Difference between revisions of "Polyominoes Exploration"
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{{Exploration}} | {{Exploration}} | ||
{{Time|45}} | {{Time|45}} | ||
| − | {{Objective|Exploring Tessellations made from polygons creaed by | + | {{Objective|Exploring Tessellations made from polygons creaed by combining squares of the same size. Topic is important for education majors.}} |
| − | [[Image: | + | [[Image:Tetromino.png|thumb|The five free tetrominoes, top to bottom I, O, Z, T, L, marked with light and dark squares.]] |
* A {{define|polyomino}} is a polygon made from squares of the same size, connected only along complete edges. | * A {{define|polyomino}} is a polygon made from squares of the same size, connected only along complete edges. | ||
| − | + | Examples: | |
* A {{define|triomino}} is a polyomino made from three squares. | * A {{define|triomino}} is a polyomino made from three squares. | ||
* A {{define|tetromino}} is a polyomino made from four squares. Another name for a tetromino is a quadromino. Anyone who has ever played tetris will be familiar with these objects. | * A {{define|tetromino}} is a polyomino made from four squares. Another name for a tetromino is a quadromino. Anyone who has ever played tetris will be familiar with these objects. | ||
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<li> How many different tilings can you create using just the "long pentomino"? | <li> How many different tilings can you create using just the "long pentomino"? | ||
| − | <li> Which of the pentomino shapes can be folded up into a cube? | + | <li> Which of the pentomino shapes can be folded up into a cube (or more precisely, a box withoud a lid)? |
| − | < | + | </ol> |
{{handin}} | {{handin}} | ||
| + | |||
| + | [[category:Tessellation Explorations]] | ||
Latest revision as of 15:12, 2 February 2010
Objective: Exploring Tessellations made from polygons creaed by combining squares of the same size. Topic is important for education majors.
- A polyomino is a polygon made from squares of the same size, connected only along complete edges.
Examples:
- A triomino is a polyomino made from three squares.
- A tetromino is a polyomino made from four squares. Another name for a tetromino is a quadromino. Anyone who has ever played tetris will be familiar with these objects.
- A pentomino is a polyomino made from five squares.
- There are exactly two triominoes. Draw both of them. (Two triominoes are considered the same if one can be obtained from the other by rotation or reflection).
- What kind of symmetry does each of the triominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
- Both triominoes tessellate the plane. Show a tessellation for each of the triominoes.
- There are five different tetrominoes. Draw them. (Two tetrominoes are considered the same if one can be obtained from the other by rotation or reflection).
- What kinds of symmetry does each of the tetrominoes have? (Rotational? What angle? Reflectional? How many lines of symmetry?)
- All tetrominoes tessellate the plane. Show a tessellation for each of the tetrominoes.
- There are twelve different pentominoes. Draw them. (Two pentominoes are considered the same if one can be obtained from the other by rotation or reflection).
- Pick five of the pentominoes that you found and for each individual pentomino draw at least one tiling pattern that can be developed with it.
- How many different tilings can you create using just the "long pentomino"?
- Which of the pentomino shapes can be folded up into a cube (or more precisely, a box withoud a lid)?
Handin: A sheet with answers to all questions.
