Mrs. Perkins's Quilt

Author

Eric W. Weisstein
December 3, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Dissections/MrsPerkinssQuilt.nb.

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

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

Additional Authors

Most diagrams compiled by Ed Pegg, Jr.; see http://mathpuzzle.com/perkinsbestquilts.txt
Diagrams from Duijvestijn transcribed by Geoffrey Morley

Catalog

quilts=Sequence@@@(Last/@DownValues[MrsPerkinsQuilts]);

Length[quilts]

SideLength/@quilts

{SideLength[#],Length[Flatten[#]]}&/@quilts

{SideLength[#],MinimalQuiltSquares[SideLength[#]]}&/@quilts

Checks

BouwkampQ/@And@@quilts

Position[Equal@@{Length[Flatten[#]],MinimalQuiltSquares[SideLength[#]]}&/@quilts,False]

Comparison with Ed's "bestquilts" (now obsolete; incorporated as of 2003/12/02)

u=Table[Complement[{bestquilts[[i]]},MrsPerkinsQuilts[i]],{i,100}];

diff=Position[u,_?(#≠{}&),{1}]//Flatten

Transpose[{diff,u[[diff]]}]//ColumnForm

{bestquilts[[20]],MrsPerkinsQuilts[20]}//ColumnForm

Show[GraphicsArray[Transpose[Function[q,{
Graphics[Squares[BouwkampConstruction[bestquilts[[q]]],MinLabel->3,Color->Green],AspectRatio->Automatic,PlotRange->All],
Sequence@@(Graphics[#,AspectRatio->Automatic]&/@(Squares[BouwkampConstruction[#],MinLabel->3]&/@MrsPerkinsQuilts[q]))
}]/@diff]]]

Example

Show[Graphics[
Squares[BouwkampConstruction[MrsPerkinsQuilts[5][[1]]],MinLabel->2,Color->Green]
],
AspectRatio->Automatic]

First Few

Show[GraphicsArray[Partition[
Graphics[Squares[BouwkampConstruction[First[#]],Labeled->False,Color->LightYellow],AspectRatio->Automatic]&/@MrsPerkinsQuilts/@Range[18],
6,6,{1,1},{}]],ImageSize->500]

size={1,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3};
Show[GraphicsArray[Partition[
Table[Graphics[Squares[BouwkampConstruction[First[MrsPerkinsQuilts[i]]],MinLabel->size[[i]],Color->LightYellow],AspectRatio->Automatic],{i,18}],
6,6,{1,1},{}]],ImageSize->500]

Lance Gay

gay=First/@MrsPerkinsQuilts/@Range[88,90]

Length/@Flatten/@gay

Show[GraphicsArray[Graphics[Squares[BouwkampConstruction[#],MinLabel->6,Color->LightYellow],AspectRatio->Automatic,PlotRange->All]&/@gay
]]