Tag Archives: Mathematics and Art

Creative Juice #28

Creative Juice #28

Fifteen articles to ignite the spark.

Creative Juice #9

Creative Juice #9

Selected to refresh your soul:

Divine Proportions

Divine Proportions

I recently attended a lecture about the interface between science and faith. One of my fellow audience members, a woodworker named Ed Bond, mentioned The Golden Ratio. Specifically, he focused on the Golden Rectangle, which influences the dimensions of the tables he creates.

I am going to oversimplify this, because I just don’t know how to explain it clearly without using a lot of words. (My mathematician daughter would do a much better job. She gets this. She also has a Fibonacci spiral tattooed on her shoulder—more about that later.)

The Golden Ratio is a phenomenon that occurs in nature and mathematics, and has been used by engineers and artists for millennia. Plato knew about it, and referred to it in his Timeas when describing three-dimensional geometric solids. It refers to the relationship between measurements a and b where a is to b as a + b is to a.

Golden ratio

The Golden Ratio is known by the Greek letter phi, and like another mathematical concept, pi, has an infinite, unrepeating sequence of numbers following its decimal point. Phi’s approximate value is 1.618. In the equation (a + b) / a = a / b, if a = 1, then (a + b) = 1.618…

Ed Bond says he likes to build tables whose sides are multiples of 1.5 x 2.5—for example, a 3-foot by 5-foot coffee table. The dimensions look good; they feel “right.” That ratio is 1:1.666…, approximating that magic number, phi. He says it’s no accident that the humble index card is 3 inches by 5 inches.

Golden Rectangle

Le Corbusier, a Swiss-French architect (1887-1965), claimed that the human form, subdivided at the navel, yields the Golden Ratio; and if you subdivide those sections further, at the knees and throat, they also fall into the same ratio. Leonardo da Vinci’s famous drawing Vitruvian Man is often used to illustrate this idea (though, actually, the math in the artwork doesn’t match).

Vitrutian Man

This drawing by Heinrich Agrippa (1486-1535) is a better representation:


Phi turns up frequently in geometry. In Salvador Dali’s The Sacrament of the Last Supper, the edges of the dodecahedron framework conform to the Golden Ratio.

Dali Last Supper

The Golden Ratio manifests again in the Fibonacci sequence, which is a sequence of numbers starting with 1 (or sometimes 0) and then you add the preceding two numbers to get the next number: (0,) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Starting with 5, if you divide any number in the sequence by its preceding number, the result is close to phi. The sequence can be used to generate a spiral shape (don’t ask me how). This is the shape tattooed on my daughter’s shoulder. It suggests the inner pattern of the multi-chambered nautilus shell and the Snail Trail quilt block.

Fibonacci spiralnautilus-cutaway-shellsnail trail

Getting back to woodworking, Ed Bond wondered how long the Golden Ratio has been used in making furniture. One day, while reading the Bible, he found God’s directions to Moses for building some of the furnishings for the Tent of Meeting. For the Ark of the Covenant, God said, “Have them make a chest of acacia wood—two and a half cubits long, a cubit and a half wide, and a cubit and a half high” (Ex. 25:10 NIV). “Make an atonement cover of pure gold—two and a half cubits long and a cubit and a half wide” (Ex. 25:17). There it is, God’s own design, executed before 1400 B.C., incorporating the Golden Ratio.

It was His idea. God determined the laws of mathematics and physics. God created all of nature. We discover the mysteries of the universe through science and math; we celebrate them through art.

If you would like a more thorough explanation of the Golden Ratio, read this article.

In your own creative work, does mathematics or science come into play? Share in the comments below.