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Projection of a Cube onto a Plane

Projection of a Cube onto a Plane
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2017-10-30 07:32
VectorSolid GeometryParametric EquationGeometric Construction
This example demonstrates the process and result of projecting a cube onto a specified plane in 3D space. Key math concepts include vectors, parametric curves, spatial geometry, and projection transformations. The construction utilizes GeoGebra commands and objects like Point, Cube, Intersect, Sphere, OrthogonalPlane, Line, and Segment as outlined in the summary. Suitable for high school students and above learning spatial geometry, vector projections, and 3D transformations, as well as university-level introductory geometry courses.

GeoGebra Commands & Parameters

  1. Point(Circle[(1, -1, -1), Distance[(-1, -1, -1), (1, -1, -1)], Segment[(-1, -1, -1), (1, -1, -1)]]) → A
  2. Cube((-1, -1, -1), (1, -1, -1), A) → a, B, faceABFE, faceCDEF, edge2, edge1, edge4, edgeAB, edge3, edgeBF, edgeCF, edgeCD, C, edge5, edgeDE, edgeAE, edgeEF, D, E, F, face1, face3, face2, face4
  3. Intersect(yAxis, zAxis) → H
  4. Sphere(H, G) → b
  5. OrthogonalPlane((-G), Line[G, (-G)]) → c
  6. Line(G, E) → f
  7. Line(G, F) → g
  8. Line(G, D) → h
  9. Line(G, C) → i
  10. Line(G, A) → j
  11. Line(G, I) → k
  12. Line(G, J) → l
  13. Line(G, B) → m
  14. Intersect(m, c) → K
  15. Intersect(l, c) → L
  16. Intersect(k, c) → M
  17. Intersect(j, c) → N
  18. Intersect(i, c) → O
  19. Intersect(h, c) → P
  20. Intersect(g, c) → Q
  21. Intersect(f, c) → R
  22. Segment(O, Q) → n
  23. Segment(O, L) → p
  24. Segment(Q, K) → q
  25. Segment(K, L) → r
  26. Segment(K, N) → s
  27. Segment(N, R) → t
  28. Segment(R, Q) → d
  29. Segment(P, O) → e
  30. Segment(P, R) → f_1
  31. Segment(M, L) → g_1
  32. Segment(M, P) → h_1
  33. Segment(M, N) → i_1