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Explore Cube Sections

Explore Cube Sections
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2016-10-03 06:02
Coordinate GeometrySolid GeometryOptimizationGeometric Construction
This example demonstrates how to dynamically explore the cross-section shapes of a cube under different plane sections. It involves core math concepts like solid geometry, cross-section geometry, and analytical geometry. Construction highlights include using commands like Intersect, Point, Cube, Plane, IntersectPath, CornerThreeD, and OrthogonalLine. Suitable for high school students and math enthusiasts to understand spatial geometry and cross-section relationships, as well as for teaching linear programming and optimization.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → cube, D, faceCDHG, faceEFGH, arêteAD, arêteAB_1, arêteBC, arêteCD, arêteAE, arêteDH, arêteEH, arêteEF, E, arêteBF, arêteFG, arêteCG, arêteGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(cube) → L
  6. Point(cube) → M
  7. Point(cube) → N
  8. Plane(L, M, N) → plan
  9. IntersectPath(plan, cube) → poly1, I, i, j, k, J, K, O, P, Q, f, g, h
  10. CornerThreeD(-1, 11) → U
  11. OrthogonalLine(A, poly1) → d
  12. Point(Circle[B, Distance[A, B], Segment[A, B]]) → R