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Divide a Cube into Two Parts

Divide a Cube into Two Parts
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2019-03-24 02:45
VectorSolid GeometryGeometric Construction
This example demonstrates how to divide a cube into two parts using a plane. Key mathematical concepts include plane cutting in solid geometry and properties of polyhedra. The construction uses GeoGebra commands such as Cube, Polygon, Vector, Translate, and Rotate. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → cubo, D, caraCDHG, caraEFGH, aristaAD, aristaAB, aristaBC, aristaCD, aristaAE, aristaDH, aristaEH, aristaEF, E, aristaBF, aristaFG, aristaCG, aristaGH, F, G, H, caraABCD, caraADHE, caraABFE, caraBCGF
  2. Herramienta2(H, F, C, A) → e
  3. Polygon(G, H, D, C) → c1, g, h, d, c
  4. Polygon(H, F, G) → t1, g_1, h_1, f_1
  5. Polygon(F, C, G) → t2, g_2, f_2, c_1
  6. Polygon(C, A, D) → t3, i, j, k
  7. Polygon(H, A, D) → t4, d_2, h_2, a_1
  8. Vector(O, (0, L, 0)) → u
  9. Translate(e, Vector[(t * u)]) → e'
  10. Translate(l1, Vector[(t * u)]) → l1'
  11. Rotate(Mirror[l1', O], 90°, yAxis) → l1''
  12. Translate(e, Vector[((-t) * u)]) → e'_1