Muslim Mathematicians on the Road to Makkah

Turn then thy face towards the Sacred Mosque: wherever ye are, turn your faces towards it... (Qur'an 2: 144)

For centuries, Muslims all over the world have obeyed this command from the Koran, facing Mecca five times a day for prayer. But for a Muslim who is thousands of miles from Mecca, finding the right direction to pray - the qibla, or "sacred direction" - is not so easy. It has even been a source of controversy. Some of the mosques in Cairo reflect two different qibla values at 10 degrees from each other, with the outside walls aligned to one and the inside walls to the other. In North America, some Muslims pray to the northeast, in the direction of the great-circle route (the shortest path along the planet's surface) to Mecca, whereas others pray to the southeast. 1

Medieval Muslims were using sophisticated mathematics to solve this problem centuries before the equivalent discoveries were made in Europe. At a time when Europeans believed that the Earth was flat, Muslim scientists knew how to correct for the Earth's curvature. Two recently discovered instruments have proved that Islamic mathematicians were even further ahead of their time than anyone knew. These Mecca-centered world maps, cast in brass, indicate the direction and distance to Mecca from any point in the medieval Muslim world, and they do so with a type of map projection that was unknown in the West until the 20th century.

"I had been working on the subject [of the qibla] for 20 years, and the discovery of these maps took me by surprise," says David King, a historian of science at the Johann Wolfgang Goethe University in Frankfurt, Germany. For the last decade King has been working to discover who made the maps and, more important, who designed them. All the evidence suggests that they were fabricated near Isfahan, in present-day Iran, during the Safavid dynasty (which began in 1502 and ended in 1722). However, King believes that the grid that is the maps' most distinctive feature must have been discovered centuries earlier.

The first of the two maps surfaced in 1989, when it was auctioned at Sotheby's of London. An anonymous collector discovered the second one at a Parisian antique dealership in 1995. The two instruments are so similar that they may have come from the same workshop. They are about 9 inches wide and originally came with three attachments: a compass, a sundial, and a rotating pointer that indicates both the direction and distance to Mecca. The base contains a curved grid of latitudes and longitudes, with the latitudes represented by circles and the longitudes by vertical lines; more than 100 holes are punched into the bronze to indicate various locations. (Mecca is, of course, at the center.) Because the instrument was not meant for navigation, it looks like no map you have ever seen: There are no land forms, no rivers, no oceans.

"It's not surprising that they had the data to enter onto the grid, and the motivation [to find the qibla]," says Len Berggren, a historian of mathematics at Simon Fraser University in Vancouver. "What is surprising is that someone discovered the map projection to do it." Not only are the lines of latitude curved and the lines of longitude unevenly spaced-both unprecedented innovations in the Islamic world-but the spacing is precisely calibrated so that the distance to Mecca on the pointer is the sine of angular distance to Mecca in the real world. If the lines had been evenly spaced, the instrument would not have worked.

According to King, the artisans of Isfahan could never have come up with such a grid themselves; they were accomplished astrolabe makers, but not mathematicians. Therefore, they had to be copying an earlier model.

Where did the original model come from? King has some intriguing speculations. As early as the 9th century, Islamic astronomers had devised a method for computing the qibla that happened to produce, as an intermediate step, the sine of the distance to Mecca. The map projections might have been discovered at the same time. Indeed, King's colleague Francois Charette has shown that the grids are, in a sense, a translation of the equations into cartographic form. Alternatively, a later scholar who was familiar with the trigonometric method might have devised the map as an ingenious simplification. King suspects Abu 'l-Rayhan al-Biruni (973-1048), considered the leading scientist of medieval Islam, who lived in Ghazna (now Afghanistan) and wrote an influential and original treatise on the qibla.

Inevitably, less romantic possibilities have been suggested. The catalogue that Sotheby's printed when the first instrument went up for auction states: "The projection is of western European inspiration ... and this unusual instrument is interesting as evidence of the assimilation of European science and technology in Persia in the 18th century." King strongly disagrees with that interpretation, citing both physical and historical evidence. Even if European mathematicians had worked on the qibla-finding problem, he argues, they would not have stumbled on a solution that was directly inspired by a 9th-century Islamic formula. "The fact that the instrument uses the sine of the distance is, to me, the most compelling argument" for its early Islamic origin, King says. There is also no evidence that the European scholars who were in Persia at the time brought with them anything like a Mecca-centered world map. Even if they could have, they would not have wanted to: They were in Persia to convert Muslims, not to make it easier for them to practice their religion.

