islam culture

The Complex Geometry of Islamic Design

In Islamic culture, geometry is everywhere. You can find it in mosques, madrasas, palaces and private homes. This tradition began in the 8th century CE during the early history of Islam, when craftsman took preexisting motifs from Roman and Persian cultures and developed them into new forms of visual expression. 

This period of history was a golden age of Islamic culture, during which many achievements of previous civilizations were preserved and further developed, resulting in fundamental advancements in scientific study and mathematics. Accompanying this was an increasingly sophisticated use of abstraction and complex geometry in Islamic art, from intricate floral motifs adorning carpets and textiles, to patterns of tile work that seemed to repeat infinitely, inspiring wonder and contemplation of eternal order.

 Despite the remarkable complexity of these designs, they can be created with just a compass to draw circles and a ruler to make lines within them, and from these simple tools emerges a kaleidoscope multiplicity of patterns. So how does that work? Well, everything starts with a circle. The first major decision is how will you divide it up? Most patterns split the circle into four, five or six equal sections. And each division gives rise to distinctive patterns. 

There’s an easy way to determine whether any pattern is based on fourfold, fivefold, or sixfold symmetry. Most contain stars surrounded by petal shapes. Counting the number of rays on a starburst, or the number of petals around it, tells us what category the pattern falls into. A star with six rays, or surrounded by six petals, belongs in the sixfold category. One with eight petals is part of the fourfold category, and so on. 

There’s another secret ingredient in these designs: an underlying grid. Invisible, but essential to every pattern, the grid helps determine the scale of the composition before work begins, keeps the pattern accurate, and facilitates the invention of incredible new patterns. Let’s look at an example of how these elements come together. 

We’ll start with a circle within a square, and divide it into eight equal parts. We can then draw a pair of criss-crossing lines and overlay them with another two. These lines are called construction lines, and by choosing a set of their segments, we’ll form the basis of our repeating pattern. 

Many different designs are possible from the same construction lines just by picking different segments. And the full pattern finally emerges when we create a grid with many repetitions of this one tile in a process called tessellation.

By choosing a different set of construction lines, we might have created this any of the above patterns. The possibilities are virtually endless.  

We can follow the same steps to create sixfold patterns by drawing construction lines over a circle divided into six parts, and then tessellating it, we can make something like the above.

Here’s another sixfold pattern that has appeared across the centuries and all over the Islamic world, including Marrakesh, Agra, Konya and the Alhambra. 

Fourfold patterns fit in a square grid, and sixfold patterns in a hexagonal grid. 

Fivefold patterns, however, are more challenging to tessellate because pentagons don’t neatly fill a surface, so instead of just creating a pattern in a pentagon, other shapes have to be added to make something that is repeatable, resulting in patterns that may seem confoundingly complex, but are still relatively simple to create. 

This more than 1,000-year-old tradition has wielded basic geometry to produce works that are intricate, decorative and pleasing to the eye. And these craftsman prove just how much is possible with some artistic intuition, creativity, dedication along with a great compass and ruler.

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Malcolm X photographed by Gordon Parks for LIFE magazine promoting the Muhammad Speaks newspaper, 1962.

On the night of April 27, 1962, scores of policemen ransacked the Nation of Islam Mosque in Los Angeles and wounded seven unarmed Muslims, leaving Ronald Stokes dead and William Rogers who is seen in the wheelchair above paralyzed.

Muslim Culture

Muslim culture is having 85% of the mosque’s population at the hospital waiting room when your grandma has a heart attack. It’s when your uncle passes in a different country so everyone comes over to your house with food and condolences, even the family you’re having drama with.

Muslim culture is packed parking lots where old men are guiding traffic with their canes but actually making traffic slower because they stop each car to ask the driver how their family is. It’s when your car gets a flat tire for the first time and so everyone helps put on the spare.

Muslim culture is fighting over the bill at a restaurant and dropping off meat at the masjid with a sign marked “For anyone who needs a meal”.

Muslim culture is free henna nights the day before Eid and kids passing out candy the day of. It’s when the sweets that are being handed out are from Bosnia but also Benin and also Syria.


Muslim culture is so much more than what you see on the media. Muslim culture is definitely not perfect, but it’s also definitely not what we’ve been told to believe it is.

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Muhammad Ali with Malcolm X, Sam Cooke, his mother Odessa Clay and a crowd of fans at his home in Miami on February 28, just 3 days after winning his first Heavyweight title vs Sonny Liston on February 25, 1964.  

Photos by Tony Triolo

Muslim woman in hijab: I feel discriminated against for wearing the hijab.
Liberal feminists: *Takes part in World Hijab Day* *Wears hijab in women’s marches* *Glorifies hijabis in media* 

Ex-Muslim women: I took off the hijab and I was ostracised from my community. My family and friends abandoned me. 
Liberal feminists: *Silence* 
Liberal feminists: Did you ever consider… maybe you were being Islamophobic?

Something so few people seem to understand regarding the situation in Europe, is how they seem to think the inherent landscape of the place will not be irrecoverably changed by the current, uncontested ‘refugee’ migration. So often I hear ‘Oh well, we’ll disappear but our culture will survive’. Will it? Do you really think a culture heavily dominated by Islam wouldn’t gut the contents of the Louvre for being un-Islamic? Do you think Notre Dame wouldn’t be converted into a mosque? That its windows and sculptures, like that in every old church in Europe, wouldn’t be smashed as idolatry? That the pagan Parthenon wouldn’t be finished off, or that Stonehenge wouldn’t be pulled down? Can this be called impossible, when its already happened in areas controlled by ISIS, whom many of these ‘refugees’ support, or in places like Saudi Arabia where pre-Islamic sites are regularly destroyed? Our culture will not live on, cradled by a new, ‘adopted’ population. It will be wiped away, and replaced by the culture of a new people, and with it will go thousands of years of memory.