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Slicing a Cube

Slicing a Cube
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2016-02-22 04:53
Solid GeometryProbability & StatisticsGeometric Construction
This example demonstrates the geometric transformations and area calculations when slicing a cube with different planes, observing the resulting cross-sections. It involves core concepts in solid geometry, geometric transformations, median lines, expected values, and distributions. Constructed using GeoGebra commands like Intersect, Point, Cube, Line, and OrthogonalPlane. Suitable for high school students and math enthusiasts exploring spatial geometry and probability statistics.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → B
  2. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  3. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  4. Line(D, F) → b
  5. Point(b) → I
  6. OrthogonalPlane(I, b) → c