Misconceptions about the Golden Ratio

Around 1990, Dr. George Markowsky, professor of computer science at the University of Maine, intended to present a talk about the wonders of the golden ratio to his school's Classics Club. Like any good scientist, he decided to double-check the "facts" before he repeated what he had read so often in textbooks, newspapers, and scholarly papers,¹ but his findings were not at all what he expected. "I collected all of the usual s! tories about the golden ratio being used to design the Great Pyramid and the Parthenon, as well as about its aesthetic properties and its use by painters," writes Markowsky. "I found the references to be quite vague, and in the process of trying to make my talk more precise, I actually began to look up measurements of buildings. Much to my surprise, the results did not support the claims that were being made about the golden ratio."² Markowsky's research resulted in a paper titled, "Misconceptions about the Golden Ratio," which appeared in the January 1992 edition of The College of Mathematics Journal.

One of the more interesting claims refuted in Markowsky's paper is the idea that the golden rectangle is the most "visually satisfying of all geometric forms."³ Using a diagram consisting of 48 randomly arranged rectangles all having the same height but with widths ranging from 0.4 times the height to 2.5 times the height,⁴ Markowsky informally surveyed attendees to his lectures to find which rectangle they most preferred. His results show the average person cannot pick out the golden rectangles within the diagram (there are two), and that, aesthetically speaking, the most pleasing rectangle has a ratio of 1.83 instead of Φ (the golden ratio).

Below is the diagram from Dr. Markowsky's paper featuring the 48 rectangles he presented to the people in his lectures. Using the format (row, column), which rectangle do you like most?

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¹ Markowsky, George (2005). Book Review: The Golden Ratio. Retrieved June 3, 2010 from {www.ams.org/notices/200503/rev-markowsky.pdf}.

² Idem.

³ Markowsky, George (1992). Misconceptions about the Golden Ratio. Retrieved June 3, 2010 from {www.math.nus.edu.sg/aslaksen/teaching/maa/markowsky.pdf}.

⁴ Idem.

How to do ratios