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Cube Division Demonstration by Diego Lieban

Cube Division Demonstration by Diego Lieban
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2019-01-30 05:20
VectorSolid GeometryGeometric Construction
In collections Developing games and puzzles with 3D printing for STEAM
This example demonstrates how to divide a cube into two parts through 3D geometric construction. Key math concepts include solid geometry, 3D vectors, and the relationship between points and planes. Construction highlights involve commands/objects like Intersect, Point, Cube, Pyramid, Midpoint, Plane, Mirror from GeoGebra. Suitable for high school and above students learning solid geometry, 3D vectors, and spatial geometric constructions.

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, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Pyramid(faceABCD, -1) → b, I, faceADI, faceABI, faceBCI, faceCDI, edgeDI, edgeAI, edgeBI, edgeCI
  6. Pyramid(faceCDHG, -1) → c, J, faceCDJ, faceCGJ, faceGHJ, faceDHJ, edgeDJ, edgeCJ, edgeGJ, edgeHJ
  7. Midpoint(edgeBC) → K
  8. Midpoint(edgeAD) → L
  9. Plane(L, I, K) → d
  10. Mirror(c, d) → c'