Fibonacci sequence, Golden Ratio, Golden Rectangle, IndustryDate: 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 |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/