The Magical Golden Ratio

It’s been said that the golden ratio (also called the golden proportion, golden mean or Phi) is the perfect proportion. The golden ratio certainly seems to have magical properties. It occurs in nature, in the human body and in animals, in ancient art and architecture, even in many of our quilt designs. Let’s do a little test. Pick out the illustration you find the most pleasing in each row. test I have given this test many times over the past decade and usually 75% will pick A, B, and B. If you picked these, you picked the shapes which have the Golden Ratio. So what is the golden ratio? OK, here comes some math. (Warning! Your eyes may be in danger of glazing over and your mind may wander. Never fear: it is only two sentences long.) It is the division of a line segment where the ratio is 1 to 1.618, one being the shorter length and 1.618 the longer one. It can also be the ratio of .618 to 1 where .618 is the shorter segment and 1 is the larger.

Shells

Most spirals found in nature fit the proportions of the golden ratio.

You will find that this ratio has been used throughout history. Some examples include the Greek Parthenon, the Great Pyramid at Giza, the paintings of Leonardo DaVinci. However, a truly fascinating aspect of this magical ratio is that it occurs so often in nature. For example, in a beehive there are fewer male bees than female bees. The ratio of males to females is the golden ratio! A pinecone has two sets of spirals, one with less spirals than the other…..the relationship between them is again the golden ratio. Look at the photos above of the shell and Romanesco broccoli as another example. The golden ratio is even evident throughout the human body, in the measurement from the top of the head to the chin and from the chin to the navel and from the navel to the floor. Measurements from the elbow to the wrist and wrist to the tip of the middle finger also fall into the golden proportion. If you are like me, you don’t like carrying a calculator around all the time and doing math, but you might be curious as to the proportions of various objects. Because of this I developed the Golden Gauge Calipers. This is a handy tool that eliminates the math and lets you see the golden proportions in objects. As the calipers are opened the shorter segment in relation to the longer one is the golden ratio and vice versa. 2. calipers open and closed When the calipers are opened so that the narrow space is the size of the width of oval A you will see that the wider portion of the calipers is the height. The same is true with triangle B. If you open the calipers to the narrow portion across the base of the triangle, the height will be the space between the wider portion of the calipers.

3. calipers on oval

Oval A

With the calipers on the Mariner’s compass B notice that the width of the smaller center circle is in “golden proportion” to the distance from the edge of that circle to the edge of the larger circle. calipers on compass Many patchwork designs contain divisions that are either very close to or exactly the golden ratio. Are designs with golden proportions more pleasing to the eye?  Take a look at Duck and Ducklings and Whirling Five Patch, shown here. It is apparent that the designs have the same basic pattern. The difference is that one is drafted on a 5 x 5 grid and the other on a 14 x 14 grid. Which one is most appealing to you? I personally find Duck and Ducklings a little clunky and like the fact that Whirling Five Patch contains divisions that are not all the same. The Golden Gauge Calipers placed on the design shows that the width of the center division to the adjacent one almost fits golden ratio proportions.

two blocks side by side

Duck & Ducklings and Whirling Five Patch

The Whirling Five Patch with calipersUnknowingly, quilters when planning widths for borders automatically choose this proportion because it “feels” right. In one of the upcoming blogs we will take a look at borders and how to determine a pleasing size.