#9 Golden Mean

#9: Golden Mean
Finished: 3/4/12
Techniques: Math Concepts of Golden Mean, Fibonacci numbers, and a logarithmic spiral
Size: 21 1/4" x 13 1/4"

Description: Quilting involves a lot of math, and this is my first quilt devoted to a mathematical concept. From measuring and cutting to matching and piecing smaller units to form larger blocks, the math is sometimes intuitive, but still there.

The Golden Mean is a ratio approaching 1:1.1618. (Or more accurately, 1: (1+√5)/2)).  If you think of a rectangle where one side measures 1 and the other measures 1.1618, you would have a golden rectangle.

To represent this concept of Golden Mean, I chose 7 golden-colored fabrics and then cut and pieced them according to the start of the Fibonacci sequence of 1, 1, 2, 3, 5, 8. (Take any two of these consecutive numbers and their sum will be the next number in the sequence.) Though not strictly a golden rectangle (this is after all just a mini-quilt) the ratios of the sides, were I to continue expanding the sequence, would approach the Golden Mean.

There’s a fascinating relationship of these math concepts to nature, too. The logarithmic spiral portrayed in white satin stitch resembles the way a nautilus shell grows, or the growth pattern of a big horn sheep’s horn. Or the arms of a spiral galaxy. Or the growth patterns of certain plants.

Speaking of plant growth, the quilting on the mini-quilt was done to represent a sunflower, which incidentally in nature, tends to form crisscrossing spirals of successive Fibonacci numbers, typically 34 spirals going one way and 55 spirals going the other.

The Golden Mean is considered an aesthetically pleasing ratio and is used in art and architecture as well. The Pyramids of Egypt and the Parthenon were built on its premise, and paintings by Leonardo da Vinci and Seurat made good use of the Golden Mean.


Did you notice the size of the quilt? It's a little off due to the binding, but 13 and 21 are consecutive numbers in the Fibonacci sequence. The backing fabric continues the Golden theme with "golden fries" fabric I probably picked up in a box of fabric I bought at a garage sale at some point.