Graphic design The Golden Rectangle What shape of rectangle is most pleasing to the eye? The ancient Greeks concluded that there was one shape, called the "Golden Rectangle." The artists of ancient Greece and of the Renaissance used the Golden Rectangle in designing many works of art and architecture. Modern designers and artists, like Mondrian, also use the Golden Rectangle in their works. Today you can find the Golden Rectangle in almost every pocket: credit cards and phone cards are shaped with its proportions. The Golden Ratio (the ratio of the longer and shorter sides of the Golden Rectangle) also appears in many natural phenomena. Lots more information about the Golden Ratio is available on the Internet, for example at: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html In this task you learn about the special property that defines the Golden Rectangle. Here is an arbitrary rectangle. From it you can create a new rectangle by cutting off a square with sides are equal to the shorter side of the original rectangle. Look at the original rectangle and at the new one. Rotate the new rectangle by 90 degrees. Note that the new rectangle is very different in shape from the original one. You can perform this exercise on any rectangle. Two rectangles are said to have the same shape if the ratio of the longer and shorter sides is the same for both. The dynamic figure below performs the process described above on different rectangles. You can use it to (approximately) find the Golden Rectangle. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) What is the ratio of the sides of a Golden Rectangle? Using the dynamic figure, find a rectangle with a ratio of sides that approximates the ratio of sides in the Golden Rectangle. Record the length of the sides and their ratio. Perform a mathematical analysis that enables you to find the precise ratio of sides in a Golden Rectangle: If you start with a rectangle in which the ratio of the longer and shorter sides is x, what will be the ratio of the longer and shorter sides in the rectangle obtained after cutting off a square? Construct a function. - Use the function you have constructed to find the ratio that x needs to be for the rectangle to be a Golden Rectangle. This ratio is called the Golden Ratio. - Compare the results of your mathematical analysis with those obtained by searching for a Golden Rectangle with the dynamic figure. Look for artifacts around you that have the shape of a Golden Rectangle.

Page Design Book design: an experimental investigation Saving paper The importance of margins Tschichold's rules Designing an invitation Designing an ad The Golden Rectangle