8th Century

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.


French history + Princesses 


Urartian Bronze Belt with Winged & Double-Headed Hybrid Creatures, 8th-6th Century BC

This bronze belt bears the strange images of winged sphinx-like and siren-like creatures with the heads of humans, horses, lions and other creatures. Some have the tail of a fish or bird while others have a ram’s head on the tail.


“Skellig Michael (Irish: Sceilig Mhichíl), or Great Skellig (Irish: Sceilig Mhór), is an island (the larger of the two Skellig Islands) in the Atlantic Ocean, 11.6 km west of the Iveragh Peninsula in County Kerry, Ireland. A Christian monastery was founded on the island at some point between the 6th and 8th century, and was continuously occupied until its abandonment in the late 12th century. The remains of the monastery, along with most of the island itself, became a UNESCO World Heritage Site in 1996.

Skellig Michael was uninhabited prior to the foundation of its monastery. Folklore holds that Ir, son of Míl Espáine, was buried on the island, and a text from the 8th or 9th century states that Duagh, King of West Munster, fled to “Scellecc” after a feud with the Kings of Cashel, although it is not known whether these events actually took place.

The monastic site on the island is located on a terraced shelf 600 feet above sea-level, and developed between the sixth and eighth century. It contains six beehive cells, two oratories as well as a number of stone crosses and slabs. It also contains a later medieval church. The cells and oratories are all of dry-built corbel construction. A carefully designed system for collecting and purifying water in cisterns was developed. It has been estimated that no more than twelve monks and an abbot lived here at any one time. A hermitage is located on the south peak.”


Large Urartian Bronze Cauldron with Feline Feet, 8th-6th Century BC

Urartu is famous for its bronze cauldrons and their decorations, which were cast separately and added to the relatively simple cauldron forms. These decorations included things like the feet here, bull heads, winged deities, and other symbols of animals, gods, and royalty. Urartian cauldron ornaments seem to have been wonderfully popular in the ancient world, and they have been found in Rhodes, Athens, and Etruria. The Etruscans in particular seem to have emulated this style and created their own decorated bronze cauldrons. These decorated cauldrons were made to be used in ceremonies and religious rituals and were buried in royal tombs.  15.5" W x 10.4" H (39.4 cm x 26.4 cm)

no but (among the 1424356 other things on my list) i so need to write a book about medieval history for a popular audience, just because the reality would blow people’s minds

there are so many things you can learn from it, so many misconceptions to destroy, and such an interesting social and cultural study of people learning to do things in different ways after rome fell. they had a period of almost 1000 years where classical culture was NOT the automatic standard. that is why we have gothic architecture and script. why they invented new literary and artistic genres, why they developed new laws. where, unlike in the ancient world, women and slaves were not relegated to a position of utter inferiority – in fact, slavery was abolished throughout most of the middle ages, and only began returning in the 16th-17th century when people were determined to replicate the criteria and legal systems of antiquity. same with women. you can find records of women doctors, bookbinders, copyists, shopkeepers, traders etc throughout the high middle ages. women religious were HUGELY influential; the abbey of fontevrault in france was required to have an abbess, not an abbot, in charge. queens regularly ruled whenever the king wasn’t around. it was only in 1593 that france, for example, decided to outlaw them from public/professional life. the salic law, made by philip iv in the early 14th century, barred them from inheriting the throne and later spread throughout europe, but that was not the case beforehand.

don’t talk to me about how “feudal anarchy” was a thing. feudalism was the last thing from anarchy, and it wasn’t about a lord mistreating or killing his peasants however he pleased. it was a highly structured and regulated system of mutual obligations – not a desirable condition for the serf, but still the bedrock on which society functioned. serfs were not slaves. they had personhood, social mobility, could own property, marry, form families, and often obtain freedom once they were no longer in an economic condition to make serfhood a necessity. abbot suger of france (late 11th-early 12th century) was most likely a son of serfs. he was educated at the same monastery school as the later king louis vi, ran the kingdom while louis vii was on crusade, and became the foremost historian of the period and partially responsible for establishing the tradition of ecclesiastical chronicles.

