Math in Art: The Golden Ratio

Golden Ratio

Composition is an important aspect of any art piece–how the subjects within a painting or photograph are arranged is just as important as the colors used to represent them. Apart from being a useful concept to keep in mind to help balance a painting, composition can often inform the viewer of a picture about the importance of the subjects within (Think of Leonardo da Vinci’s iconic Last Supper–where is Jesus Christ in the painting?) One important tool to help with the composition of a painting is the golden ratio.

Given two quantities a and b, the golden ratio is when the ratio of the sum of the quantities to the larger quantity (a) is equal to the ratio of the larger quantity to the smaller one (b). So, a: a+b= a: b. When this ratio is achieved, in painting or in architecture, it is more aesthetically pleasing as well as more balanced. Artists and architects use this ratio in the form of the golden rectangle, where the length of the sides are in a golden ratio, as well as the golden triangle, where the length of the legs of the triangles exist in a golden ratio as well.

The Golden Triangle in “The Mona Lisa”

The Golden Rectangle in “The Mona Lisa"
















The golden ratio is also seen photography. The infamous rule-of-thirds (where it is desirable to line up subjects at the 1/3 and 2/3 intersections) is a product of the intersection of several golden triangles, as shown in this graphic.

Rule of Thirds