 Academic journal article Australian Mathematics Teacher

Academic journal article Australian Mathematics Teacher

## Article excerpt

Four congruent squares

The standard rule for joining congruent (geometrically identical) squares to make polyomino shapes, such as pentominoes does not allow any way of joining two or more squares, other than by a whole edge, against a whole edge. We will change this rule, so that four identical squares can join any way. These four squares may even be joined if they just touch one another at a single corner. Here are two mathematically distinct ways of joining four squares, only by corners (not that "swivelling" at a corner is not regarded as resulting in a mathematically different arrangement).

* How many mathematically (geometrically) distinct ways can you join four identical squares so they only connect by corners?

* If four identical unit squares are joined together in a 2 x 2 array, they have a perimeter of 8 units.

* If four identical squares are joined only by touching successive corners, the perimeter of the whole arrangement is 16 units.

* Join four identical squares to form figures that have a perimeter of 15 units.

* Join four identical squares to form figures that have a perimeter of 14 units.

* Join four identical squares to form figures that have a perimeter of 13 units. …

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