TT2 Dissections

Author : Gavin Theobald

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TT2 dissections, like TT1 dissections, are created using two T strips. But whereas for all the dissections that we have looked at so far, the area of overlap of the two strips has been equal to the area of each shape, now the area of overlap is twice this amount. In effect, we dissect two shapes to two shapes, but since each piece is duplicated, we can throw half the pieces away.

Each strip must again be placed so that its edges pass through the anchor points of the other strip. There are at most sixteen possible ways of combining the strips.

We now look at an example by dissecting a triangle to a square:

Triangle strip Square strip

The strips are overlaid. Note how the edges of the triangle strip pass through the red anchor points of the square strip and the edges of the square strip pass through the red anchor points of the triangle strip. This causes the central red intermediate anchor points to coincide. Since the blue anchor points do not have a role in TT2 dissections they are not shown in the diagrams below.

Here is the finished dissection:

TT2 dissections frequently give good clean solutions requiring few pieces. So although the arrangement of the strips is very restricted, because T strips often require fewer pieces than similiar P strips, then TT2 dissections often give records. The main problem is to find good T strips.

Below are some more examples:

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