How Many Pyramids in a Cube? by Jimi Grover

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2019-05-14 22:16

This example demonstrates finding multiple pyramids within a cube. Key mathematical concepts include solid geometry and similarity transformation. Using GeoGebra commands such as Point, Cube, Pyramid, Vector, Translate, etc., the construction of a cube and multiple pyramids is illustrated. Suitable for middle school and above students learning solid geometry.

GeoGebra Commands & Parameters

Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
Cube(A, B, C) → a, D, faceCDHG, faceEFGH_1, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF, edgeFG_1, edgeCG, edgeGH_1, F, G, H, faceABCD_1, faceADHE_1, faceABFE, faceBCGF
Pyramid(H, E, F, G, I) → b, faceEFGH, edgeHI, edgeEI, edgeFI, edgeGI, faceEHI, faceEFI, faceFGI, faceGHI, edgeEH_2, edgeEF, edgeFG, edgeGH
Pyramid(D, C, B, A, J) → c, faceABCD, edgeDJ_1, edgeCJ, edgeBJ, edgeAJ_1, faceCDJ, faceBCJ, faceABJ, faceADJ_1, edgeCD, edgeBC, edgeAB, edgeAD_2
Vector(K, L) → u
Translate(b, u) → c'
Pyramid(D, A, E, H, J) → d, faceADHE, edgeDJ, edgeAJ, edgeEJ, edgeHJ, faceADJ, faceAEJ, faceEHJ, faceDHJ, edgeAD, edgeAE, edgeEH, edgeDH
Vector(M, N) → v
Translate(d, v) → d'