[TheForge] Golden mean

Wed Sep 25 13:25:59 2002

Forget the high math and remember this story.

Fibonacci was playing a numbers game using arabic rather than Roman
numerals.  He thought ...what if I start with one rabbit, then add another -
I have 2, which then becomes 3 then 5 then 8 then 13 ... each number results
from adding the previous two numbers together.

A real rough ratio approximation is 3x5 - two sequential Fibonacci numbers.
After about the 13th number in the sequence, the ratio becomes finite and is
the Golden Section.

There are sites like:
http://galaxy.cau.edu/tsmith/KW/goldengeom2.html
that show how to take this and make a spiral but I don't like the process
shown.  This site uses a subtractive process and a compass and is more
complicated than required.  All you need is a ruler and a right triangle.

Instead, draw a Fibonacci rectangle like .... 3w x 5h.  If you want to go
counterclockwise, using the right side 5 as a new right end, draw another
rectangle that is 8w x 5h and has the original rectangle in it.  Now using
the top 8 as a new end, draw a rectangle down that is 8w x 13h and has the
other two rectangles in it.  Continue in a counter-clockwise direction
building rectangles.

After several iterations of this sequence, draw a spiral that connects the
centers of the rectangles (or the same corner of each when rotated).

 Walt
-----Original Message-----
From: John Chobrda <[email protected]>
To: The forge <[email protected]>
Date: Wednesday, September 25, 2002 11:30 AM
Subject: [TheForge] Golden mean

>Can any one give me, or point me in the right direction where I can get
>a simple explaination of the golden mean, and how to draw it.
>
>Thanks in advance
>John C.
>
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