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Liu Hui's Cube Dissection

Liu Hui's Cube Dissection
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2017-02-27 18:42
TrigonometrySolid GeometryOptimizationGeometric Construction
This example demonstrates Liu Hui's geometric puzzle of cube dissection, dynamically visualizing the partitioning process. Key math concepts include solid geometry, Pythagorean theorem, trigonometry, and optimization problems. Construction highlights GeoGebra commands like Intersect, Point, Cube, Segment, Pyramid, Prism, and LaTeX. Suitable for high school students and math enthusiasts studying geometric dissection and optimization.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD, faceADHE_1, faceABFE, faceBCGF
  5. Segment(H, F) → f
  6. Segment(D, B) → g
  7. Segment(B, E) → h
  8. Segment(H, B) → j
  9. Pyramid(D, A, E, H, B) → c, faceADHE, edgeBD_1, edgeAB, edgeBE_1, edgeBH_1, faceABD, faceABE, faceBEH_1, faceBDH, edgeAD, edgeAE, edgeEH_2, edgeDH_2
  10. Pyramid(F, E, B, H) → d, faceBEF, edgeBH, faceEFH, faceBEH, faceBFH, edgeEF, edgeBE, edgeBF, edgeFH, edgeEH
  11. Prism(D, C, B, H) → b, I, edgeBD, edgeDH, edgeCI, edgeBJ, edgeHI, edgeIJ, edgeHJ, J, faceBCD, faceCDHI, faceBCIJ, faceBDHJ, faceHIJ, edgeCD, edgeBC
  12. LaTeX(B, true, true) → text1