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The Cummer Museum of Art & Gardens is committed to engage and inspire through the arts, gardens and education. A permanent collection of nearly 5,000 works of art on a riverfront campus offers more than 95,000 annual visitors a truly unique experience on the First Coast. Nationally recognized education programs serve adults and children of all abilities.

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The Golden Ratio




The Golden Ratio is a ratio by many names, golden or divine, mean, proportion, section, cut, number or ratio, to name a few. It is represented by the Greek symbol Phi (φ Φ). The ratio is established when  the sum of two different numbers  divided by the largest number is equivalent to the largest number divided by the smallest. That is to say  if A > B then A and B are in the Golden Ratio if (A+B)/A = (A/B).

The Golden “Ratio”, φ Φ, is actually an irrational number like Pi (π Π). Perhaps the irrationality can account for the avoidance of the word “ratio” in its other names. It has an approximate value of 1.618. . .  and can also be approximated by sequential Fibonacci numbers. Things get a little more irrational when you learn one of the special characteristics of this ratio. It can be defined in terms of itself. That is to say that  φ = 1+(1/φ). Furthermore this can be expanded indefinitely resulting in what is known as a “continued fraction”.

According to Priya Hemenway, a Greek sculptor, painter and architect by the name of Phidias, knowingly incorporated the ratio into his Parthenon statues around 5th century B.C. The ratio has been observed in Ancient Egyptian constructions including the pyramids, however most are still unsure  if the ratio was employed purposefully or was harmonious side effect of  Egyptian mathematics. Interestingly enough, and more recent as well, Books from 1550 A.D. through 1770 A.D. were purposefully constructed with proportions of the golden variety, accurate to within a millimeter.

Perhaps one may observe the Golden Ratio in action in the permanent collection?

If you’ve enjoyed this brief historic glimpse of art and math, feel free to like and comment below!




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Director of Art Education

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