The Golden Rectangle - Task

What shape of rectangle is most pleasing to the eye? The ancient Greeks concluded that there was one shape, called the "Golden Rectangle" (see its description below). 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.
  • 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.