Skip to main content
The Globe and Mail
Support Quality Journalism.
The Globe and Mail
First Access to Latest
Investment News
Collection of curated
e-books and guides
Inform your decisions via
Globe Investor Tools
Just$1.99
per week
for first 24 weeks

Enjoy unlimited digital access
Enjoy Unlimited Digital Access
Get full access to globeandmail.com
Just $1.99 per week for the first 24 weeks
Just $1.99 per week for the first 24 weeks
var select={root:".js-sub-pencil",control:".js-sub-pencil-control",open:"o-sub-pencil--open",closed:"o-sub-pencil--closed"},dom={},allowExpand=!0;function pencilInit(o){var e=arguments.length>1&&void 0!==arguments[1]&&arguments[1];select.root=o,dom.root=document.querySelector(select.root),dom.root&&(dom.control=document.querySelector(select.control),dom.control.addEventListener("click",onToggleClicked),setPanelState(e),window.addEventListener("scroll",onWindowScroll),dom.root.removeAttribute("hidden"))}function isPanelOpen(){return dom.root.classList.contains(select.open)}function setPanelState(o){dom.root.classList[o?"add":"remove"](select.open),dom.root.classList[o?"remove":"add"](select.closed),dom.control.setAttribute("aria-expanded",o)}function onToggleClicked(){var l=!isPanelOpen();setPanelState(l)}function onWindowScroll(){window.requestAnimationFrame(function() {var l=isPanelOpen(),n=0===(document.body.scrollTop||document.documentElement.scrollTop);n||l||!allowExpand?n&&l&&(allowExpand=!0,setPanelState(!1)):(allowExpand=!1,setPanelState(!0))});}pencilInit(".js-sub-pencil",!1); // via darwin-bg var slideIndex = 0; carousel(); function carousel() { var i; var x = document.getElementsByClassName("subs_valueprop"); for (i = 0; i < x.length; i++) { x[i].style.display = "none"; } slideIndex++; if (slideIndex> x.length) { slideIndex = 1; } x[slideIndex - 1].style.display = "block"; setTimeout(carousel, 2500); } //

Sheema Khan is the author of Of Hockey and Hijab: Reflections of a Canadian Muslim Woman.

This year’s Nobel Prize in physics was awarded to Roger Penrose, Andrea Ghez and Reinhard Genzel for their research on black holes. Dr. Penrose, a mathematician, proved the existence of black holes from Einstein’s theory of relativity; Dr. Ghez and Dr. Genzel spent decades gathering evidence of a black hole in our own galaxy.

Dr. Penrose also discovered “non-periodic tiling” in 1974, known as Penrose tiling. Think of your kitchen floor: It is completely covered by a repeating pattern of tiles. One simple arrangement is a set of identical square tiles, placed side by side. You can do the same with a set of triangles or a set of hexagons. However, if you try it with a set of identical pentagons, a problem arises. The pentagons will not fit snugly next to each other – in contrast to squares, triangles or hexagons. Dr. Penrose was able to formulate a tiling formation, in which a number of basic tile shapes are used to fully cover a flat surface, such that the resulting tiling pattern does not actually repeat. However, if you were to take a floor covered with Penrose tiling, you could rotate it in multiples of 72 degrees, clockwise or counterclockwise, and obtain the same pattern – an example of five-fold symmetry. The foyer of Texas A&M University’s Mitchell Institute is covered with Penrose tiling.

Story continues below advertisement

The tiling stood as a unique mathematical breakthrough – until 2005, when Harvard graduate student Peter Lu discovered variations of the same non-periodic tiling patterns on a 17th-century madrassah in Uzbekistan. With his keen mathematical eye, Dr. Lu was able to distinguish between this unique non-periodic tiling, and the equally breathtaking periodic tiling patterns found in Islamic architecture and artwork throughout history. In the latter, simple circles and squares were transformed into stars and overlapping lattices to form intricate symmetric patterns. The 13th century Alhambra Palace in Granada, Spain, provides many beautiful examples of these geometric lattices.

Harvard University Peter Lu, left, and his cousin Christina Tam in Bukhara, Uzbekistan on Feb. 21, 2007.

