Assembly of cubes for illustrating various infinite series
Sándor Kabai
Series of cubes are created with 1/2 reduction factors within a larger cube. This assembly can be used for illustrating various series, such as sided, face, volume of a cube, including diameter of a square.
Series of cubes are created with 1/2 reduction factors within a larger cube. This assembly can be used for illustrating various series, such as sided, face, volume of a cube, including diameter of a square.
In[]:=
u=1;vs=Table[{Sin[i2Pi/4+Pi/4],Cos[i2Pi/4+Pi/4],0},{i,5}];sq1=Polygon[vs];cub=PolyhedronData["Cube","Faces"];sq1=cub;sq2=Translate[sq1,{u,0,0}];sq3=Translate[sq1,{0,u,0}];sq4=Translate[sq1,{0,0,-u}];sq4=Translate[{Pink,sq1,Yellow,sq2,Cyan,sq3},{0,0,-u}];u1={Pink,sq4,Pink,sq1,Yellow,sq2,Cyan,sq3};u2=Translate[Scale[u1,1/2],{u/2,u/2,u/2}];u3=Translate[Scale[u1,1/4],{u/2+u/4,u/2+u/4,u/2+u/4}];u4=Translate[Scale[u1,1/8],{u/2+u/4+u/8,u/2+u/4+u/8,u/2+u/4+u/8}];u5=Translate[Scale[u1,1/16],{u/2+u/4+u/8+u/16,u/2+u/4+u/8+u/16,u/2+u/4+u/8+u/16}];u6=Translate[Scale[u1,1/32],{u/2+u/4+u/8+u/16+u/32,u/2+u/4+u/8+u/16+u/32,u/2+u/4+u/8+u/16+u/32}];u7=Translate[Scale[u1,1/62],{u/2+u/4+u/8+u/16+u/32+u/64,u/2+u/4+u/8+u/16+u/32+u/64,u/2+u/4+u/8+u/16+u/32+u/64}];Graphics3D[{sq4,u1,u2,u3,u4,u5,u6},Boxed->False,SphericalRegion->True,ViewPoint->{100,40,40},ImageSize->400]
Out[]=
