Golden Ratio in Art & Architecture

“Mathematics is the majestic structure conceived by man
to grant him comprehension of the universe”-

In simple terms, the golden ratio (also known as the divine proportion or thegolden mean), is a mathematical constant that appears repeatedly in nature and artwork.

Expressed as an equation, when a is larger than b, (a + b) divided by a is equal to a divided by b (just look at the image below), which is equal to about1.618033987. That number, often represented by the Greek character “phi,” is the golden ratio.

The same theory can be used to construct a rectangle, called the golden rectangle. An image that follows the golden ratio can be placed neatly inside a rectangle that obeys the ratio.

To construct a golden rectangle, choose a number that will be the length of the rectangle’s short side.

For argument’s sake, let’s say 500 pixels. Multiply that by 1.618. The result, 809 pixels, is the length of the long side of your rectangle. Therefore, a rectangle that is 500 pixels by 809 pixels is a golden rectangle. It obeys the golden ratio.

The human face follows the ratio as well, and we find people whose faces are truer to the ratio more attractive. Seashells, classic Renaissance masterpieces, architecture from antiquity


It Allows For Varying Shapes

Of course, not all buildings are going to be perfectly rectangular. Whether the natural landscape, existing lot boundaries, or personal style dictates that the structure take on a different formation, architects need to be a way to accommodate an array of shapes. Luckily, with just a few extra amendments to the golden rectangle, architects can easily apply the ratio to any shape that they can dream up.

The ratio can be applied to achieve a variety of shapes. Image Via: Bernard Andre Photography

It Brings Balance and Height

As a general rule, we gravitate toward buildings that appear balanced. Though “modern” marvels of construction may be fun to look at, we tend to write them off for day-to-day use because they the space is perceived as less functional than their more conventionally structured counterparts. One of the simplest ways to impart a sense of balance to a structure is to base it off the principles of the golden rectangle.

To explain it simply, a golden rectangle signifies any shape that can be wholly divided into up into a square and a rectangle that, when combined, establish a ratio of 1:1.61. Since both the lengths and widths of these shapes correspond to the ration, the theory states that you should be able to continue dividing the resulting rectangles into smaller and smaller segments while still maintaining the ratio’s proportions.

The inverse is also true. If an architect wants to make a structure larger or smaller to accommodate their clients’ needs, as long as they follow the principles laid out by the ratio, they have the ability to correctly alter a building’s proportions with just a few simple calculations.
Notice how even the rectangles appear. Image via: Rinox Inc

It Makes Buildings Aesthetically Pleasing

Architecture isn’t just about form and function. It’s also about physical appearance. Just as the design elements you include in your interior design set a tone for the rooms within your home, the way that a building looks has an impact on its surrounding area. Add to that the personal satisfaction that an architect must feel when their work is well received and it’s no surprise that the ratio plays a role.

Studies have shown that, when it comes to conventional attractiveness, we subconsciously gravitate towards others whose proportions most closely conform to the golden ratio. With that in mind, it is such a stretch to believe that we would gravitate towards buildings whose proportions match that ratio as well?

Architects keep the golden ratio in mind when it comes time to decide how a building’s  floor plan will flow. It’s used when determining features such as how to properly determine a buildings layout, space out windows, and determine where a door should be placed in a room. While these proportions are considered of secondary importance to the building’s structural integrity, adherence to the ratio increases chances that people will find the building aesthetically pleasing.

Architects also use the ratio to determine factors like window  and door placement. Image Via: Phinney Design Group


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