Pentominoes

A pentomino is a polyomino composed of five congruent squares, connected along their edges (which sometimes is said to be an orthogonal connection).

There are twelve different free pentominoes. Ordinarily, the pentomino obtained by reflection or rotation of a pentomino does not count as a different pentomino.

I discovered pentominoes as a nerdy kid, probably when I read one of Martin Gardner's books based on his "Mathematical Games" columns in "Scientific American". Many of them are still available and I recommend them to anyone who has a mathematical mind (or whose children have).

The logo at the top of each of my pages is one example of a 5x12 tiling of free pentominoes and the the strip at the bottom is repeated copies of a 3x20 tiling.

Pentominoes tiled in various ways

The logo and strip are derived from the above work by a Wikipedia contributor and are used under a Creative Commons licence. See here for the gory details.

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Wiblog:
A Christmas of Films

If anything has marked out this Christmas as something out of the ordinary it's been the quality and variety of the films I've seen. As usual much respect to the great Dr Kermode for pointing me in the right direction for some of the less obvious choices. Some of these are DVDs Santa Beth gave me, the others are movies I caught on iPlayer. read more ...