PP2 Dissections

Author : Gavin Theobald


For PP2 dissections the strips must be overlaid so that the area of overlap is only half that of the shapes. This means that only half the shapes are yet dissected so that it is necessary to overlay the strips a second time.

So to dissect a hexagon to a rectangle we first obtain strips for these two polygons:

Hexagon strip Rectangle strip

These strips are now overlaid twice. Note that when overlaying the second strip it can only be positioned in one of two ways, the second position being obtained by rotating the strip 180 degrees.

Rectangle - Hexagon

This gives the following dissection:

Rectangle - Hexagon

Here is a second example of a PP2 dissection. One piece is shaded to make it clear that it is a single piece.

Square - Decagram Square - Decagram

Finally, if PP2 dissections are possible, why not PP3 or even PP4 and above?


Home    Methods    Previous    Next    Index