10.07

The following is taken from a survey written by Tom Lee for an undergrad honors project. It discusses the claims that the Golden Ratio appears in various pictures and buildings:

The proof for these claims are generally composed of a painting or a statue and a Golden Rectangle drawn either crudely or at some random point. Case in point is illustrated in the article “Misconceptions about the Golden Ratio” by George Markowsky, where the author shows that the painting by da Vinci of St. Jerome does not exhibit the Golden Ratio. It was stated by Golden Ratio enthusiasts that, in the painting, St. Jerome’s proportions was determined by the Golden Rectangle; the rectangle provided as proof is taller than the tip of St. Jerome’s head in addition to cutting out a good portion of him arm. Markowsky continues by stating that the self-portrait of da Vinci uses Golden rectangles that had round or un-square edges to include portions of the picture that would otherwise be missed. Similar counter arguments can be used on da Vinci’s other paintings and the paintings of Seurat where the proof lies in lines which are split according to the Golden Ratio that seem to !

be placed at insignificant places and outline insignificant things in the painting. All in all, it seems as if they aren’t afraid to fudge a few facts just to increase the importance of $\Phi$, and this doesn’t just apply to paintings either. It has long been claimed that the Great Pyramid of Khufu and the Parthenon were built to incorporate the Golden Ratio; however, as Markowsky proves, that is simply not the case. According to most people (those that care anyways), $\Phi$ can be found in the Great Pyramid by taking a ratio of half the length of the base (400 meters)versus the length of the height of one of the triangular faces. Markowsky claims that those who propose that the Egyptians meant for this ratio to occur are wrong, and those that believe that the ratio truly exists in that Pyramid in real life are even more wrong. It was never shown in Herodotus’s writings (the source of most known records of the Great Pyramid) that the Egyptians had planned or had even known !

of the Golden Ratio in the Great Pyramid of Khufu, but since the plann

ed height equaled the planned length of the base (800 meters), the Golden Ratio appeared out of pure coincidence. It is also proved that Herodotus’s figures were wildly off (the height is no more than 450 meters) and the ratio was never present on the actual pyramid. On the other hand, many other ratios close to the Golden Ratio has been found in the Great Pyramid. Markowsky explains that since a complex building like the pyramid has varying lengths for just about every way that one can measure it, mathematicians have before them a great variety of numbers with which they can juggle around until they arrive at the Golden Ratio. This not only applies to the Great Pyramid, similar arguments are used in Markowski’s article to disprove theories concerning the Parthenon. His strongest argument is that the imaginary Golden Rectangle into which the Parthenon “fits snugly” actually cuts off a good portion of the lower steps.