Fibonacci sequence, Golden Ratio, Golden Rectangle, Industry

Date: Wed, 16 Nov 1994 0:18:26 -0600 (CST)
From: Anonymous

Do you know of any industries that purposely employ the Fibonacci Sequence
in their product design? Just curious...

Thanks...

Date: Wed, 16 Nov 1994 11:12:43 -0500 (EST)
From: Dr. Ken
Subject: Re: your mail

Hello there!

As a matter of fact, I do happen to know one industry that employs the
Fibonacci sequence, although you'd probably be hard pressed to get them to
admit that they do it purposely (and to tell the truth, I'm not sure that
they do).  That industry is the credit card industry.  Are you familiar with
the Golden Ratio?  Well, if you go out far enough on the Fibonacci sequence,
you'll find that the ratio of each term to the preceding term approaches a
certain value, the value (1 + Sqrt[5])/2.  This value is a rather important
one in mathematics, as it shows up all over the place.  In particular,
suppose we have the following rectangle:

                                    X
                          ______________________
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                        Y |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |                    |
                          |____________________|

where X and Y are the lengths of the sides as labeled.  Let's suppose that
there's a nice relation between X and Y:

                    X       Y
                   --- = ------
                    Y     X + Y

Stated another way, Y is the geometric mean of X and (X + Y).  If we
actually compute to find what the ratio of Y to X is, we find that it's 
(1 + Sqrt[5])/2.  Pretty neat.  This rectangle is known, appropriately
enough, as the Golden Rectangle.  There have been a number of psychological
tests that show (if you believe them) that the Golden Rectangle is the most
pleasing to the human eye.  So it comes as no surprise that the credit
card industry has made the dimensions of their cards very close to the
dimensions of this Golden Rectangle.  

Actually, come to think of it, there's certainly another industry that has
made use of the Golden Rectangle; the visual art industry.  Not surprising.

If you're interested in learning more, I heartily recommend the book "The
Joy of Mathematics" by Theoni Pappas.  That's where I learned a bunch of the
things I've told you.

Thanks for the question!

-Ken "Dr." Math