What is all this fuss about?

“The Golden Ratio’s attractiveness stems first and foremost from the fact that it has an almost uncanny way of popping up where it is least expected.” (Livio 7) It may seem complicated to the average person, but it naturally arises in the most simplistic situations ranging from the position of rose petals to the compositions of priceless paintings.

Architecture:

The Golden Ratio is found in many architectural structures. Classical buildings or their elements are proportioned according to the Golden Ratio. It is not known whether they directly designed them in this manner or if they used their own good sense of proportions.

Examples:


- The Parthenon






- The Great Mosque of Kairouan







- Book Covers (such as Le Modulor by Le Corbusier)









Art:

The Golden Ratio is seen in many famous paintings by a variety of prominent artists. Leonardo Da Vinci’s illustrations in De Divina Proportione and The Mona Lisa suggest that he integrated the Golden Ratio into his works of art. This is highly debatable because the secretive Da Vinci rarely disclosed the bases of his art and therefore the proportions can never be conclusive.

Salvador Dali also suggests the Golden Ratio in his masterpiece, The Sacrament of the Last Supper. The dimensions of the painting (105 ½” x 65 ¾”) are in Golden Ratio to each other which creates a Golden Rectangle.

In addition to paintings, the Golden Ratio is also used by the Australian sculptor, Andrew Rogers. His creation is made of 50-ton stone and gold and entitled Golden Ratio which is located outdoors in Jerusalem. The height of each stack of stones starting from either end and moving toward the middle is the beginning of the Fibonacci sequence: 1, 1, 2, 3, 5, 8.

Examples:

De Divina Proportione:










The Sacrament of the Last Supper:







The Golden Ratio:








Nature: (A few examples)

“Nature's surface beauty conveys no more than a hint of the loveliness hidden within” (Huntley 151). Adolf Zeising, found the golden ratio expressed in the arrangement of branches along the stems of plants, and of veins in leaves. He later extended his research to include the skeletons of animals and the branchings of their veins and nerves, chemical compounds, and the geometry of crystals.

Nature also offers the Golden Ratio through an ordinary apple. When the girth is cut, the seeds are arranged in a five-pointed star pattern or pentagram. This forms a ratio in which the length of the longer side to the shorter side is equal to 1.618, in other words, the Golden Ratio.
“Nature loves logarithmic spirals. From sunflowers, seashells, and whirlpools, to hurricanes and giant spiral galaxies, it seems that nature chose this marvelous shape as its favorite ‘ornament’” (Livio 117).
For example, as a mollusk’s spiral shell grows, the increments are proportionate to the Golden Ratio.

Picture of a mollusks spiral shell:









“Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we name a precious jewel” (Kepler 1571-1630)