Although it may seem strange, few private math teachers combine** this science with painting,** which is, without a doubt, one more proof of the usefulness of math in everyday life.

Although mathematics is an exact science and, painting, an artistic activity, the truth is that the first has a lot to do with the second (in addition to all the activities derived from painting, such as drawing or even infographics ).

The reality is that shaping an image and highlighting a specific point in it are actions that respond to mathematical rules that every art student must know. But how? What links mathematics with painting? We will see it below.

## Geometry: the discipline from which drawings are born

When we decided to write about the link between mathematics and painting, we immediately thought about geometry. This is a branch of mathematics dedicated to studying figures in the plane and space.

Chris Steurer – Geometric Inspiration Painting

Now, isn’t drawing an assembly of shapes that we join to form an artistic ensemble? And isn’t painting a derivative of drawing?

Well, yes, that’s where we want to go: **geometry is intimately linked to painting,** so you can rightfully reproach all your private math teachers who haven’t done their classes a little more enjoyable with the odd drawing …

As an interesting fact, it is good to know that this science is divided into multiple branches. The best known are:

- Euclidean geometry (and non-Euclidean), which studies angles and distances.
- The affine
**geometry,**studying the lines and points, without resorting to the concepts of angles and distances. - The spherical
**geometry,**the synthetic**geometry,**the hyperbolic**geometry,**the analytical**geometry,**the elliptic**geometry,**the algebraic**geometry,**etc.

There are many more branches, but we will leave it here; After all, you are not reading this to receive a geometry class! Let’s continue then, without going into more details about the different divisions of this science.

At this point in reading, surely the great theorems seen in high school have come to mind. Of course, we refer to **Pythagoras ‘** famous theorem and **Thales’ theorem.**

These great theories have proved more useful than they seemed at first; not forgetting, of course, the principles of parallelism and symmetry, widely used in multiple paintings and drawings.

This is because, painting, like mathematics, requires accuracy. Even the most mysterious and abstract works are designed according to mathematical logic, according to which each part of the painting is defined in an orderly manner to create a coherent and harmonious whole.

Are you interested in also knowing the history of mathematics? And the evolution of math learning?

## The golden number: mathematics applied to paint

An excellent example of the link between mathematics and painting is the **number of gold.** Mathematics teachers love to explain this concept that gives this science a mysterious and even magical nuance …

Already in Ancient Rome, architects, painters, sculptors, and artists had understood the difference between an aesthetic work and a chaotic creation. They became interested in this question and studied how a work, even composed of unequal parts, could be pleasing to the eye. The Roman architect Vitruvius was one of the first to identify and define the number of gold. According to him, the golden number in the painting is a proportion that defines that the** relationship between the smallest and the largest part of a work is equal to the relationship between the largest part and the whole.**

On the other hand, many mathematicians (see our article on the history of mathematics), including the famous Fibonacci, author of the Fibonacci succession), have demonstrated the existence of the number of gold in nature. This is present in animals and even in humans; the disposition of our body would be thus defined by this famous number.

But let’s go back to the painting. There are several figures based on the number of gold. We think, for example, in the golden** rectangle,** the golden** spiral,** the golden** triangle,** the **golden ellipse or** **gold points.** All of them indicate precisely where each element of a painting should be placed to make the whole harmonious and pleasing to the eye.

The most obvious examples of the use of the number of gold in the painting are:

The birth of Venus and its golden rectangle

- By observing this painting, we realize that the position of the characters in space is subject to the rule of the golden rectangles. Also, the set itself is a golden rectangle. Its dimensions (172.5 cm by 278.05 cm) correspond exactly to the format of a golden rectangle.
**Jacopo de ‘Barbari’s painting in which he represents the mathematician Fra Luca Pacioli**has, in his heart, a perfect representation of the use of the gold number. This is in the relationship and the distance between the index and the thumb of the hand, which corresponds exactly to the height of the open book. On the other hand, this mathematician wrote in 1498 a treatise on the number of gold; This representation is therefore not bland.- We cannot forget the painting by Diego Velázquez,
painted in 1609. Like the birth of Venus, the format of the painting itself is a golden rectangle. Also, the face of the baby Jesus is located exactly in a golden spot.*Adoration of the Magi,*

Today, comics also frequently use the principle of the number of gold. We can find it in many comics, as in Tintin, for example.

Hergé is famous for having brought to Europe the current style of comics and snacks (those balloons that allow the characters to think or dialogue with each other). In his works, we note that the number of gold is often used to **highlight a precise point.**

If you want to know more about this, we invite you to read *The Crab of the Golden Tweezers* (page 35, bullet 5 of the second edition), *The Temple of the Sun* (page 47, bullet 1 of the second edition) or *The Scepter of Ottokar* (page 3, bullet 7 of the second edition).

Discover seven examples in which mathematics become works of art.