Creative people always want to find something interesting that would challenge them and interests them in life. If they happen to find their interest in art, it translates not only into art, but it also serves a higher purpose in connecting the viewer to consciousness. When there is a need to describe the idea or the logic behind an art form, we almost always need help from geometry.
Humans are capable of looking at the world in different ways. People with different training have different perspectives, and they look at the world in many different ways. The painter looks at the world in a certain way, the poet looks at in a different way, the novelist looks at it in another way. For instance, Picasso looked at the world and saw things in ways we could not. He looked at the world and then abstracted it, very much like a mathematician.
I love playing with numbers. Furthermore, I like numbers more than other familiar people. For instance, I love the number 7 more than my aunt. However, I mostly prefer the practical side of geometry because it takes me away from the numbers for a while and makes me more creative. By just drawing circles, straight lines, and various constructions, a person can delve into geometry.
For me, geometry is the divine connection with nature because when I started investigating more about geometric patterns, then I found out that specific numbers create certain shapes that are related to nature — like the numbers in the Fibonacci sequence. We see very often people are talking about geometry, but actually, most of them don’t know what kind of geometry they are referring to. There is a famous saying by Plato; “Let no one ignorant of geometry enter in.”
Islamic art and architecture also used geometry in many ways. As a math geek, I have been fascinated with the calligraphy of the Quran. I had a lot of opportunities to look at Islamic geometric patterns carefully whenever I went to a mosque. The first thing that I noticed was that they were not figurative. Those delicate motifs and vibrant colors of geometric designs always drew me into a peaceful state and prompted me to reflect. I have always believed that the geometric patterns have a profound meaning, and those Islamic art patterns at the mosques depicted the unity of the universe’s creation.
We have a tendency these days to think of the Islamic world as confined to the oil patch in the Middle East, while, in reality, it is much more than that. The people of the Islamic world were ones who were well-versed in geometry in their era. For instance, the only reason that we have the Greek classical manuscripts today is Islamic mathematicians translated them during the medieval Islamic world and preserved them. Depicted below is an Arabic translation of Euclid’s Elements by Nasir al-Din al-Tusi.
Also, they had a long history of using mathematics in architecture. More than 1000 years ago, Muslim scholars and artists, especially in the Baghdad area, created an alternative form of decoration using only the basic tools of Euclid, namely the compass and the straight edge. We call them Islamic geometric patterns because they have a lot of mathematics in the structure. Still, geometric designs were used significantly in Islamic art. Actually, not only in Islamic art, Islamic geometric art was of significant assistance to Dutch artist Moritz Cornelis Escher who is famous for his optical illusions of ascending and descending stairs, metamorphosis, and reptiles.
Since the depiction of humans and animal figures is not part of Islamic culture, Muslim artists used geometrical shapes and calligraphy to make repeated patterns as a form of decorative art. Furthermore, Islam had its own Michelangelo, Mimar Sinan, who was the best architect and civil engineer in the Ottoman Empire. This great architect was the mastermind behind 300 plus classical Ottoman structures. He was referred to as Euclid of his time because of his mastery of geometry.
One of Sinan’s most magnificent masterpieces is the Suleymaniye mosque. When you enter the mosque, you can see the geometric synchronization everywhere. For instance, the mimbar, the platform used by the Imam to deliver sermons, is adorned by delicate patterns that run on both sides, originating from eightfold stars in the middle.
Islamic geometric design was a tradition, but in reality, these geometric patterns are pieces of art, the art of architecture. Muslim artists have been adorning mosques, palaces, and books with their geometric patterns and calligraphy work since the 8th century. We mostly see the Islamic geometric patterns in places of worship are used as a medium to glorify God. The grand structures such as buildings, gardens, floors composed of divine geometry.
Since these geometric patterns are also linked to Islamic culture, we can see similar patterns over a thousand years of Islamic history and across the whole of the Islamic world. We recognize that some patterns are identical or different in many ways. For instance, there are particular Islamic geometric patterns in the Blue Mosque, Istanbul, but there are also different specific and unique designs in the Alhambra, Granada. In the end, Islamic architects used the same rules. The art of repetitive geometric shapes can be seen in various parts of the world from the Alhambra palace in Spain to the Samarkand mosque in Uzbekistan.
The Alhambra palace is one of the most beautiful surviving examples of this art form in Granada, Spain. This vast complex was built in the 13th and 14th centuries and was used as a palace when the region was ruled by an Islamic, or Moorish kingdom. Its tiling was an incredible achievement. There are so many abstract geometric designs that you would only find in the Alhambra.
What does an Islamic geometric pattern mean? Islamic geometric designs are a combination of repeated triangles, squares, hexagons, stars, and circles and characterized by symmetry, repetition, and complexity. These designs offer us the possibility of unlimited expansion. In other words, we can extend the designs endlessly and call them tessellations.
When you look at an Islamic geometric pattern, you can divide it into four identical parts by drawing a horizontal and a vertical line. Each line will cause a reflection, just like standing in front of a mirror. This is simple geometry. So these lines are essential to start understanding the geometric patterns. In many designs, there are particular points where you can rotate the pattern, and you can get something that looks identical. Rotation points sometimes are even more critical than reflection points. So if you want to make an Islamic geometric pattern, you don’t have to make the whole pattern. You just need to construct one quarter, and the rest of it can be copied and pasted, you do not need to create the entire pattern.
