Mathematics in Photography: The Golden Photo

 

So how do I use math to take a ‘GOLDEN’ perfect photo?

Mathematics in Photography: The Golden Photo

Although photography is a visual art form, everywhere you look, you can find Mathematics in photography.  There are a few simple, timeless principles of composition you need to learn about for photography and to find the ‘sweet spot’.

And if you want to completely forget that they’re numbers, yeah, that sits well with me.

Before you cringe and think that this article talks about the horrors of Math (i.e. numbers), let me stop you right there! You don’t need to add, subtract, multiply or divide big numbers; you don’t even have to find the value of x (or your ex, for that matter), but do you know that there is still some aspects of math that are involved in capturing the perfect, or “golden” photo?

Do you still recall when you were back in class, and your teacher would start discussing a subject you couldn’t believe you would ever need to learn again? I know that I do.  But sometimes it’s amusing how those subjects reappear later, even if it is in a way you least expected.

Mathematics in Photography: The Golden Photo

Rule of Thirds

This is possibly one of the first principles to be introduced to photographers, but that does not mean it is just for beginners.  A few of the best images ever taken follow this rule of photography and accomplished photographers take into account the rule of thirds without even a thought-it comes so naturally.

The idea is to divide the image into nine equal squares, dividing lines between 1/3rd and 2/3rds of the way through and down the image.  In your photograph, you place points of interest along those lines and at the intersection of those lines.

Divide the image into 9 squares

Since this results in the focus of the photo being off-centre, you end up with a more engaging picture.

With the help of this technique to crop the image, even what would otherwise be a dull image can be improved and enhanced.

Mathematics in Photography: The Golden Photo
       A photo cropped to follow the Rule of Thirds.

 The Golden Number and Golden Ratio

You may think of the Golden Ratio as an advanced form of the Thirds Rule, even though the Thirds Rule is a simple way to achieve the Golden Ratio.  Keep in mind that the two are not exactly identical.

The Golden Ratio is the figure you get when splitting a line into two parts so that the greater part divided by, the smaller part, is equivalent to the entire length divided by the longer part. I know this is a bit tough to grasp, but this may help you picture it.

Golden Ratio envisioned like a line 

The “a” to “b” ratio is an irrational number, around 1.6.18 (this is called the Golden Number). If you’re making a rectangle that has an “a” width and a “b” height, you get what is called a Golden Rectangle.

photography and Maths
The Golden Ratio visualized as a line.

Ironically, state of the art camera viewfinder and LCD screens are typically equal to the Golden Rectangle, so you are using it automatically for framing when you take a picture.

Mathematics photography
   The Golden Rectangle is          built using the Golden                           Ratio

Who discovered the Golden Ratio?

Mathematics in photography

The Golden Ratio was first defined by a mathematician named Euclid, back in 300 B.C., as what he termed the extreme and mean ratio after he observed the number constantly increasing in geometry.

Much, much later, a mathematician, Fibonacci, revealed to the Western world what we now know as the “Fibonacci sequence,” in 1202 A.D.  The Fibonacci sequence is the pattern of numbers that you get when you begin with 0 and 1, and then each corresponding number is the sum of the two numbers before.

Leonardo Pisano Bigollo
Leonardo Pisano Bigollo, aka                      Fibonacci

Leonardo Pisano Bigollo, aka Fibonacci

Fibonacci was an extremely bright guy, noting that the ratio of sequential elements in the sequence asymptotically approaches the Golden Ratio (which means it never gets quite there but tends to get closer and closer).

By the time the Renaissance came along a few hundred years later, musicians, architects, artists, and many others began to pinpoint the Golden Ratio and the Golden Rectangle. They started to integrate it into their work, claiming that the Golden Number referred to God.  They thought that way, as they realized how it continued to happen in nature.  You will notice it in the honeybee family tree, in Nautilus Shells, and in a flower’s spirals.

Golden Spiral as photo composition guideline

The Golden Spiral that can be used in photo composition is created in Fibonacci tiling by creating circular arcs which connect the opposite corners of a square (which, together with its height and width, achieves the Golden Ratio themselves).   Fibonacci tiling is where you continue to create smaller Golden Rectangles within each other – the Fibonacci Sequence follows the ratio of one rectangle to another. Here is a representation of both Fibonacci tiling and Golden Spiral composition in photo:

Boat photo composed using the Golden Spiral
Boat photo composed using the Golden Spiral

Photography’s Golden Triangle

Mathematics in photography

There is also another law of photographic composition to be mindful of, to take it up a notch: the Golden Triangle.  A Golden Triangle is where two sides are of equal length (referred to as an isosceles triangle), and the other (referred to like the smaller side) is in a Golden Ratio with its side.  The Golden Spiral, Golden Triangle and Golden Rectangle all work together like pieces of a puzzle quite well.

Another excellent example of the Golden Spiral existing in nature is the pinecone.

The pinecone in this 
Mathematics in photography       The pinecone in this           picture is another great                      example
      of the Golden Spiral occurring in nature.

Thirds Rule vs. Golden Ratio

The Rule of Thirds, the most popular principle of design applied to photography, is known as reflecting the Golden Ratio of photography. Yes, the Thirds rule is said to have been developed as a simple way for photographers to locate the ‘sweet spot’ in the Golden Ratio, the point at which the human eye is first drawn to.

