The Story of the Polygons
... or how the quadrilaterals made everyone mad
Once upon a time, on Planet 2-D, all the figures played happily together.
(It figures. Hahaha. OK, bad play on words. Sorry.)
    But one day, someone looked at the round figures and said, "Hey, those figures don't have any angles -- they're curved. We don't want to play with anyone who's round."  So they rolled all the curved figures out of their play group.
    "All of us have many angles," noticed another figure. "We should have a special name.  Why don't we call ourselves polygons?  'Poly' means 'many,'  and 'gon' means 'angles.' "
     "What a great idea!" everyone agreed.  		( "Ha! Polygon!" sneered the circle. "It sounds like a dead parrot to me. I didn't like playing with them anyway."
    The oval nodded. "And I was always bruising myself when I'd run into their pointy vertices. Let's go play hoops with the line segments."
    But that's another story...)
    For a while, the polygons played together, happy with their new name.  They played polygon basketball using an octagon, because of course they didn't have a circle anymore in their group.
     One of the polygons was learning how to count in French.  "Un, deux, trois, quatre..." it would run around the polygon basketball players, counting their sides and angles.
     Suddenly, it gave a big yell, "�coutez!"  Everyone stopped to listen.
     "Un, deux, trois, quatre," it said, as it pointed to one polygon.
     "Un, deux, trois, quatre," it said, as it pointed to another polygon.
     "Un, deux, trois, quatre," it said, pointing to itself and its angles and sides.
     "Un, deux, trois, quatre.   Un, deux, trois, quatre.   Un, deux... trois!" it shouted at an isosceles triangle.  Everyone looked horrified at the poor red-faced triangle, who turned scalene in embarrassment.
     "But wait!  Listen to this:  un, deux, trois, quatre, cinq, six, sept, HUIT! Can you believe it? Huit! Eight!"
     "Stop! There's nothing wrong with having eight sides," protested the octagon hotly.
     But no one listened.
     All of the four-sided polygons gathered together.
    "�coutez," said the French-counting polygon, the one who had started the commotion. "There are lots of us four-sided polygons.  We don't need to play with any polygon who doesn't have four sides."
     "That's fine with me," declared its friend, known to all as Polygon ABCD. "I didn't like playing with Octagon anyway; it was always telling me to stop.  And I always got into a fight with Pentagon."
     "And what about those triangles," added Polygon PQRS. "One of them always has to be right. That really bugs me.  I don't want the same name as those annoying polygons."
     "Well, we could call ourselves quadrilaterals. 'Quadri' means 'four' -- just like the French 'quatre' -- and 'lateral' means 'side.'  None of the other polygons can call themselves quadrilaterals because they don't have four sides."
     "Yay for quadrilaterals!" they cheered -- four times.
    Well, can you guess what happened next?  Of course, these fussy quadrilaterals fought amongst themselves.
    The ones with opposite sides parallel ganged up on the others.  They started to call themselves parallelograms.

(I can understand the "parallel" in "parallelogram," but why would they call themselves after their grandmothers?  They wouldn't explain it to me -- they were too busy making sure their opposite angles were equal.)
    Needless to say, even the parallelograms couldn't agree.  The ones with 90� angles thought they were extra-special and so they gave themselves an extra name: rectangle.
    The other parallelograms got mad. One of them, the one with equal sides, decided to call itself a rhombus.  
     Square, who had 90� angles and equal sides, stated it was both a rectangle and a rhombus, and thought the others should make it the Prime Minister.
What a mess Planet 2-D was in.  Everyone was arguing with everyone else.  Everyone thought they were extra-special.  It went on like this for years.
UNTIL
one day...
Donald Coxeter, the world's greatest geometer,
pulled them all into the 4th dimension,
where they aren't really real, so they aren't
bothering anyone at all anymore.


THE END
(OK, I like the ending, even if some of you don't.  Just be glad I'm not making you do a novel study with this story.  Hmmm. Not a bad idea...)

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A polygon chart to help you
figure 1          figure 2     figure 3  figure 4   figure 5  figure 6  figure 7  figure 8
figure 1 is a
   polygon (has many angles)
   quadrilateral (has 4 sides)
   parallelogram (opposite sides parallel)


figure 3 is a
   polygon (has many angles)
   quadrilateral (has 4 sides)
   parallelogram (opposite sides parallel)
   rhombus (all sides equal)



figure 5 is a
   polygon (has many angles)
   triangle (3 sides, 3 angles)

figure 7 is a
   polygon (has many angles)
   hexagon (6 sides, 6 angles)		 figure 2 is a
   polygon (has many angles)
   quadrilateral (has 4 sides)
   parallelogram (opposite sides parallel and equal)
   rectangle (all angles are 90� )

figure 4 is a
   polygon (has many angles)
   quadrilateral (has 4 sides)
   parallelogram (opposite sides parallel and equal)
   rectangle (all angles are 90� )
   rhombus (all sides equal)
   square (all sides equal and all angles  90� )

figure 6 is a
   polygon (has many angles)
   pentagon (5 sides, 5 angles)

figure 8 is a
   polygon (has many angles)
   octagon (8 sides, 8 angles)
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