Transcript PENTOMINOES - Home Page, MSTE, University of Illinois

PENTOMINOES
A Power Point Presentation
By: Jillian St.Leger
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.
POLYMINOES
are shapes made from combining
a certain number of squares
edge to edge.
The figure that results after combining is a polygon.
PENTOMINOES
are a type of polygon/ polymino
that uses FIVE square blocks joined
edge to edge.
The other classes of polyminoes are….
Other
Monominos
using 1 square
Dominoes
using 2 squares
Triominoes
using 3 squares
Tetrominoes
using 4 squares
Pentominoes
using 5 squares
Hexominoes
using 6 squares
And so forth
It is possible to make
Shapes
NOTE: They are named after the letters they resemble
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.
PENTOMINO GAMES
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.
To play: http://www.math.clemson.edu/~rsimms/java/pentominoes/
Since the twelve pieces are each composed of five
squares the rectangle figures constructed will
contain an area of 60 units squared.
12x5=60
Since the area of the rectangle will be 60 units
squared when using all twelve pieces, the
pentominoesRectangle
will be able toGame
fit into the following
dimensions, each containing a certain number
of solutions.
6x10
2339 solutions
5x12
1010 solutions
4x15
368 solutions
3x20
2 solutions
NOTE: The dimensions equal 60 units squared
To play:http://www.math.clemson.edu/~rsimms/java/pentominoes/
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.
The game triplication
will have
the following
Triplication
2 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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