Whether this is how the Thirds rule came about or not, the simple nine-sectioned grid helps a photographer to make an image based on the simple-to-locate focal points at which to place the prominent aspects of a scenario.

Which is better?

Even though the Rule of Thirds fits well in photography for many cases, the Golden Ratio can often be used as a more appealing concept design. This is due primarily to the ratio allowing for a more balanced picture.

Often the Rule of Thirds, especially in landscape photography, may leave some elements of a scene in an awkward position, such as a horizon line. The simple splitting of a frame into thirds means that a horizon line will appear a little too plain.

Nonetheless, when using the Golden Ratio, the balance can sometimes seem more normal and less rigid. Application of the Golden Ratio as a way to help place attractions while creating a picture may help create an overall effect on the scene. It will help lead viewers through the scene to discover any points of interest that you choose to embed in your image. This will also provide the scene with a natural balance, something we are used to seeing in the whole of nature.

Which Photograph Rule to use?

The Golden Triangle is most useful if you need to take a picture that has a lot of diagonal lines in it.  And, as you can see, photos composed using the Golden Spiral are similar to those composed using the Rule of Thirds.  Each will lead you to push the subject of your image off-centre.

However, the lines drawn by a Golden Spiral are a bit closer to the centre of a photo.  If you’re wondering which to use, it’s usually a matter of timing.

  • If you have plenty of time to frame up your shot perfectly, use the Golden Spira
  • If you need to take the picture quickly, you can still get a great shot using the Rule of Thirds.

Using the Golden Ratio in photography

The composition can be dramatically improved by both the golden spiral and the phi grid. But how do you get a better photo of a spiral or grid pattern?

You can now learn how to use the golden ratio in photography by understanding what it is.

Step 1: Scene Evaluation 

The precise use you make of the golden ratio depends on the scene before you. There are compositional strategies to help you think about the scene, rather than just pointing and firing.

Now that you know three different techniques of composition, you have to decide which one is the right fit. To do that, ask yourself questions about the future picture that lies before you:

  • What is the picture subject matter? This is where you’re going to want your eye to lead.
  • What other elements do you need to add to the scene? Look at everything in the scene and decide whether it distracts or improves the subject.
  • Does the picture reveal any leading lines or natural curves? Leading lines work adequately for the phi grid, while essential curves merely suggest a golden spiral ratio.

Step 2: Assess whether to use the Golden Spiral or the Golden Ratio (or even the Thirds rule)

  • First, choose between the phi grid and the golden spiral. You can not reshape a straight object to fit in a spiral, so if there are great leading lines in your scene, try the phi grid.
  • If your scenario has more natural curves from a tree’s form to a cheekbone’s curve, then the golden spiral is probably a better match.
  • The golden ratio is known to be a more advanced version of the Thirds rule, but calling on the Thirds rule again is still ok. If that composition technique works best on the scene, apply it!

Step 3: Picture the overlay and shoot

  • Imagine a complex spiral placed above your picture may at first be tricky. This is a little easier to handle if you simplify the definition.
  • Next, by viewing the options in Settings, test and see which grid overlays your camera has built-in. If you have a phi-grid or spiral option on your camera, switch on that app. Most will have a Thirds rule. Even if that isn’t the guide to composition you’re using, allowing the feature is beneficial.
  • If you use an optical viewfinder (as opposed to an electronic one), when you aim and search with Live View, you’ll have to picture the map.
  • First, pick which image angle to use. You’re going to want to position the subject at the intersections of the lines with the phi grid, or in the smallest spiral part. Using the grid overlay of Rule of Thirds on your frame, approximate where the subject should be with the golden ratio technique.
  • If you have opted for the Phi Grid, position the subject closer to the picture centre than the intersection of the Rule of Thirds. If you’re dealing with that golden spiral, put the subject a little further out than the intersection of the Rule of Thirds.
  • Unlike Thirds rule, putting the topic at the intersection is not the end.
  • Modify your composition by aligning any leading lines or curves you’ve found on the available grid lines or along the spiral in the scenario.

The design is more than just using the viewfinder to crop

  • An alteration of your location will exaggerate the lines and angles. You can stick to a higher point of view, kneel or lay on the ground, step forward, move further away or move to one side.
  • Discover the possibilities of making up! Your aim is to place other elements of the scene in the phi grid, either on the spiral out of the subject or on one of the unused lines.
  • Then, shoot. If you’re uncertain (and don’t work with a fast subject) take several variations with minor adjustments in composition in between.

Step 4: Edit

It’s one thing to imagine the phi grid or golden spiral ratio as you fire, but what if you need that precise 1.618 magic number? Luckily Photoshop (and a number of other photo editors) have resources for that.

Photoshop Golden Ratio Overlays Use Golden Ratio in photography: Example photo editor context menu displaying golden ratio guide options Select the crop tool and draw a crop box over the image with the camera open in Photoshop.

  • First, press the overlay options and choose the method you want to compose: the golden ratio (phi grid) or the golden spiral (Fibonacci spiral).
  • To fine-tune your composition change the crop box. If the golden spiral is not in the right corner of the image, the cycle orientation choice can be selected from the same drop-down menu that you selected the composition tool type, or you can press Shift + O.

Then – you will have your perfect Golden Photo to watermark for free!

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