THE GOLDEN RATIO

In mathematics a ratio is a comparison between two numbers. It relates the "size" of one number when compared with another number. For example, the ratio " 2 : 1 " (we read this by saying 2 to 1) expresses the relationship between the numbers 100 and 50.

There is a ratio between numbers that occurs in many different places. It is approximately 1 : 1.62, and it is called the "Golden Ratio." A rectangle whose length and width are in this ratio is called a "Golden Rectangle." If the width of this rectangle were 1, its length would be 1.62.

Exercise 1: Constructing a Golden Rectangle.

This exercise can be done using the drawing tools in Microsoft Word.

  1. Be sure that the Drawing toolbar is displayed. (From the View menu, choose Toolbars, and then click Drawing).
  2. Click on the rectangle tool. As you move the pointer, be sure to hold down the Shift key; this will allow you to draw a perfect square.

    3. After you draw the square, select it and then choose Copy and then Paste to create an exact duplicate.          Click on this copy to select it; then right-click , choose Format Auto Shape, and the under Scaling make           the width 50%.

  1. Move this half-square so that it overlaps the original, and then draw the diagonal of the second half-square as indicated.
  2. Copy this diagonal and rotate it so that it extends the base of the original square.
  3. The resulting rectangle will be a "Golden Rectangle," whose width and length are in the ratio 1 : 1.62

 

NEXT: The Golden Rectangle in Art