The Golden Ratio in Everyday Objects

You will need some measuring tools in this activity. Rulers, tape measures, and/or yardsticks should do the trick.

The Golden Ratio is not just some number that math teachers think is cool. The interesting thing is that it keeps popping up in strange places - places that we may not ordinarily have thought to look for it. It is important to note that Fibonacci did not "invent" the Golden Ratio; he just discovered one instance of where it appeared naturally. In fact civilizations as far back and as far apart as the Ancient Egyptians, the Mayans, as well as the Greeks discovered the Golden Ratio and incorporated it into their own art, architecture, and designs. They discovered that the Golden Ratio seems to be Nature's perfect number. For some reason, it just seems to appeal to our natural instincts. The most basic example is in rectangular objects. Look at the following rectangles:



Now ask yourself, which of them seems to be the most naturally attractive rectangle? If you said the first one, then you are probably the type of person who likes everything to be symmetrical. Most people tend to think that the third rectangle is the most appealing. Measure each rectangle's length and width, and compare the ratio of length to width for each rectangle. Answers:

Rectangle 1:

Rectangle 2:

Rectangle 3:

Have you figured out why the third rectangle is the most appealing? That's right - because the ratio of its length to its width is the Golden Ratio! For centuries, designers of art and architecture have recognized the significance of the Golden Ratio in their work. We will learn more about that later. For right now, let's see if we can discover where the Golden Ratio appears in everyday objects. Use your measuring tool to compare the length and the width of rectangular objects in the classroom or in your house (depending on where you are right now). Try to choose objects that are meant to be visually appealing. Some suggestions are listed below, but by all means add to the list. It might be a good idea to print out the following table and use it as a guide:

index card
picture frame
door frame
computer screen
TV screen

Were you surprised to find the Golden Ratio in so many places? It's hard to believe that we have taken it for granted for so long, isn't it? I know....




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©2001 by Mr. David L. Narain

Last Updated January 3, 2003