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Exploring the Golden Rectangle

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In this activity, students will construct a golden section and a golden rectangle and study their characteristics and connections with the Fibonacci series. They will import pictures from the internet and download them into the Sketchpad. Using their "golden" construction, they will discover the use of the golden rectangle within famous works of art. This exploration was adapted from an activity developed by Elizabeth Boiardi while she was a graduate student at the University of Virginia in the summer of 1998.

Mathematics: Students will construct a golden section and a golden rectangle and discover the following properties:

  • The point at the golden mean divides the segment into a long and short segment, such that the ratio of the long segment to the short segment is defined by Phi, f = . 
    This ratio does not change even if the lengths of the segment changes.

  • In a golden rectangle, the ratio of the length of the long side to the length of the short side also equals f = . 
    This ratio does not change even if the lengths of the sides of the rectangle changes    .

  • f 2 = f + 1 as well as, f = 1 + 1/f .

Mathematical Thinking: Students will hypothesize and prove the above properties. They will also generalize the properties to other situations.

Technology: Students will practice importing pictures into a sketch window. They will also be introduced to the Create Axes and Plot Points commands.

The following picture illustrates a possible location of where the golden rectangle is found in art.

      



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Last modified on June 11, 2002.