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Cube Cross-Sections

Cube Cross-Sections
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2015-03-20 22:23
Solid GeometryCalculusGeometric Construction
This example demonstrates the variety of cross-section shapes obtained by rotating a cube, exploring concepts like rotation, intersection, statistics, and curve sketching. It uses commands such as Polygon, Prism, Line, Ray, Point, Segment, Plane, PointIn, and IntersectPath to construct the geometry and observe the sections. Ideal for high school solid geometry and introductory mathematical modeling.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Prism(poly1, a) → e, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  3. Line(C, G) → g
  4. Ray(C, B) → q
  5. Ray(C, D) → r
  6. Ray(C, G) → s
  7. Point(r) → X
  8. Segment(X, XY) → n
  9. Plane(faceCDHG) → o
  10. PointIn(o) → ZX
  11. Segment(ZX, X) → f
  12. Segment(ZX, XY) → h
  13. Plane(ZX, X, XY) → i
  14. IntersectPath(i, e) → poly2, J, m, p, t, K, L, M, N, O, j, k, l