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Plane Intersecting Cube: Cross Section Analysis

Plane Intersecting Cube: Cross Section Analysis
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2016-06-10 05:57
Coordinate GeometrySolid GeometryGeometric Construction
In collections Area, Surface Area, Volume, Cross Section, 3D
This example demonstrates the cross-section analysis problem when a plane intersects a cube. Key mathematical concepts include the intersection of planes and polyhedra in solid geometry. Using GeoGebra commands such as Point, Cube, Segment, Intersect, and Polygon, the construction of the cube and its faces and edges is illustrated, followed by the analysis of the cross-section shape. Suitable for high school geometry courses.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D_1, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E_1, edgeBF, edgeFG, edgeCG, edgeGH, F_1, G_1, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Segment(E_1, F_1) → f
  6. Segment(F_1, G_1) → g
  7. Segment(A, B) → i
  8. Segment(B, C) → k
  9. Sphere(B, e) → b
  10. Intersect(edgeBC, b) → F, G
  11. Intersect(edgeAB, b) → I,
  12. Sphere(F_1, i - c) → d
  13. Intersect(edgeFG, d) → D, E
  14. Intersect(f, d) → J, K
  15. Segment(G_1, E) → h
  16. Segment(E_1, J) → j
  17. Segment(B, G) → l
  18. Segment(B, I) → m
  19. Polygon(J, E, G, I) → poly1, j_1, e_1, g_1, i_1
  20. Angle(E, G, I) → α
  21. Angle(G, I, J) → β
  22. Angle(J, E, G) → γ
  23. Angle(E, J, I) → δ