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Cube Cross Section by C.P. Cheung

Cube Cross Section by C.P. Cheung
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2017-10-22 17:23
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the various cross-sectional shapes formed by slicing a cube at different angles and positions. It involves core math concepts like solid geometry, cross-section analysis, and spatial visualization. Constructed using GeoGebra commands such as Point, Cube, Translate, IntersectPath, and Rotate to build the cube, move the slicing plane, and calculate intersection points. Suitable for high school geometry teaching or developing students' spatial reasoning skills.

GeoGebra Commands & Parameters

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. 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
  3. Translate(Rotate[Rotate[Plane[xAxis, yAxis], tt, xAxis], rr, zAxis], Vector[(0, 0, ud)]) → b
  4. IntersectPath(b, a) → poly1, I, i, j, k, J, K, L, M, N, f, g, h
  5. Rotate(Rotate[Translate[poly1, Vector[(0, 0, (-ud))]], (-rr), zAxis], (-tt), xAxis) → poly2