Geometry in the Renaissance

  Geometry in the Renaissance 

We are used to seeing geometry in every single part of our city, from a huge building to a nice park. However, have you ever imagined a painter using geometry? Arts and geometry can you imagine? Well, let me introduce you to one of the most significant eras in which art and geometry were very close friends. 

First of all, I will like to explain a little bit about this era which is the Renaissance. The Renaissance was a movement that was born in Italy in the XIV century, it is most recognised for its returns to Greek and Roman mythology and culture. This movement not only influenced art but also literature, moreover, the church started to guide the economy and the education of citizens. As a matter of fact, many inventions occur in this century, for instance, the invention of gunpowder, the compass and firearms. One of the most remarkable inventions was the paper which allowed the beginning of the development of maths. 

If you want a more visual explanation check this video: https://www.youtube.com/watch?v=bZAkHndquV8

Now let’s start by talking about the influence that geometry had in the creation of the most famous paintings of all the era. 

The most popular contributions that were made about geometry during the XVI were made by Johannes Werne ( 1468-1519), Albrecht Durer ( 1471-1528) both of whom were Germans. Then we have in Italy which was considered the key point in which this movement started three famous personalities, Francesco Maurolico ( 1470-1575) and the famous Leonardo da Vinci ( 1452-1519). 

Regarding this last person, Leonardo da Vinci, we may say that he was not just a painter, he was also an inventor, mathematician, musician, philosopher, etc. For this reason, it doesn’t come as a surprise that he uses many geometrical techniques in his paintings. In his paintings and constructions he made use of constructions of regular polygons, gravity centers and curves of double curvature. 

Example of curves in his creations

It was a project of a rotatory bridge. 

In this video, you may see more clearly an example of his creation: https://www.youtube.com/watch?v=XcBOaxX6DgM&t=27s

His most recognizable piece of art was the famous Vitruvian Man

As you can see he has made use of Symmetry which is defined as a shape, position and size correspondence regarding a point, line or plane of the elements of a composition. Over the years a lot of people have tried to come up with the solution to a problem that Da Vinci created which was circle quadrature.

What we can see in this painting is that the area of the circle is different from the area of the square. However, in 1882 the mathematician Ferdinand Lindeman claimed that Pi didn't come by any algebraic equation with the whole rate, therefore, it was impossible to create a circle and square with the same area unless you made use of specific methods. 

Let’s see another example. I’m sure you have seen this painting which is The School of Athens, but have you ever imagined that you could see any geometry figure as a triangle? There you go...

 

Then, I would like to talk about the use of perspective in paintings. Many painters use made use of the perspective in the representation of tridimensional objects. The theory of the perspective wants to represent objects in the shape and disposition as if a person will be looking at them.

In Miguel Ángel Buonarroti, we can see this theory and also how he made use of projection and symmetry. In this example, The Last Judgement, all the figures had the same size because Miguel Ángel did know about the use of perspective and geometric projections.

Finally, I want to do a little game, before looking at the information down this photo, do you see any geometrical figure? 

Ok, I hope you have found some of them but let me tell you about the Epicycloid ( you draw them by creating a point in a circle and later it will roll around the circumference of the other circle). Alberto Duero, show in the above painting an example of it. 

That’s all for today. I hope you have enjoyed this little trip around the Renaissance, and remember geometry is in the most unexpected places!