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Cube Dissected into Three Yangma: Solid Geometry Demo

Cube Dissected into Three Yangma: Solid Geometry Demo
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2016-08-30 05:34
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric dissection of a cube into three congruent yangma (pyramids). It covers solid geometry concepts, specifically volume relationships and the historical Chinese mathematical term yangma. Construction utilizes GeoGebra commands including Cube for the base shape, Point and Intersect for defining vertices and cross-sections, and Pyramid to form the three internal quadrangular pyramids. Suitable for high school mathematics education, illustrating spatial partitioning and volume conservation principles effectively.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xOyPlane) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG_1, faceEFGH, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_2, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD_1, faceADHE, faceABFE, faceBCGF_1
  5. Pyramid(C, D, A, B, E) → b, faceABCD, edgeCE_1, edgeDE_1, edgeAE, edgeBE_1, faceCDE_1, faceADE, faceABE, faceBCE_1, edgeCD_1, edgeAD, edgeAB, edgeBC_2
  6. Pyramid(G, H, D, C, E) → c, faceCDHG, edgeEG_1, edgeEH, edgeDE, edgeCE_2, faceEGH, faceDEH, faceCDE, faceCEG_1, edgeGH, edgeDH, edgeCD, edgeCG_2
  7. Pyramid(F, G, C, B, E) → d, faceBCGF, edgeEF, edgeEG, edgeCE, edgeBE, faceEFG, faceCEG, faceBCE, faceBEF, edgeFG, edgeCG, edgeBC, edgeBF