramid to build a tetrahedron, Centroid for centroid, Vector for vectors, and Textfield for labels; objects include planes (a,b,c,d), tetrahedron (pyramidfromPointsABCD), faces (faceABC etc.), edges (edgeAB etc.), and the tetrahedron from planes (tetrahedronfromPlanesabcd). ④ Suitable for high school or university courses in analytic geometry and solid geometry, useful for interactive teaching of plane equations and spatial relationships.

GeoGebra Commands & Parameters

  1. IntersectPath(c, d) → k
  2. IntersectPath(a, d) → h
  3. IntersectPath(a, c) → f
  4. Intersect(f, k) → I
  5. IntersectPath(a, b) → e
  6. Intersect(e, h) → H
  7. Intersect(e, f) → E
  8. Pyramid(A, B, C, D) → pyramidfromPointsABCD, faceABC, edgeCD, faceABD, faceBCD, faceACD, edgeAB, edgeBC, edgeAC, edgeAD, edgeBD
  9. IntersectPath(b, c) → i
  10. IntersectPath(b, d) → j
  11. Intersect(k, j) → F
  12. Pyramid(I, F, H, E) → tetrahedronfromPlanesabcd, faceFHId, edgeEH, faceEFIc, faceEFHb, faceEHIa, edgeFI, edgeFH, edgeHI, edgeEI, edgeEF
  13. Centroid(faceEHIa) → C_a
  14. Vector(T_a, C_a) → u_a
  15. Centroid(faceFHId) → C_d
  16. Vector(T_d, C_d) → u_d
  17. Centroid(faceEFHb) → C_b
  18. Vector(T_b, C_b) → u_b
  19. Centroid(faceEFIc) → C_c
  20. Vector(T_c, C_c) → u_c
  21. Textfield(a) → InputBoxa
  22. Textfield(b) → InputBoxb
  23. Textfield(c) → InputBoxc
  24. Textfield(d) → InputBoxd