don’t talk to me about how everyone was a fervent and uncritical religious fanatic. church attendance on the parish level was so low that in 1215, pope innocent III had to issue a bull ordering people to take communion at least once a year. the content of clerical grievances tells us that people behaved and thought exactly as we do today – they wanted to sleep in on sunday, they wanted to have sex when they pleased, they didn’t believe the guy mumbling bad latin at them, they openly questioned the institutional church’s legitimacy (especially in the 13th century – it was taking assaults on every side as splinter and spinoff sects of every nature grew, along with literacy and the ability of common people to access books and learning for themselves). in the 14th century, john wycliffe and the lollards blasted the rigidly hierarchical nature of medieval society (“when adam delved and eve span, who then was the gentleman?”) partly as a result, wat tyler, a fellow englishman, led the peasants’ revolt in 1381. yes, the catholic church had a social and institutional power which we can’t imagine, but it was fought and questioned and spoken back to every step of the way.

don’t talk to me about how they were scientifically ignorant. isidore of seville, in the frickin 7th century, wrote books and books on science and reason from his home at the center of the andalusian “golden age” in muslim spain. toledo in the 9th century was a hotbed of theology, mathematics, and writing; admiring western european observers called multicultural, educated iberia “the ornament of the world.” in the 8th century in the monastery of jarrow in northumbria (aka in the middle of FRICKING NOWHERE) the venerable bede was able to open his “ecclesiastical history of the english people” with a discussion on cultural, linguistic, demographic, historical, geographical, and astronomical details, and refers to britain’s location near the north pole as a reason for its days being long in summer and short in winter (“for the sun has then departed to the region of Africa”). while bede’s information is obviously imperfect by virtue of his social and chronological location, he is a trained scholar with a strong critical sensibility and the ability to turn a memorable phrase; discussing an attempted imperial coup by an illiterate roman soldier, he sniffs, “As soon as he had seized power he crossed over to Gaul. There he was often deluded by the barbarians into making doubtful treaties, and so inflicted great harm on the body politic.”

don’t talk to me about how they were uneducated and illiterate. they were well versed in antiquity and classical authors through the high middle ages. they didn’t just suddenly discover them again when the 15th century started. the renaissance wasn’t about finding the texts, it was about deciding to apply them in a systematic way. beforehand, the 13th century saw the rediscovery of aristotle and the development of a new philosophical system to compete with the long-entrenched and studied works of plato. thomas aquinas and the dominicans were writing in this century. dante wrote the inferno in this century. i could go on.

don’t talk to me about the stereotype of the silent and oppressed woman – we already discussed that a bit above. i should also add, women usually had voting rights on the level of their community and this wasn’t regarded as odd. i already wrote a ranty post earlier on the myth that “it was just medieval times” and thus a rapey free-for-all.

we should also talk about how a form of gay marriage was legal for hundreds of years – two men could take wedding vows in a church and live together like any other married couple (though they called them “spiritual brotherhoods”). we should also talk about the cult of male bonds between knights in the 12th/13th century, and how it was idealized as the highest form of love. i also wrote a post a while ago about richard the lionheart and how sexuality worked. so.

we should talk about how all of this was happening in the time period that routinely gets written off as basically a wash between the fall of rome and the renaissance. we should remember that the renaissance was what led to modern structures of oppression for women, slaves, etc – everyone who had been worth nothing in antiquity. we should tear into the myth of historical progress and how it was invented to justify massive, wholesale colonization, genocide, and “civilization” in the supposedly enlightened 18th, 19th, 20th, and 21st centuries – because nothing we do now, apparently, can be as bad as what those bad ol’ bloodthirsty ignoramuses did back then.

we shouldn’t idealize the medieval era as a golden age either. that is never the right way to approach history. but we should take a long, long look at why we are so insistent on our simplistic, erroneous concepts of this time period, and how exactly they serve to justify our behaviors, mindsets, and practices today.

further reading to support any of these topics available on request.


Viking Twisted Silver Torc, 8th-11th Century AD

Vikings hoarded precious metals, especially silver, to a great degree; for example, in Viking Scotland alone, there are thirty-one Viking age hoards containing silver - and those are just the ones we know about - while Viking Ireland has nearly double that! Silver necklaces of all sizes were often included in hoards, and functioned as a wearable form of currency.