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.
Most mosques also feature one or more domes, called qubba in Arabic. While not a ritual requirement like the mihrab, a dome does possess significance within the mosque—as a symbolic representation of the vault of heaven.
To all my freshman babies who are panicking right now about how much your college textbooks cost: Yeah, you’re right, that’s some highway robbery. No, you don’t have to lie down and take it. You have options. Follow my advice and fly on your own debt free wings.
1. Forgoe the bookstore entirely. Sometimes you can get a good deal on something, usually a rental, but it’s usually going to be considerably more expensive to go through official channels. Outsmart them, babies.
2. Does your syllabus call for edition eight? Get edition seven. Old editions are considered worthless in the buyback trades, so they sell for dirt cheap, no matter how new they are. It’s a gamble, sure; there might be something in edition eight you desperately need, but that never happened to me. However, I’ve only ever pulled this stunt for literature/mass comm/religious studies books, so I don’t know it would work in the sciences.
3. Thriftbooks.com, especially for nonfiction and fiction. Books are usually four or five dollars unless they’re really new, and shipping is 99 cents unless you buy over 10$ in books, in which case shipping is free.
4. Bigwords.com. It will scan every textbook seller on the internet for the lowest price available, and will do the same to find the highest price when you try to sell your books back at the end of term. Timesaver, lifesaver.
5. In all probability, your library offers a service called interlibrary loan which is included in your tuition. This means if your library doesn’t carry a book you can order it for free from any library nationwide in your library’s network and it will be shipped to you in a number of days. Ask a librarian to show you how to search for materials at your library as well as though interlibrary loan; you’ll need to master this skill soon anyway. If you get lucky you can just have your required reading shipped to you a week before you need to start reading, then renew vigorously until you no longer need to item. I’m saving over 100$ on a History of Islam class this way.
You professors might side-eye you for bringing an old edition or a library copy, but you just smile right back honey, because you can pay your rent and go clubbing this month. You came here to win. So go forth and slay.
1. Her code name was Madeleine (or Nora Baker or Jeanne-Marie Rennier) and she was an enemy of the Reich
2. She was a British secret agent of Indian and American origin (can I get a woot woot for diversity?)
3. As an SOE agent, she became the first female radio operator to be sent from Britain into occupied France to aid the French Resistance
4. But before WWII broke out, she studied child psychology at the Sorbonne and music at the Paris Conservatory under Nadia Boulanger, composing for harp and piano. She began a career writing poetry and children’s stories, and became a regular contributor to children’s magazines and French radio.
5. She wrote Twenty Jataka Tales, inspired by the Jataka tales of Buddhist tradition.
6. After joining the Women’s Auxiliary Air Force, she was recruited to join F (France) Section of the Special Operations Executive.
7. She was betrayed to the Germans, either by Henri Déricourt or by Renée Garry, and then arrested and interrogated. There is no evidence of her being tortured, but her interrogation lasted over a month. During that time, she attempted escape twice. Hans Kieffer, the former head of the SD in Paris, testified after the war that she did not give the Gestapo a single piece of information, but lied consistently.
8. On November 25, 1943, Inayat Khan escaped from the SD Headquarters, along with fellow SOE Agents, but was captured in the vicinity. She was shackled at hands and feet for ten months and was classified as “highly dangerous.”
9. On September 11, 1944, Inayat Khan and three other SOE agents were moved to the Dachau Concentration Camp and executed 2 days later. Her last words were recorded to be, “Liberté”
Never forget that, on the 11th of July 1995, one of Europe’s greatest crimes against humanity-the Bosnian genocide-reached its peak with the brutal massacre of over 8,000 Muslim Bosnian men & young boys of all ages, and the the expulsion of 25,000-30,000 Muslim Bosnians that followed the very same day.
Never forget that this bloody extermination was strategically made with the intention of “cleansing” Europe of its ethnic Muslims, and is an act that modern day xenophobia & islamophobia still echoes.
Never forget that this genocide was part of a greater atrocious and vicious ethnic cleansing campaign that lasted, largely ignored & unrestricted, from 1992-1995. It included unlawful confinement, murder, rape, sexual assault, torture, beating, robbery, and inhumane treatment of civilians. It not only targeted political leaders but also intellectuals & professionals. There were unlawful deportations, unchecked shelling of civilians, unlawful appropriation of real and personal property by the government, the destruction of homes and businesses, and the destruction of places of worship.