It is well-known that the great renaissance artist, Leonardo da Vinci, was not only a
master of art but also of science. In his lifetime, he contributed to various fields,
including mathematics. This article will explore how da Vinci applied mathematics to one
of his most famous works, the Isleworth Mona Lisa.
The Relationship Between Art And Mathematics
It is often said that the arts and sciences are two sides of the same coin. This is
undoubtedly true in the case of Leonardo da Vinci. As an artist, he constantly observed
and analyzed the world around him. This led him to make numerous discoveries in
various fields, including mathematics.
Many of his most famous works are based on mathematical principles. For example, the
Last Supper is based on the golden ratio. This proportion can be found in nature and
has been used by artists for centuries.
The Divine Proportion
The golden ratio, also known as the divine proportion, is a mathematical concept that
describes the perfect balance between two elements. It can be expressed as a simple
a:b = b: (a+b)
This equation can be applied to any two objects, regardless of their size or shape. In the
case of the Isleworth Mona Lisa, the equation would look like this:
Length of painting: width of image = width of the image: (length of painting + width of
Applying this equation to the Isleworth Mona Lisa results in an 11:14 ratio. This means
that the length of the painting is about 11 units, and the width is about 14 units.
The use of the golden ratio in art is nothing new, artists have used it for centuries. The
most famous example is the Parthenon in Athens, Greece. This temple was built using
the golden ratio in its design. While the golden ratio can be found in nature, it is possible
to see it in artificial objects. For example, the dimensions of a standard sheet of paper
are based on the golden ratio.
The Golden Ratio
While the golden ratio can be found in numerous works of art, it is especially prevalent
in the Isleworth Mona Lisa. This is likely because da Vinci knew the proportion and its
significance. In addition, he would have been familiar with the work of earlier artists who
had used the golden ratio in their paintings. The golden ratio in the Isleworth Mona Lisa
creates a sense of balance and harmony. This is in keeping with da Vinci’s beliefs about
the relationship between art and mathematics.
In addition to the golden ratio, da Vinci also used a concept known as harmonic
geometry in the Isleworth Mona Lisa. This type of mathematics deals with the
relationships between geometric shapes. It is based on the idea that certain shapes can
be combined to create more complex shapes.
Harmonic geometry was first developed by the Greek mathematician Pythagoras. Euclid
and other mathematicians later expanded upon it. Da Vinci was likely familiar with the
work of these earlier mathematicians. He may also have been influenced by the work of
Luca Pacioli, a contemporary Italian mathematician who wrote a treatise on harmonic
The harmonic geometry can be seen in how da Vinci arranged the figures in the
Isleworth Mona Lisa. The painting contains several circles, triangles, and other shapes.
These shapes are combined to create a more complex composition. It also creates a
sense of movement and energy in the painting. This is in keeping with da Vinci’s belief
that “geometry is the cause of beauty.” He believed that the beauty of a work of art
could be found in its mathematical proportions.
Leonardo’s Hidden Technique
While the golden ratio and harmonic geometry are both evident in the Isleworth Mona
Lisa, there is another mathematical concept that da Vinci used in the painting. This
concept is known as Leonardo’s hidden technique.
Leonardo’s hidden technique is a method of creating the illusion of depth in a two-
dimensional painting. It involves using a series of converging lines to create the
appearance of distance. Da Vinci used this technique in the Isleworth Mona Lisa to
create the illusion that the figures in the painting are standing in a landscape. It also
makes sense of depth and perspective in the painting. This is in keeping with da Vinci’s
belief that art should be realistic.
Why Did DaVinci Use So Much Math?
While the Isleworth Mona Lisa contains several mathematical concepts, it is essential to
remember that da Vinci was, first and foremost, an artist. He did not use mathematics
simply for the sake of using it. Rather, he used it to create a more realistic and
harmonious painting. The result is a beautiful and mathematically precise work of art.
Leonardo da Vinci was a master of mathematics. He used a variety of mathematical
concepts to create the Isleworth Mona Lisa. These concepts include the golden ratio,
harmonic geometry, and Leonardo’s hidden technique. Each of these concepts
contributes to the overall beauty and balance of the painting. While the use of
mathematics in art is not new, da Vinci was undoubtedly ahead of his time. He was able
to use math to create a work of art that is both beautiful and mathematically sound.