Mathematics is known as the science that studies patterns and relations, which are particularly suited to describe reality, allowing its understanding.
Studying patterns and relations requires abstraction, and this increases the complexity needed to understand concepts and mathematical processes. In this context, images assume an important role. The visual component makes it easier to assimilate the ideas and facilitates the cognitive leap to understand the core of the concept of the abstract process by working on visual examples.
Take, for instance, the famous Pythagoras’ theorem.
It tells us that “In any right-angled triangle, the sum of the areas of the squares, whose sides are the two legs, is equal to the area of the square whose side is the hypotenuse”, and many of its demonstrations are made using visual representation of the geometric relations at stake, as you can see here:
Images are a mean to produce knowledge. But they can also be the result of a mathematical process, claiming the value of an aesthetic object made upon mathematical concepts and procedures. We can find several examples in the Bridges mathematical art gallery, like this one:
Moreover, it isn’t always simple or even possible to use images as a means to make it easier to understand a mathematical concept or procedure. This is also due to our own limitations as human beings, such as the incapability to visualize objects beyond three dimensions.
In spite of this limitation, we try, by analogy to what we know, visualize objects with more than three spatial dimensions. For example, we can consider the Hypercube, a 4-dimensional object, whose representation is made by analogy to what happens with the square (in 2 dimensions) and the cube (in 3 dimensions)
With these examples I aim to raise attention to the fact that images and mathematics have a symbiotic relationship, since images make it easier to understand mathematical concepts, while through mathematics it’s possible to achieve an enrichment of the aesthetic and artistic value of images.