Join Dave Schultze for an in-depth discussion in this video Golden section, part of Design Foundation 3D: Shape and Form.
- The Golden Section is a mathematical ratio that generates a very special rectangle. It is special because it's thought to have timeless, harmonious proportions, but does it really? Well, there are examples of it in all of the arts and architecture, music, painting, and a whole lot more. Also called the Golden Mean or Golden Ratio, and a few other names, it was first formally described by the mathematician Euclid around 300 BCE but was also believed to have been used even earlier.
In print and everyday objects, the same ratio appears in a wide variety of surprising places, like playing cards, books, posters, and even widescreen TVs. If you want to draw this shape yourself, there are a lot of tricky steps as seen in this animation. Fortunately, mathematician Michael Maestlin calculated a simple decimal ratio back in 1597. So use the value of 1.618. That's a factor to determine the long side multiplied by the short side.
Now you can create your very own Golden Ratio where ever you go. Related to this proportion is the mathematical Fibonacci sequence. This series of numbers are where every number is the sum of the preceding two numbers. I'd love to give you the whole list right now, but it's infinitely long, and we just don't have time today. How this all relates back to the Golden Section and other things, is the idea of recursiveness. Instead of throwing around any more numbers, let's illustrate this visually. This tin package designed for Droste Cocoa in 1900, shows a woman holding the same cocoa package she is already on.
On that smaller package is another version of the same scene. For a three dimensional example of recursion, we can look at the set of Russian nesting dolls. Each one is related to the next one in the sequence, just smaller. So that's recursion, when a thing is described in terms of itself, but continues to repeat at a different size or location. The Fibonacci sequence can then be used to generate our Golden Section through some similar recursive and sequential steps, but it gets even better.
The most surprising and beautiful part of the story is how the Fibonacci sequence appears throughout nature. You can find it in the smallest organism, inside sea shells, in hurricanes, all the way up to spiral galaxies. That's pretty cool. Returning to the Golden Section, let's see how it relates to architecture. This is the Parthenon, built in Athens, Greece, in 432 BCE. It was originally created to be a temple to the god Athena.
It is believed to have been designed using the Golden Section for every major dimension and proportion. For reference, here's an illustration showing how it looks today versus when it was built. As this twenty-five hundred year old structure has been weathered by time, damaged by earthquakes, plus a little looting, we forget that these now ancient temples were often built with vibrant colors. As we now look at the building floor plan and then the front elevation, we can see these Golden Section shapes super-imposed in many locations.
Even here, we can see it in the layout and spacing of columns. When I first started architecture school and heard about this Golden Ratio, it was powerful stuff. I felt like I was receiving an ancient sacred email, direct from the design gods. Now, I can definitely see the Golden Section proportions in the Parthenon, and it's a gorgeous structure by any measure. The problem is that these systems are often over applied, like this Renaissance era illustration of a man hanging out in some geometry.
There may be more art than science, but there's still a lot to learn and appreciate.
First, see how the same idea can be applied in a smaller 2D scale—like graphics and print, fine art, and advertising. Dave then blows it up in 3D, and showcases examples from product design, furniture, architecture, and urban planning.
Projects and concepts are presented in an engaging and sometimes irreverent manner with images, videos, and personal and professional stories from Dave. Check out this fast-paced tour as it covers topics ranging from grids and axes to designing with humor.
- Design exploration with sketching
- 3D exploration with organic forms
- Grids and axes
- Defining space
- Color and contrast
- Texture and patterns
- Minimalism. Less is more.
- Retro. It's back!