## Ah, the Golden Section (or Golden Mean), that mysterious mathematical concept found in nature, art, architecture, and music. A little-understood principle of design that people like to talk about to sound smart, myself included.

Once you become aware of it and understand it, you start to see it everywhere. I’ll tell you a little about what it is (without going into too much detail because there are entire websites dedicated to the topic) and how it is used in art and how I use it myself.

## What is the Golden Section?

First of all, the Golden Section is a Mathematical concept that is seen in nature and used in art, architecture, and music. It’s based on something called the Fibonacci sequence, which is a sequence where each number is the sum of the two numbers preceding it. It goes like this:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

If you get far enough along in the sequence, the ratio between the numbers is very close to 1:1.61803. What that means in art is you can use it to draw a rectangle or use a canvas where the sides have a ratio of 1:1.61803. So it is close to a two-thirds ratio or more accurately, a 5-to-8 ratio. It’s considered one of the most harmonious and pleasing ratios in the universe. There are several ways you usually see this expressed:

### Golden Rectangle

Simply create a square, divide it in half, and draw a diagonal line from the bottom left to the top corner of the half. From the center, extend that same length of line and the end of that is the end of the rectangle. Square it off from there and you have a Golden Rectangle where the short side is 1 and the long side is 1.618. Or the long side is 1 and the short side is .618 of the long side.

If you take a Golden Rectangle and cut out a square, the remaining section is also a Golden Rectangle. You can keep doing this to infinity.

## Dividing Rectangles

With any canvas, you can find the Golden Mean point between the edges by multiplying the length by .61803. It’s close to a third — more on that in a bit. You can place these lines on the canvas coming from all directions, then where the lines converge, place important elements there. It gives it a harmonious structure.

### Golden Spiral

This is perhaps the most well-known depiction of the Golden Mean. If you connect the points of a bisected Golden Rectangle and make a curve from it, you get the Golden Spiral. You see it everywhere in nature. Make a fist, and look at the spiral of your pinky finger to your hand. That’s pretty close to the same spiral. The shell of the Chambered Nautilus looks like this when you cut it open. Each chamber is 1.6108 times the size of the previous chamber.

By Jahobr – Own work, CC0, Link

### Golden Triangles

Golden Triangles are a bit more complex. You can find them in the Golden Spiral, and by joining the “big” and “little” triangles, you get another Golden Triangle, similar to how the Golden Rectangle repeats itself. A regular pentagram contains Golden Triangles.

### The “other” Golden Section: The Rule of Thirds

The Rule of Thirds is a simpler, yet related concept. Since 1: 1.6180 is so close to the 1:1.5 ratio, which is the same as 2:3, you can fudge a little and work with thirds instead. Divide your canvas into thirds vertically and horizontally, and place your focal point on one of the four intersections. Chances are you won’t be right on the nose on that point but in the vicinity of that point as well as the Golden Mean point, which is often close enough.

**The rule of thirds:** divide the canvas into thirds, and place the most important element at one of the intersections.

## Some famous examples of the Golden Section from Art History

**The Parthenon:** Many have said that the Parthenon was built on a 1:1.618 ratio, but it’s actually more like 4:9. The effect is similar, though.

**Leonardo Da Vinci** famously used the Golden Section (or Golden Mean) in his artwork. I think people look too hard for it in his work, which is highly detailed with lots of elements which can be construed as lining up a certain way. Was it intentional or coincidental? Who knows? That’s probably how Da Vinci wanted it.

**Salvador Dali** intentionally used the Golden Ratio in his artwork, as you can see in this preliminary sketch for “Leda Atomica.” He was influenced by the book *The Geometry of Art and Life* (1946) by Matila Ghyka. He cast his wife Gala as Leda, in love with Zeus as the swan, and set her inside a pentagram inside a circle, aligning elements of the painting with the lines of the “divine” shapes.

*Salvador Dali, “Leda Atomica,” 1949. Oil on Canvas, 61.1 cm × 45.3 cm (24.1 in × 17.8 in). Dalí Theatre and Museum, Figueres.*

## Demonstration of how I use it

When I use the Golden Mean when I paint I usually just find the lines from the edges and place important elements there. It’s most often where I put the horizon line.

*“Hope,” 2018. acrylic and gold leaf on canvas. 30 x 24 inches*

*Golden section lines overlaid on “Hope” painting*.

In my painting “Hope,” you can see where most of the gold “cloud” fits between the lines, and the peak is at one of the intersections.

If I’m not using a square canvas, I use a 2:3 proportion, or something close to it. A 5:8 canvas proportion is more exact. I’m not a slave to using this proportion, since I actually prefer painting on squares. I use the Golden Mean as a general guideline.

When I’m doing page layout as a graphic designer, I like to start with a 6×9 page, and divide that into a 9 x 9 grid, which is easy to build on. I totally stole this idea from Jan Tschichold, who created the classic Penguin book covers.

I like this 2:3 method which works well for creating a nice page grid. Most of the time I don’t get to use that page proportion, but I often create a 9×9 grid on the page and use that as a general guide.

## The Golden Section is not a hard and fast rule

I don’t think you have to use the Golden Mean (Golden Ratio or Golden Section) in artwork for it to be good. This is just one tool among many, and I don’t always use it. Some people draw lines all over stuff and then say it means something profound when it doesn’t mean anything at all. I just use it as a rule of thumb and then break the rules as I see fit.