More clues to the origin of these instruments may yet come to light. "So many Arabic manuscripts lie not only unstudied but uncatalogued in the libraries of the world," Berggren says. They may contain descriptions of similar qibla-finding world maps, which went unrecognized before because historians didn't know what they were reading about. Says Berggren, "Not only do we know what to look for now, but we know it's worth looking."


This article is published by written permission from American Scientist.

IslamiCity Note:

1. Most of the Muslims in North America pray towards northeast and there are a few who pray to the southeast.

Related posts from similar topics:

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  28 Comments   Comment

  1. Aminu Tukur Argungu from Nigeria

    Ever since this world was created,the first settlers were muslims.That we understand from The HOLY QUR'AN,all other deviations came up later. So, it will never surprise me if discoveries of these nature 're traced to muslim scholars of yester years. The fact that in the field of mathematics alone the contribution of such scholars will remain unwashed forever (talking about Algebra) and many inventions known to originate from muslim scholars before.What we have are genarations of People who always try to deny Islam its proper place in history.








  3. Yusuf Muhammad Kurawa from Nigeria

    Assalamu Alaikum,

    It was really an educative and well researched article. please keep it up and God bless abudantly.

  4. S. LADAN from NIGERIA


  5. Waseem Hassan from India

    I don't think this topic could benefit the ummah.You should put such articles on your websites which could help the people to know what is Islam,how we can gain benefits in our daily life.I am reading your articles for last 2 years, but i think i have gone through very few articles at ur website which are really meaningful for common people.Plz try to benefit the muslim ummah & show them what the authentic Islam is all about & how it can benefit people in all the fields of their life.


  6. SAADA from KENYA




  7. Dr. S.M. Ghazanfar (Univ. of Idaho) from USA

    Excellent article, but this is not the only field where massive "learned ignorance" in literary history prevails; the mainstream books barely mention the early Islamic contributions and their enormous impact in stimulating European Renaissance, Enlightenment, and Reformation.

    For those interested in this particular subject, I recently encountered a book in connection with a book I am doing: J.L. Berggren, EPISODES IN THE MATHEMATICS OF MEDIEVAL ISLAM, Spring-Verlag, New York; 1986. Here is a quote from the author: "The Islamic contribution affected the development of all branches of mathematics in the West and was of prime importance in many. Despite this, no textbook on the history of mathematics in English deals with the Islamic contribution in more than a general way. This is unfortunate, not only from a scholarly point of view but from a pedagogical one as well." Unfortunately, such "gaps" in literary history are massive and endemic--and the paradigm is so stubbornly enshrined.

    Incidentally, I have recently published a "gap-filling" book in economics--"Medieval Islamic Economic Thought: Filling the 'Great Gap' in European Economics," RoutledgeCurzon Publishing, London, U.K., 2003; many libraries have the book now. For a "civilizational dialogue," we need such 'gap-filling' in just about every field of knowledge--mathematics, medicine, geography, astronomy, philosophy, humanities, etc. etc. There is so much one can explore and discover.

    Incidentally, the Greeks belonged in the East originally, where their knowledge was further synthesized, and then it traveled West, but it was buried in Alexandria for centuries, and rediscovered by the Islamic civilization in during the eighth century chiefly via the Byzantium. However, often one observes complete ownership of the Greeks by the West so that the Islamic influences could then undermined or ignored.

    Best wishes.

  8. Dr. S.M. Ghazanfar from USA

    I see that this article was originally published in the American Scientist. Could you please tell me which particular issue of this journal published this fine article? Many thanks.

  9. Dr. Anas Abdunoor Kaliisa from Uganda

    It is suprising and yet it is true!

    In my study of sharia and other related knowledgewe have never come to some information like this.

    the only mesures we knew was about the movement of the son etc.