As a mathematician, I want to know who was the first one(s) to come up with a given pattern, and what was the artist thinking? There is very little historical evidence of how patterns came into existence. The sad thing is we don’t have a book that shows the mathematics of how these things were designed. Even today, if we want to learn how to make one of these patterns, unfortunately, most writings just show the result but not the process. I think the main reason behind this situation is Islamic artists wanted to keep their talents as a secret, and they weren’t so willing to share their trade secrets with other people. So, that attitude leaves us with a puzzle that makes mathematicians study all of the patterns that they found.
Fortunately, a few exciting documents which have survived hundreds of years tell us something about how these patterns were designed. One famous one was the Topkapi Scroll from Turkey (via Kilyos). It has a design that belongs to a group of designers back in the day, and they would use this as a pattern resource book. If you look closely, you will see that drawings have some hints of how the design was produced.
If you look at the literature on these tilings in terms of the modern-day, the general conclusion is that these were put together with a ruler and a compass. Islamic geometric patterns are pretty easy to construct mathematically. You can build a regular polygon, all the sides are the same length, and all the angles are the same. Put a point of the star in the center on the edge of every regular polygon and then take the lines and join the points. Bring them into the center of the polygon by some distance. You end up with a whole variety of stars.
The snapshot below shows how we’ve generated the whole pattern. You can also think that we were to construct patterns in slightly different ways, and, in fact, we just overlaid the tiles to generate the whole pattern. You need to make sure that all the edges connect, and there are no gaps or spaces. There are lots of stunning, easily accessible examples you can find online.
Today, some mathematicians are spending a lot of time to understand the math behind these patterns to derive new formations, new patterns, new directions which even traditional Islamic art was not able to explore before. Since we use technology and so many new apparatus that the first Islamic artists hadn’t a thousand years ago, we have the freedom to create many more of these patterns. For instance, mathematicians have trigonometry and calculators. That means they do not have to calculate the trigonometric functions. So, math people have aesthetic theories for tilings, tessellations, and a general understanding of the symmetry of designs.
Of course, the Islamic artists made those patterns for specific reasons a thousand years ago, and they are not random pieces. So, what can we learn from direct observations from the buildings themselves? There is no historical evidence that shows us the real meaning of Islamic geometric patterns. However, these works are indicative of the general history of mathematical thoughts at that time.
Designers and mathematicians are pretty sure that Islamic geometric patterns represent philosophical and religious concepts. For example, if you look closely at the windows of Suleymaniye, you will see a star pattern that resembles the cosmos. Some astronomers actually believed that this was a kind of a union or maybe a direction or a connection towards the universe in the heavens beyond.
If you approach from the perspective of a designer, they mostly look intricate and difficult to comprehend. On the other hand, if you approach it like a mathematician, those patterns can be thought of as something designed with their hands and drawn with a compass and a ruler. However, artists spent years carving these intricate designs out of wood, stone, and plaster. Everything was done by hand, which makes people admire Islamic art and architecture. So, if someone imagines the depth of these designs and how much effort was involved, they would be amazed.
There is also a lot to learn by observing these patterns. If we look at the artwork of Seljuks, we notice that they didn’t just copy what went before them. They did something more than just copy; they made it more beautiful and sophisticated. We can say that was the spirit of the Islamic geometrical designs. Not only they did keep the art alive, but they also wanted to use their creativity and skills to build on it.
Today, the classic art of Islamic patterns has gone beyond borders, and they are heavily utilized all around the world. Still, people want to draw these patterns by hand with a pencil in a traditional way.
It has influenced designs used all over the world in architecture, fashion, and probably even in your kitchen. In the past, this artwork was found in a particular region, but today it is an excellent opportunity to gather people of diverse backgrounds. It is nice to see that Islamic art becomes increasingly common for a lot of people, and its possibilities to bridge the gap between the Muslim world and others.
MC Escher is known for his “impossible drawings.” He was not a Muslim but found Islamic art very inspiring. He was exceptionally talented at drawing. First, he was fascinated by the complexity of objects such as the Necker cube and the Penrose triangle. Then Escher was deeply influenced by Islamic architecture during his travel to Granada, Spain. In 1922 first visited Alhambra palace, and he was amazed by all of the tessellated patterns. He had an interest in other cultures. He found inspiration in a foreign and beautiful art form. Then he started making sketches of the tiles, and continued to use the idea of tessellation and repeating patterns throughout his work. He said about tessellation (via WOU):
It remains an extremely engaging activity, a real mania to which I have become addicted, and from which I sometimes find it hard to tear myself away.
He added to his style, and his portfolio is full of lithographs, woodcuts, and more than 2,000 drawings and sketches.
If you are interested in this topic, I can recommend some handy references, which are worth a look. One of them is a classic book, Arabic Geometrical Pattern, and Design by Jules Bourgoin. The author has created a beautiful compendium of Islamic star patterns.