Why are so many objects we use in our daily lives rectangular? A square will enclose more area than a non-square rectangle of the same perimeter, yet items we use are overwhelmingly rectangular but not square. In 1876, a German psychologist named Gustav Fechner made thousands of measurements of everyday rectangular items. On average, he found the ratio of length to width was close to the golden ratio. He presented rectangles to hundreds of people asking them to choose the one they preferred. The majority chose a rectangle whose proportions were close to the golden ratio. Later, this experiment was repeated by psychologists Lalo, Thorndike, and Witmer.
a. Research the experiments conducted by Lalo (1908), Thorndike (1917), and Witmer (1984). Did they come to the same conclusion as Fechner? What other interesting conclusions did they come to?
b. Conduct your own experiment. Draw several rectangles with differing proportions. Be sure to include a square and a golden rectangle. Ask at least 30 people to select one rectangle. What percentage of people selected the golden rectangle? Present your findings in a short report and include all data in a table.
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