    We want to thank you and encourage you for more of this nature

    jazakum Llahu Khairan

  10. Ray from USA

    To Sirrus:

    One thing you are right about; science is not a cultural property but a tool. But that is exactly the west forgets, they have a blackout, when it comes to giving tribute to the Muslim scientist and that is just because, yes you guessed it right, they are Muslims. 'Those savages on the outskirt of western civilization know any thing, let alone science'. West thinks their scientific/intellectual accomplishments are directly connected to their Greek and Roman ancestors and they are the heir of those civilizations. West is a child of Islamic civilization, and its secular liberties are product of instigation directly caused by Islam. Like it or not that is some thing west can not stomach. Your post is a prime example of western duplicity, one hand you denounce cultural owner ship of science but have no problem claiming to be a bastard child of Greece and Roman civilization, even feeling proud, no matter how far reaching a proposition might be. But oh no Muslims can not claim a simple gratitude for ideas they fostered and contributed let alone claim copyrights. If it was left to west's hubris they would declare Roger bacon as inventor of every thing and Da'vinci would be the father of modern scientific thought, and that is it.

  11. Shagufta from USA

    This article is very intriguing, especially anyone who is intrested in history.

  12. Sirius from Finland

    The author wrote:

    "Medieval Muslims were using sophisticated mathematics to solve this problem centuries before the equivalent discoveries were made in Europe. At a time when Europeans believed that the Earth was flat, Muslim scientists knew how to correct for the Earth's curvature."

    I'm a bit embarrassed. To be frank, this sounds quite artifical self-made face-lift. What is the purpose? To tell westeners they didn't invent science? Hey, scientists know that and the ordinary people may never get it. On the other hand, "ordinary people" never bother to think of the origin of sciences anyway. This, I think, is valid anywhere anytimes.

    Muzammil wrote:"Europe and the world owes a great deal to Muslim scientists who help to revive and develop the knowledge that Europe decided to throw during the Dark Ages."

    Yes, many muslim authors quite fluently forget of Greese and Rome. As far as I remember they were european cultures. Before "the dark ages". By the way, this consept of "dark ages" is 100% european, and not so widely used nowadays.

    Some summing up

    -science isn't any culture's property, it's a tool. Sumers 5000 years ago, greeks 2000 years ago, muslims...,europeans..., who knows wholl be it, say, after 100, 1000 000 years from now?

    -there are uphills and downhills in every culture. And cultures change to form new cultures.

    -muslims were up in the past and, as far as I see many of you think, is down nowadays. Maybe you should focus on being up IN THE FUTURE than remembering days of glory IN THE PAST.

    -I recall one program on finnish TV, where a guy outspoke old arabic poems inspired by WINE. They were composed at the time widely seen as the highlight of islamic culture. Is this only a weird coinsidence? Or does it display the fact that only in "quite liberal" atmosphere do sciences and arts flourish?

  13. muhammad lawan from nigeria

    Assalam alaikum warahmatullah.

    infact we muslims should not forget that the whole world of science today and tomorrow has its own root from islam and we shouldn't forget that. we should at all time give thanks and praises to Allah (swt)for that favour. we should study maths and the other science subjects and always relate what we study to what Allah (swt) said in the kuran.

  14. Safiulla from India

    Its enlightening to know how much muslims of medievel times valued knowledge and were in pursuit of it inspired by islamic teachings. In contrast its sad to see the state of the Muslim Ummah of present time. Its really good to know some people are unbiased, can speak the truth, credit the actual discoverers with their corresponding discoveries and stand by their findings. I would like to thank the author, Mr.David King, Mr. Len Berggren and all those involved in bringing to light such facts of immense values. May Allah reward you, bless us and guide us all.

  15. Umar from USA

    Salaam Alaikum! A truly refreshing article for every Muslim. Seeking knowledge of Allah s w t and his creations should be the priority of an Islamic existence. May Allah s w t put us Muslims on the correct collective path, and may we return to setting an example for all of mankind in every dimension of life.

    "Rabbana la tuzigh quloobana baaada ith hadaytana wahab lana min ladunka rahmatan innaka anta alwahhabu 3:8"

  16. Muzammil from Malaysia

    It is well known fact that past Muslims were the step-fathers of scientific knowledge during the Dark Ages when Europe decided to do away with the sciencific knowledge that their forefathers had amassed.

    Thus, God willing, if it were not for Muslim scientists who take the baton left by the European scientits before the Dark Ages, the world may not be as advanced as it is today.

    Europe and the world owes a great deal to Muslim scientists who help to revive and develop the knowledge that Europe decided to throw during the Dark Ages.

