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by Enrique Meza C

You may have noticed that if you have a Golden Rectangle and you cut off a
square with side lengths equal to the length shorter rectangle side, then what
remains is another Golden Rectangle.

This could go on forever. You can just keep cutting off these big squares and
getting smaller and smaller Golden rectangles.

The idea with the Fibonacci series is to do the same thing in reverse. So the
quiz:

What you do is start with a square (1 by 1), find the longer side, and add a
square of that size to the whole thing to form a new rectangle.

So when we start with a 1 by 1 square the longest side is one, so we add another
square to it.  Now we have a 2 by 1 rectangle

Then the longest side is two, so we connect a 2 by 2 square to our 2 by 1
rectangle to get a 3 by 2 rectangle.  This continues, and the sides of the
rectangle will always be a successive Fibonacci number.  Eventually the
rectangle will be very close to a Golden Rectangle.

I will do a few steps to let you see it in action:

###
# #    1 by 1, so we add 1 by 1 to get...
###

######
# ## #  Now it is 2 by 1, so we add 2 by 2 to get......
######

######
# ## #
######
######
#    #   Now it is 2 by 3, so we add a 3 by 3 to get.......
#    #
#    #
#    #
######

###############
# ## ##       #
#######       #
#    ##       #
#    ##       #  Now it is 3 by 5, so we would add a 5 by 5 square.
#    ##       #
#    ##       #
###############

```