Square Packing

Author

Eric W. Weisstein
April 16, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/ComputationalGeometry/SquarePacking.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SquarePacking.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Squares in Circles

Show[GraphicsArray[Partition[
Graphics[#,AspectRatio->Automatic]&/@Table[Packing[{n,Square},Circle],{n,6}],
3]
]]

Squares in Squares

Show[GraphicsArray[Partition[
Graphics[#,AspectRatio->Automatic]&/@Table[Packing[{n,Square},Square],{n,6}],
3]
]]

No longer current?

s[11]:=Module[{
x1=(5/64+1/96 Sqrt[83/3])^(1/3),
x2=(5/64-1/96 Sqrt[83/3])^(1/3),
y},
y=Sqrt[x1+x2-1/2]+Sqrt[Sqrt[(x1+x2+1)^2+3(x1-x2)^2]-x1-x2-1];
3+((2y-1)/y^2)
]

N[s[11],20]

RootReduce[s[11]]

N[%,20]

NRoots[9-46x+35x^2-10x^3+x^4==0,x]

Squares in Triangles

Show[GraphicsArray[Partition[
Graphics[#,AspectRatio->Automatic,PlotRange->All]&/@Table[Packing[{n,Square},Triangle],{n,6}],
3]
]]