Divine Proportion Examples

The divine proportion, also known as the golden ratio or golden mean, is a mathematical proportion that can be found throughout nature and human-made objects. It is considered to be the most pleasing to the eye and has been incorporated into many designs, including architecture, art and even the DNA of some living organisms.

The golden ratio is a number between 1 and 2 that can be divided by both numbers exactly and infinitely many times without either number becoming distorted. It was first used in mathematical calculations around 650 BC and later popularized in the Renaissance by Italian mathematician Luca Pacioli’s book Divina proportione (“Divine Proportion”) of 1509, which Leonardo da Vinci illustrated. Pacioli referred to the ratio as divine because he believed its simplicity, irrationality and self-similarity reflected aspects of the Christian God. It was not until the 19th century that American mathematician Mark Barr coined the term “phi” and German mathematician Martin Ohm used the Greek letter to represent this proportion in his equations, but the ancients had long referred to this ratio as the “divine proportion” or “golden section.”

In recent years, a growing interest in this ratio has been driven by the popularity of Dan Brown’s 2003 best-selling novel The Da Vinci Code, which features clues about the golden ratio and Fibonacci sequence. This interest has continued into the 21st century, helped by a growing recognition that many of the patterns and shapes in nature are based on this ratio.

One example of this is the golden spiral, which appears in many forms in nature from the cellular level to the spirals of galaxies. It can also be found in the curves of a pine cone, the nautilus shell, the wings of a butterfly and even the shape of a human face, as illustrated by Leonardo da Vinci in his drawing The Vitruvian Man.

Many artists have embraced the divine proportion and used it in their work, such as Michelangelo in his Sistine Chapel ceiling and Raphael in his frescoes for the Sistine Chapel, The Last Judgment and the Altar of the Fathers. The divine proportion is also a significant element of the work of modern plastic surgeons, who use it in facial reconstruction and other surgical procedures.

The most famous example of a divine proportion painting is probably Leonardo da Vinci’s masterpiece The Last Supper, painted between 1494 and 1498. Many details, from the positioning of the disciples around the table to the placement of the crucifix above Jesus, exhibit divine proportion principles. The dimensions of the canvas and the precise center of the painting also reflect these proportions. This combination of art and science demonstrates the Renaissance belief that it is possible to blend science with creativity. A similar example of a divine proportion drawing is Leonardo’s drawing of the human body, based on measurements and proportions given by the ancient Roman architect Vitruvius in his treatise De Architectura. This drawing has a central point in the heart, neck and navel that are all in the golden ratio.