The Golden Ratio in Art is One of the Coolest Things You'll Ever Encounter · Craftwhack

"What makes a single number so captivating that it has persisted in our imagination for more than 2 thousand years?" -Gary B, Meisner The Golden Ratio: The Divine Beauty of Mathematics

We're going to swoop into what was hands downwardly my favorite thing to learn about in art history class: The Aureate Ratio.

I know just enough nigh The Golden Ratio to be equally in awe of it and completely baffled by information technology.

It'south one of those concepts that lights upward your brain when you observe but is difficult to grasp unless you are mathematically inclined.

The more you learn about it, the more y'all volition encounter Golden Spiral Ratio proportions everywhere.

Luckily for u.s., there are a handful of people who understand the concept clearly and tin explain it to the remainder of us cotton-headed ninny muggins.

I will be focusing mostly on the Aureate Ratio in art and compages hither, but I tin't aid but touch on how it pops upwardly in nature also. Become your geek pants on, fellas!

What is the Gilt Ratio?

Definition

The Golden Ratio is an irrational number, approximately 1.618, which is prevalent in nature, fine art, architecture, and design. (Other names for information technology are gilded mean, golden department, Phi (in mathematics), divine department, golden number, Fibonacci sequence.)

Actually, the Fibonacci sequence is super-closely related to the Gold Ratio, but not exactly the aforementioned. This is ane example of math confusion.

The Golden Ratio Rectangle

Visually, it is a rectangle, that when cut into a square, results in the remaining rectangle existence the same proportion as the original rectangle.

I absolutely cannot explicate the math backside it, so go here to understand it in a more practical way.

Try this: If you feel like drawing a rectangle using the Gold Ratio, hither's how y'all do it:

Draw a square.
Describe a dot halfway beyond the bottom line.
Draw a line from that dot to either the opposite corner.
Drop that line downwards and then information technology overlaps the bottom line of the square.
Wherever the end of it lands is where you can draw a lineup and over to make your rectangle.
Notice that the new rectangle y'all just drew can be separated into the same proportions every bit the large rectangle. So can every subsequent little rectangle y'all depict!

Accept it a step further by breaking down the new rectangle into smaller aureate rectangles and so drawing a spiral using lines going from one corner to the opposite corner in each square of the golden rectangle.

Huh? Here, take a look at this:

I also felt the need to draw a page of phi symbols, and please notice I used a lovely golden colour in keeping with the theme.

Who Discovered the Gilt Ratio?

I did! In the early 1600s. JK.

According to this site, Euclid explained the Aureate ratio formula in his book The Elements, even though he didn't name information technology anything. It isn't clear where he might have learned of the thought.

The number phi was named (in the 1900s) for the Greek sculptor and mathematician Phidias who lived from 500 BC – 432 BC.

The Golden Ratio in Nature

This is so, so absurd, and will make yous like nature, even if you abhorred nature previously. Nature is RIDDLED with The Golden Ratio, in plants, faces, microscopic whatevers.

The Golden Ratio tends to show upwards in nature in many flower seed formations (sunflower), seashell patterns (nautilus), and even galaxies!

Read this article on examples of the Gilt Ratio in nature to accident your mind.

image credits: hurricane, sunflower

Your Face is a Gilded Ratio

Keep that comeback handy the next time you're at a loss for words. It's probable the recipient volition have no idea what yous're talking about, and you tin can giggle at your hole-and-corner joke.

Supposedly if you lot await at a human confront straight on, the closer to ideal dazzler information technology is, the more measurements y'all can take all over it that work out to exist the Aureate Ratio.

Here are some examples of the Golden Mean institute on the perfect face up:

Divide the height of your face (from the top of your head to the bottom of your chin) by the width of your face at the widest point, and yous will get somewhere correct effectually phi. (1.618)
The distance between your eyes is about the same width as one heart.
The measurement from the hairline to correct between the optics, and from between the optics to the tip of the nose, and from the tip of the nose to the bottom of the chin should all be shut to equal to achieve perfect beauty.