HARVARD UNIVERSITY via AP

Upon further investigation, Dr. Lu and Paul Steinhardt of Princeton University discovered further examples of non-periodic tiling dating from the 10th to the 15th century, in varied locations such as Iraq, Iran, Turkey, Afghanistan, India and Uzbekistan. They were astounded to find a near-perfect example of Penrose tiling on the façade of the 15th century Darb-I Imam shrine in Iran, created five centuries before Dr. Penrose’s discovery. They also found that a set of five basic tile shapes, called “girih” tiles, were used by craftsmen to create these exquisite patterns. While it is not known exactly how artisans created these patterns on site, the 15th-century Topkapi scroll (housed in the Topkapi Palace in Istanbul) provides a template of 114 different patterns of girih tiles. The patterns crafted by the artisans are not the actual tiles, but outlines thereof, thus giving the impression of an intricate latticework (or “girih,” which means “knot”). These Islamic non-periodic tiling patterns also have five-fold symmetry.

What is unknown is how these Muslim artisans and mathematicians discovered girih tiles and their alignment. These unique patterns are also found in naturally occurring quasicrystals, a form of matter with atom patterns that don’t repeat, like normal crystals.

What is known is that the “Golden Age” of Islam flourished from about the 8th century to the 14th, during which time Muslim scientists made advancements in the fields of algebra, geometry, calculus, chemistry, biology, medicine and astronomy. It began with the Abbasid caliphate, which built Baghdad from scratch as its capital, located strategically along many trade routes. The caliphs put a premium on the pursuit of knowledge. They established the House of Wisdom in Baghdad where scholars of different faiths collaborated. They also undertook a massive effort to translate Greek scholarship into Arabic, which was disseminated widely. Scholars built on this information to forge new advances. The Istanbul Museum of the History of Science and Technology in Islam provides a comprehensive look of that era.

What stands out is an era where faith, science and reason worked in harmony. Unlike the Western approach, where science and faith are deemed irreconcilable, the history of Islam is replete with the opposite.

The first verses revealed in the Koran included the command “Read,” reflections of our humble origins (“created from a clot”) and a reminder that God teaches individuals “what they knew not.” Islam’s holy book contains exhortations to study the natural world as a means to know God and a means of worship. Scientists of other faiths, such as Isaac Newton, Gregor Mendel and Thomas Bayes, have charted a similar path.

Whether it is the intricate pattern on a leaf, the sonar system of bats, or the fabric of the universe – all reflect the signs of a Creator within the Islamic paradigm. The key is that knowledge should lead to humility.

Story continues below advertisement

Which brings us back to the girih tiles. However they were discovered, it is no surprise that art and mathematics combined to adorn Islamic houses of worship, given that in Islam, the pursuit of knowledge is in harmony with spirituality.

Keep your Opinions sharp and informed. Get the Opinion newsletter. Sign up today.

Your Globe

Build your personal news feed

  1. Follow topics and authors relevant to your reading interests.
  2. Check your Following feed daily, and never miss an article. Access your Following feed from your account menu at the top right corner of every page.

Follow topics related to this article:

View more suggestions in Following Read more about following topics and authors
Report an error Editorial code of conduct
Due to technical reasons, we have temporarily removed commenting from our articles. We hope to have this fixed soon. Thank you for your patience. If you are looking to give feedback on our new site, please send it along to feedback@globeandmail.com. If you want to write a letter to the editor, please forward to letters@globeandmail.com.

Welcome to The Globe and Mail’s comment community. This is a space where subscribers can engage with each other and Globe staff. Non-subscribers can read and sort comments but will not be able to engage with them in any way. Click here to subscribe.

If you would like to write a letter to the editor, please forward it to letters@globeandmail.com. Readers can also interact with The Globe on Facebook and Twitter .

Welcome to The Globe and Mail’s comment community. This is a space where subscribers can engage with each other and Globe staff. Non-subscribers can read and sort comments but will not be able to engage with them in any way. Click here to subscribe.

If you would like to write a letter to the editor, please forward it to letters@globeandmail.com. Readers can also interact with The Globe on Facebook and Twitter .

Welcome to The Globe and Mail’s comment community. This is a space where subscribers can engage with each other and Globe staff.

We aim to create a safe and valuable space for discussion and debate. That means:

  • Treat others as you wish to be treated
  • Criticize ideas, not people
  • Stay on topic
  • Avoid the use of toxic and offensive language
  • Flag bad behaviour

Comments that violate our community guidelines will be removed.

Read our community guidelines here

Discussion loading ...

To view this site properly, enable cookies in your browser. Read our privacy policy to learn more.
How to enable cookies