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Difficult Section of a Cube by Plane (IJK)

Difficult Section of a Cube by Plane (IJK)
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2017-03-16 01:44
Coordinate GeometrySolid GeometryGeometric Construction
This GeoGebra example demonstrates the complexity of sectioning a cube with a plane defined by points I, J, and K, resulting in a challenging cross-section. Key mathematical concepts include solid geometry principles, plane-section intersections, and polygonal geometry. Construction highlights: using Point commands to create vertices like A, B, C, etc., Cube to model the solid, Plane to define the cutting plane, Intersect to compute intersection lines, and Line and Segment to draw the section edges. Objects include cube faces, edges, and section points such as G, H, I. This resource is suitable for high school or college-level solid geometry instruction, aiding in visualizing section problems.

GeoGebra Commands & Parameters

  1. Point(Circle[(1, 0, 0), Distance[(0, 0, 0), (1, 0, 0)], Segment[(0, 0, 0), (1, 0, 0)]]) → A
  2. Cube((0, 0, 0), (1, 0, 0), A) → a, B, faceABFE, faceCDEF, arête2, arête1, arête4, arêteAB, arête3, arêteBF, arêteCF, arêteCD, C, arête5, arêteDE, arêteAE, arêteEF, D, E, F, face1, face3, face2, face4
  3. Intersect(arête5, arête1) → G
  4. Intersect(arête3, arête2) → H
  5. Point(arêteCD) → I
  6. Point(arête4) → J
  7. Point(arêteBF) → K
  8. Plane(I, J, K) → b
  9. Line(I, arêteBF) → f
  10. Intersect(f, arête1) → L
  11. Line(L, B) → g
  12. Line(I, K) → h
  13. Intersect(h, g) → M
  14. Line(J, M) → i
  15. Intersect(i, arêteAB) → N
  16. Segment(N, K) → j
  17. Segment(J, N) → k
  18. Line(N, K) → l
  19. Line(E, F) → m
  20. Intersect(l, m) → O
  21. Line(I, O) → n
  22. Intersect(arêteCF, n) → P
  23. Segment(I, P) → p
  24. Segment(P, K) → q
  25. Line(H, G) → r
  26. Intersect(i, r) → Q
  27. Line(I, Q) → s
  28. Intersect(s, arête5) → R
  29. Segment(R, J) → t
  30. Intersect(arêteCD, s) → S
  31. Segment(R, I) → c

AI Drawing Prompt Reference

Draw a unit cube with a square base and labeled vertices. Select three points on three different edges of the cube, which define a cutting plane. This plane intersects several edges of the cube, producing a series of intersection points that, when connected, form a complex polygonal cross-section. Show all edges of the cube, the cutting plane, and the edges of the cross-section, highlighting the intersection points between the plane and the cube's edges. Construct the cube first, then place the three points on specified edges, define the plane through them, and sequentially find the intersections of this plane with the cube's edges, finally connecting these points to form the section.
The prompt above was compiled from the original drawing commands and is for reference only.