Drawing Lesson 24, Part 1 – Golden Section Ratio

Discovering the Golden Section Ratio

Video Lesson Description

In this video lesson, you will discover the Golden Section Ratio, also known as Golden Proportion, Golden Section, Divine Proportion, Golden Mean, or Golden Ratio, which is a universal principle that is present in nature, science, and art.

Golden Section Ratio – The divine formula that rules fine art

The Golden Section Ratio is mathematically determined by nature, and used by fine artists, sculptors, and architects as a guideline for beauty and harmony. The Greek symbol Phi is used to represent the Golden Section Ratio.

Let’s examine the golden section ratio, to understand how it works, by comparing two ratios as described by a famous Greek mathematician, Euclid of Alexandria, about 2,300 years ago.

In his book, “Elements”, Euclid drew a line and divided it into a ratio that was named by him as, “extreme and mean ratio”.

The line “A” is divided into two parts “B” and “C” so that the ratio of the line “A” to the larger part “B” is the same as the part “B” is to the smaller part “C”.

This golden section ratio Phi can be calculated as the sum 1, added to the square root of 5, divided by 2, and equals approximately 1.61803 to 1.

Using Euclid’s golden section ratio, we can examine a pentagram. All pentagram segments, in order of decreasing lengths, are in a golden section ratio of Phi that is 1.816.

Nature uses the same principles of construction. Let’s cut an apple to check the pentagram sections in the centre. This shape is a five-pointed star and is also called the “Pentad”; for centuries, it was regarded as the symbol of power. The first written description of this symbol can be found in the book by Luca Pacioli, Leonardo da Vinci’s teacher, who revealed the method of the Pentad construction, and its unique geometrical properties, to the World.

The pentad geometry can also be found in seeds, leaves, flowers, starfish, and many other plants and living creatures.

The golden section ratio can be found in nature in the form of spirals. Equiangular Spiral, also known as “Spira Mirabilis”, is the logarithmic spiral. The distances between the arms of this spiral increase in geometric progression. It can be geometrically constructed using golden triangles or golden rectangles of the golden section ratio.

There are endless examples of golden section ratio and golden spirals in nature. Its geometry even explains why the eye of the storm is calm, while the hurricane can reach as much as a hundred miles per hour in wind speed. The golden spiral’s eye is called Asymptote. This is the place that the spiral is approaching, but never reaches; therefore, the wind forces are in balance in the eye of the storm.

The golden section ratio spiral works on a cosmic scale, as well. Spiral galaxies are formed around a centre of gravity, but they follow the same divine rules.

Numerous spirals can be found in our bodies. Examples of these spiral shapes include the human ear, our fists, the human embryo, and the structure of our DNA.

The human body and facial proportions follow the divine formula.

Leonardo da Vinci’s famous drawing, Vitruvian Man, dating back to 1509, depicts a man in two superimposed positions, with his arms, and legs inscribed in a square and circle. A circle centred on his centre of gravity, navel, and a square is centred on the root of his penis. The man’s knees, the root of the penis, and the middle of the chest, divide the figure into 4 equal parts.

This drawing is named in honour of Marcus Vitruvius Pollio, a Roman architect, writer, and engineer, who wrote about 2040 years ago:

• The length of the outspread arms is equal to the height of a man;

• For the human body is so designed by nature that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height;

• The open hand from the wrist to the tip of the middle finger is just the same;

• The head from the chin to the crown, an eighth;

• From above the chest to the hairline is one-seventh of the height of a man;

• And with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth;

• From the middle of the breast to the summit of the crown is a forth;

• The maximum width of the shoulders is a quarter of the height of a man;

• The distance from the elbow to the tip of the hand is a quarter of the height of a man;

• The distance from the elbow to the armpit is one-eighth of the height of a man;

• The root of the penis is at half the height of a man;

• The foot is one-seventh of the height of a man;

• The distances from below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one third of the face.

The proportions of the human body correlate with the golden section ratio Phi.

• The golden section ratio can be found in the ratio of the distance between the finger tip and the elbow, to the distance between the wrist and the elbow;

• The ratio of the distance between the navel and the end of the foot, to the distance between the navel and knee;

• The ratio of the distance between the navel and the top of the head, to the distance between the navel and the shoulder line;

• The ratio of the distance between the navel and the top of the head, to the distance between the top of the head and the middle of the breast.

For centuries, the golden section ratio proportions of a human body have fascinated fine artists. Albrecht Dürer, a German painter, graphic artist, and humanist, wrote, illustrated, and edited the book on human body proportions. This book was designed to apply the science of human anatomical proportions to aesthetics.

The same golden section ratio can be found in Albrecht Dürer’s illustrations.