I measured this skillful-lookin' dude and found that his 3 vertical measurements don't match, and his face elevation divided by his face up width came out to be roughly 1.72 inches.

We had to wing information technology because of his hairdo plainly, but it does work out to exist close.

Attempt this: Print out a photo of your face and mensurate information technology to see how perfect you are. I haven't washed this yet, but I am assuming my giant brow will throw everything off. 🙂

epitome source

Think my Faces are Mathy post? You can find more face up measurements there that help when drawing faces.

The Golden Ratio Fine art

Okay, here we are at the good stuff. Since the Golden Ratio was discovered, information technology'due south not a surprise that it has been widely adopted by artists, designers, and architects to determine the nigh visually pleasing proportions to make their creations.

There are many ways artists accept used the golden ratio in art; using the golden rectangle itself to determine the limerick of the artwork, using the path of the spiral in the gilded rectangle, and fifty-fifty placing important subject matter at measured points inside the rectangle.

The Aureate Ratio Fine art in Painting

Leonardo da Vinci

Probably the near famous artist to put information technology to use is Leonardo da Vinci. Da Vinci illustrated a volume written by Luca Pacioli in the late 15th century all about the Divine Proportion.

He used the measurement in many of his paintings, including Mona Lisa and The Last Supper. This mail shows instances of The Golden Ratio in some of his works.

Effort This: I had fun playing with a transparent png of the Aureate ratio rectangle over Mona Lisa. Here is the png if you want to download it and effort it, also:

Here is Mona Lisa:

I opened her upwardly in PicMonkey, then added the Fibonacci spiral as an 'Add your own' graphic and moved it, resized it, rotated information technology in all sorts of ways.

Salvador Dali

Salvador Dali's painting, The Sacrament of the Concluding Supper (1955) is widely cited equally utilizing the Gold Ratio, and it's pretty cool to break it down in these terms:

The room is a dodecahedron, which is related to a gold rectangle in a mathematical way I absolutely cannot understand.
The entire painting is a golden rectangle.
The table and 2 disciples next to Christ are positioned perfectly at the sections of the golden rectangle.

Piet Mondrian

Mondrian is said to accept used the Golden Ratio in his abstruse paintings, but when I have the trusty golden rectangle to some of them, nada ever quite lines up perfectly.

Obviously some of his paintings line upwards improve with the proportions than others, so maybe he wasn't likewise picky almost precise measurements.

Interestingly, my obsession with placing the golden rectangle over everything I tin can get my hands on led me to place it over this photo of Yves Saint Laurent models wearing Mondrian dresses in front of a Mondrian painting.

Look how beautifully that works out. 🙂

Mark Rothko

Look at his paintings with a new sense of proportion, eh? Simply some of his paintings piece of work out this style, then I'm not sure if this was intentional or not on his office.

image source

The Aureate Ratio Art in Photography

The rule of thirds is commonly taught to first photographers equally a way to ready the composition of their photos.

It is based on the idea that your photo can be separated into a grid of nine equal spaces, and the focal points of the image should line upwards with one or more spots where the lines intersect.

The phi filigree is used in photography as some other fashion to break up the image, following the 1:i.618 ratio. The lines are laid out in a grid, but they are not spaced evenly every bit in the dominion of thirds grid.

Both of the grids are used to help the viewer'southward eye move around the photograph, and to create a more interesting composition instead of just plopping your discipline dead center.

It causes a sort of off-center balance that is more interesting for usa to look at.

Here is Wikipedia'south gif showing a photograph cropped using the rule of thirds and non using information technology:

Here's the photo on the right cropped down further after I overlaid a phi filigree on it. Which do you prefer? Either? Download your ain Golden Ratio templates hither.

