Pentominoes in Math and Art

Fall 2012Cheryl McAllister

Polyominoes – general information

• Word coined by Solomon W. Golomb in 1954

• Definition – a polyomino is the joining of congruent squares at a side, vertex to vertex.

• The domino, the joining of two squares, is the most common of the polyominoes.

Types of Polyominoes

• Monomino – 1 square – 1 form• Domino – 2 squares – 1 form• Triomino – 3 squares - 2 forms• Tetromino – 4 squares – 5 forms• Pentomino – 5 squares – 12

forms• Hexomino – 6 squares – 35 forms

Mathematical Concepts that can be explored using

polyominoes• Area• Perimeter• Symmetry• Tessellations• Folding nets• Problem solving

Pentomino Solution as Arthttp://pentomino.classy.be/meninge.html

How are Pentominoes used in art?

• Guenter Albrecht-Buehler

Polyominoes can be a puzzle or a game

• Have you played Tetras?• Determine what the 12 different

pentomino shapes are.• Use all 12 shapes to make a

rectangle – 3719 solutions• Blokus – a board game using

Polyominoes• 2001 A Space Odessey