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A Power Point Presentation By: Jillian St.Leger PENTOMINOES

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POLYGONS Are closed plane figures with three or more sides and angles. These shapes help in the study and exploration of many different mathematical concepts, one of these being polyominoes.

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POLYMINOES are shapes made from combining a certain number of squares edge to edge. The figure that results after combining is a polygon.

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are a type of polygon/ polymino that uses FIVE square blocks joined edge to edge. PENTOMINOES

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Other The other classes of polyminoes are…. Monominosusing 1 square Dominoesusing 2 squares Triominoesusing 3 squares Tetrominoesusing 4 squares Pentominoesusing 5 squares Hexominoesusing 6 squares And so forth

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Shapes It is possible to make NOTE: They are named after the letters they resemble

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History Pentominoes come from the the fictional story of William the Conqueror and the dauphin of France who were playing chess. The story tells of a tale how the dauphin threw the chessboard at his opponent in a fit of frustration and how the son of William the Conueror responded by breaking the chessboard over the dauphin’s head, breaking it into thriteen pieces—twelve pentominoes and one square.

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Games PENTOMINO GAMES There are several different types of games that can be played and constructed using pentomino pieces. The most basic of these games is trying to use all the pieces in order to form a rectangular figure. Since the twelve pieces are each composed of five squares the rectangle figures constructed will contain an area of 60 units squared. 12x5=60 To play: http://www.math.clemson.edu/~rsimms/java/pentominoes/

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Rectangle Game Since the area of the rectangle will be 60 units squared when using all twelve pieces, the pentominoes will be able to fit into the following dimensions, each containing a certain number of solutions. 6x102339 solutions 5x121010 solutions 4x15368 solutions 3x202 solutions NOTE: The dimensions equal 60 units squared To play:http://www.math.clemson.edu/~rsimms/java/pentominoes/

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TRIPLICATION This is another game where one of the twelve pentomino pieces is chosen and the player uses nine of the other pieces to form a copy of the chosen piece.

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Triplication 2 The game triplication will have the following results… - The duplicate will have dimensions three times that of the original. -The duplicate will have an area nine times larger than the original. This is because the new figure is made of 9 pentomino shapes and each one has the same area as the original shape drawn.

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