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You're playing with a square. You notice that you can move the square
some ways without making it seem like you moved the square. For
instance, you can flip it around one of its diagonals. Or, you can
rotate it 90 degrees clockwise (or counter-clockwise). You notice
that sometimes, you can follow such a motion by another such motion
and get something new which doesn't affect the square.
You want to understand these motions. You decide to simplify things
by simply denoting the rotation by 90 degrees clockwise by R and the
90 degree counter-clockwise rotation by L. examples on math forum;
You decide to write RR for
the motion you get when you do R twice. You find that RRRR is really
the same as doing absolutely nothing. You notice that RRR is the same
as L, and LLL=R. You find that RR=LL. You find that you can't get the
flip about the diagonal using just R and L, so you call it F.
learn more on online math forum.
You're playing with a square. You notice that you can move the square
some ways without making it seem like you moved the square. For
instance, you can flip it around one of its diagonals. Or, you can
rotate it 90 degrees clockwise (or counter-clockwise). You notice
that sometimes, you can follow such a motion by another such motion
and get something new which doesn't affect the square.
You want to understand these motions. You decide to simplify things
by simply denoting the rotation by 90 degrees clockwise by R and the
90 degree counter-clockwise rotation by L. examples on math forum;
You decide to write RR for
the motion you get when you do R twice. You find that RRRR is really
the same as doing absolutely nothing. You notice that RRR is the same
as L, and LLL=R. You find that RR=LL. You find that you can't get the
flip about the diagonal using just R and L, so you call it F.
learn more on online math forum.
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