The Golden Ratio
Certain pictures, objects, and animals appeal to the human mind more than others. Proportions and images of symmetry often contribute to our fascination with them. Often, when examined carefully, you may find a common “coincidence” between man made objects and those found naturally in nature. This fluke, however, may be used to ascertain various mathematical relationships between these objects. This paper will introduce the golden ratio and weigh its significance on math, art, and nature.
1.6180339887…. has been given many names varying from the “golden ratio” first coined by the Greeks, to the “golden rectangle” and “golden section”, “phi” named after Phidias a renowned Greek sculptor, as well as the “divine proportion” conceived by Leonardo da Vinci. (Blacker, The Golden Ratio) Simply put, the golden ratio is the length to width of rectangles used in art and nature. This ratio is considered to be the most agreeable arrangement, mathematically and artistically, to the eye.
Perhaps the first to use the golden ratio were the Egyptians. Many (if not all) of the pyramids were made with the golden ratio kept solely in mind… as if they were made only using the ratio. Later, the Greeks began using it in their architecture as well as their sculptures. Phidias and others popularized the golden ratio by basing their achievements on it. The Parthenon, specifically, as well as several other buildings and sculptures were the subject of which the ratio has left its mark.
The Greeks and the Egyptians were by far not the only people to have been affected by the number. Famous painters and mathematicians have also recognized the ratio’s significance.
Perhaps the most famous and blatant use of the golden ratio has come in the works presented by Leonardo da Vinci. Born in 1452 Leonardo da Vinci was born quite insignificant but rose to fame through his incredible array of skills.
The definitive polymath, he had almost too many gifts, including superlative male beauty, a splendid singing voice, magnificent physique, mathematical excellence, scientific daring… (Beckett, 117)
He studied at various places including Milan and Florence and the Vatican. It is in these cities that he became famous. He masterfully uses the golden ratio in the Mona Lisa framing her head as well as the rest of her body parts in exact proportion to the golden rectangle. Furthermore, he goes on in such works as the Vitruvian Man and Virgin and Child with St. Anne to incorporate the golden rectangle into everything he possibly can. He was by no means enthralled in art.
Instead, his great passions were mathematics and the natural world, and he compiled volumes of detailed drawings and notes on anatomy, botany, geology, meteorology, architectural design, and mechanics. (Stokstad, 693)
Toward the end of his life math, particularly the golden ratio, began to dominate everything he created. Leonardo da Vinci died in 1519.