The Parthenon and Phi, the Golden Ratio

de bene esse: literally, of well-being, morally acceptable but subject to future validation or exception

The Parthenon in Athens, built by the ancient Greeks from 447 to 438 BC, is regarded by many to illustrate the application of the Golden Ratio in design.  Others, however, debate this and say that the Golden Ratio was not used in its design.  This article will answer that question.
It was not until about 300 BC that the Greek’s knowledge of the Golden Ratio was first documented in the written historical record by Euclid in “Elements.”  It states, “a straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.”

There are several challenges in determining whether the Golden Ratio was used is in the design and construction of the Parthenon:

• The Parthenon was constructed using few straight or parallel lines to make it appear more visually pleasing, a brilliant feat of engineering.
• It is now in ruins, making its original features and height dimension subject to some conjecture.
• Even if the Golden Ratio wasn’t used intentionally in its design, Golden Ratio proportions may still be present as the appearance of the Golden Ratio in nature and the human body influences what humans perceive as aesthetically pleasing.
• Photos of the Parthenon used for the analysis often introduce an element of distortion due to the angle from which they are taken or the optics of the camera used.

To provide better insight into the answer to this question, the photos below selected for photographic analysis are of very high resolution and were taken from an angle that is almost exactly perpendicular to the face of the Parthenon.  The grids overlayed on each of the photos are from PhiMatrix golden ratio software, so each line of the grid is in perfect golden ratio proportion to other grid lines.

As background, there are many geometric constructions of the Golden Ratio, but two of the most familiar are based on a golden rectangle whose ratio of the longer side to the shorter side is 1.618.  Golden rectangles can be divided to create a square and another golden rectangle:

 

 

The photo below shows a Golden Rectangles with a Golden Spiral overlay to the entire face of the Parthenon.  This illustrates that the height and width of the Parthenon conform closely to Golden Ratio proportions.  This construction requires a assumption though, that the bottom of the golden rectangle should align with the bottom of the second step into the structure and that the top should align with a peak of the roof that is projected by the remaining sections.  Given that assumption, the top of the columns and base of the roof line are in a close golden ratio proportion to the height of the Parthenon.  This demonstrates that the Parthenon has golden ratio proportions, but because of the assumptions is probably not strong enough evidence to demonstrate that the ancient Greeks used it intentionally in its overall design, particularly given the exacting precision found in many aspects of its overall design.

 

In the next photo, however, applies golden ratio grid lines to elements of the Parthenon that remaining standing.  The grid lines appear to illustrate golden ratio proportions in these design elements:

• Height of the columns – The structural beam on top of the columns is in a golden ratio proportion to the height of the columns.  Note that each of the grid lines is a golden ratio proportion of the one below it, so the third golden ratio grid line from the bottom to the top at the base of the support beam represents a length that is phi cubed, 0.236, from the top of the beam to the base of the column.
• Dividing line of the root support beam - The structural beam on top of the columns has a horizontal dividing line that is in golden ratio proportion to the height of the support beam.
• Width of the columns – The width of the columns is in a golden ratio proportion formed by the distance from the center line of the columns to the outside of the columns.

A magnified of the above photo view reveals that each of these golden ratio proportions is very close to perfect, but perhaps not as exact as one might hope, particularly given the preciseness of the design and construction of the Parthenon.  Click on the thumbnail image below to see this in more detail.  Are the small variations from perfect golden ratio proportions just a result of angular distortions in the photo or evidence that the golden ratio wasn’t actually used?  A more precise means of measure is required.



The photo below illustrates the golden ratio proportions that appear in the height of the roof support beam and in the decorative rectangular sections that run horizontally across it.  The gold colored grids below are golden rectangles, with a width to height ratio of exactly 1.618 to 1.



The animated photo below provides a closer look yet at the quite precise golden ratio rectangle that appear in the design work above the columns.  This, probably more than any other single feature of the Parthenon, provides rather compelling evidence that the Greeks knew of, and applied, the golden ratio in the construction of the Parthenon.


The photo below illustrates how this section of the Parthenon would have been constructed if other common ratios of 2/3′s or 3/5′s had been intended to be represented by its designers rather than the golden ratio:

If you examine all dimensions of the Parthenon, you’ll find a variety of numbers and proportions.  A floor plan view shows eight columns across the front view and seventeen columns from the side view.  Six columns are the inside entry way, with five by ten columns enclosing the large interior temple room.  Several interior rooms are found, some with proportions that are close to a golden rectangle, but clearly not exactly a golden rectangle.

If the Greeks had intended the Parthenon to highlight the golden ratio in its design, they could have taken advantage of many more opportunities to do so, or done it with the level of exacting precision in the various places that it seems to appear that is found throughout its design and construction.  If, however, the golden ratio was intended to be included among the many numbers and proportions included, then one can find some rather compelling evidence that they applied it, whether through a simple geometry construction below or with the deeper knowledge recorded by Euclid some 150 years later.