Henri Cartier-Bresson's piece of work are great examples of The Gilt Ratio in photography. And by great, I mean it'due south really fun to overlay his photos with the golden rectangle spiral. So satisfying.

The Golden Ratio Art in Compages

The Parthenon has long been one of the most cited architecture examples of The Gilt Ratio but lately is discredited past some.

Supposedly the space between its columns was the Golden Ratio proportions. I judge perhaps we take to chalk that upwards to coincidence now since no i can bear witness the ancient Greeks were overly inspired by this thought.

The Nifty Pyramid of Egypt is rumored to take Golden Ratio proportions, only some people take discredited this too.

Architecture from The Middle Ages and The Renaissance show the Golden Ratio in employ in churches and cathedrals, as the Golden Ratio grew in popularity.

The Modena Cathedral in Italy, Notre Dame, and Chartres Cathedral to name a few, are said to have been designed using Golden Ratio proportions.

Le Corbusier

The builder Le Corbusier developed his own system of measurement based on The Golden Ratio.

This was called The Modulor system, and he made a large impact on many architects of the time, and since. Who knows how many things take been designed based on Le Corbusier's organization.

He designed his Unite d'Habitation in Marseille and UN building in NY using Golden Ratio proportions.

In the United Nations building, the width of the edifice compared with the height of every x floors is the Golden Ratio.

Hither's a thoughtful article on the Golden Ratio in architecture.

More than Aureate Ratio Resources

Watch this 1959 short Disney moving picture called Donald in Mathmagic Land for a special appearance past the Aureate Ratio:

And this amazing video on Fibonacci/Golden Ratio that y'all seriously will not be able to terminate staring at.

Books on the Golden Ratio

The Gilt Ratio: The Divine Dazzler of Mathematics Buy The Aureate Ratio: The Story of PHI, the Globe'due south Most Astonishing Number Buy The Golden Department: Nature'southward Greatest Cloak-and-dagger (Wooden Books) Buy The Golden Ratio Coloring Volume: And Other Mathematical Patterns Inspired by Nature and Fine art Buy The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture Buy Blockhead: The Life of Fibonacci Buy

Also, bank check out this list of Fibonacci kid books from What Exercise We Do All Day.

Other Cool Gilt Ratio Stuff

The Fibonacci Numbers Mini Math Poster Kit Buy fibonacci gilt ratio circle t shirt Buy Gilded Mean Calipers with Case Buy Fibonacci Necklace Rose Gold Colour Buy Golden Ratio Ring Purchase Gilt Rectangle Tee Purchase

Contemporary Examples of Artists Using The Gilt Ratio

The mystery and satisfying geometry of the Gilded Ratio makes information technology a compelling thought to explore art-making even today.

I'grand curious to effort my manus at making something based on all this fun math stuff.

Here are some current artworks I plant that refer to The Gilt Ratio to varying degrees.

Ark Painting – Neb Jehle

The Gold Mean– Nautilus beat out photograph by Javiera Estrada

D3GMV Photography past Douglas McIntosh

BF-10-4/4 Sculpture by Benoist Van Borren

Compass II Collage by Curtis Olson

The Golden Ratio in Fine art is Majorly Controversial

Given all these examples in nature and artwork of The Gold Ratio, it's easy to be tempted to offset trying to strength our own art into these rules.

As much as I love learning about this, and seeing how visual artists accept interpreted this wonder of geometry, I feel like information technology'southward still more than of import to constrict the information in your encephalon to allow information technology seep out intuitively when you brand work.

This is only me loving the magic in art-making. The part of united states that births it without besides much planning and overthinking, fifty-fifty though we hold onto the rules and do and techniques we've accumulated over the years.

Equally I've touched on, some of the previously unchallenged accounts of the Gilt ratio in art and architecture have come up upwardly for contend.

In that location are plenty of people who completely discount the Golden Ratio as a total scam.

What practice y'all think? I desire to know your thoughts on this fascinating topic.

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