    Sadly, the Muslim contribution to global scientific development has been forgotten by the west and the world.

    Now, the west tries to equate Muslim and Islam to ignorance when in fact it was and is Islam who promote the search for knowledge and sciences.

    At the time when Christian world persecuted those who said earth was round, Muslims had no problem to accept that the earth is round or egg-shaped.

  17. Hassan from Saudi Arabia

    In this article written as 'Mecca' for Makkah. The correct to write is Makkah; and for Quraan written as Koran. When reading this, getting some bad feeling. 'Quraan' is the correct, to write. Hope, will correct in the future areticles.

  18. Engr Isma'il Badmus from Nigeria

    I'm most impressed and at the same time challenged to work harder on my chosen field. Each time I read or hear about our Islamic past I have a feeling that we're yet to meet the standards set by our great predecessors. I thank the dicoverers of this great intellectual legacy for a job well done.

  19. Alia from United States

    Assalamu Alaikum.

    Thank you for a wonderful article which sheds light on our rich histroy. As an elementary school teacher in an American Islamic School the first thing that has come to my mind as I read the article is; we are not embraching our history! We are not including our Islamic History and all of the contributions made during the Islamic Rennisance from Muslims in the curriculum of our Islamic schools. This is important to teach our youth (which is our future)about who we are and what we have accomplished before.

    I hope that in the future the Islamic schools in this country will unite on a curriculum that will include not only the History that is required for the schools but also the enriched history of Muslims. This can help establish a greater sense of who we are and our responsibility to use the greatest gift Allah has given to us; The Holy Quran.

  20. Rizwan Kadir from USA

    Great and inpiring article. However, it's saddening that Muslims haven't figured this out yet. While the rest of the humanity is able to send rockets around the solar system and beyond, we Muslims are still dealing with the basics.

    The science of trigonometry was developed partially in response to determine the direction of Qibla from cities outside of the Arabian peninsula. Al-Beruni was a major figure in the development of this field.

  21. shamaz from india

    how i identify mecca is there in right position . excately in westside can u help me i am staying in chennai reguraly visiting ur website

  22. toufeeq anwar from India

    Excellent article and excellent discoveries. May Almighty Allah enlighten us about our past so that we can face the challenges of today,s world.

  23. Shamim Rahman from USA

    This is a remarkable article. As a NASA engineer, I can appreciate what an achievement it is for medieval Islamic scholars to know that the earth is curved, and the potential consequences. I would be interested in knowing a lot more about the Islamic knowledge base of the time; this could mean that Copernicus and other later scientists may have been inspired by others centuries before them!!

    Great post.


  24. Ahmad Zaka-ur-Rehman from Pakistan

    The article mentions that there are many uncatalogued arabic manuscripts in different libraries of the world which could reveal the advancement of mathematics in the Islamic world a thousand years ago. I would love to contibute in whatever way I can to decipher such manuscripts.

  25. NooN from usa

    Arabic "0" in relation to the Greek 3.14 pi


    studying the "0" in relation to the globe =

    regarding farming or parts of the field or tree(s);

    applied or practical geo.metry ..

    geometry & maps :

    how to get there;

    what portion belongs to whom;

    and a "permanent map" made of a metal material

    would be "practical" & art worthy of being a

    (magnificant & legal & mathmatically correct)

    family heir.loom.

  26. Usman Ali from Bangladesh

    A true scholarly article. The critical contribution of Muslim mathematicians is often undermined these days. However, Muslim mathematicians played a crucial role in developing mathematics including fundamental ideas like zeroes (0, they might have borrowed this concept from India, but they used it smartly), algebraic representation of numbers, quadratic equations and astronomical measurements. If these foundations were not set by them, it is doubtful whether Newton would have ever come up with laying down the grammar of 'Analysis (or Calculus )'.

    It is very important these days that Muslims take mathematics very seriously. And by saying this I specially point to the Islamic scholars. Many such scholars are well versed in rhetoric, Qur'an and hadiths but when it comes to mathematics, they show a poor understanding.

    If Muslims are to come up seriously with an alternate interest-free economic system, if they are to lay smart budgets based on Sharia, if they want to make smart trade deals with non-Muslim countries that complies with Islamic principles, if they want to excel in Islamic banking and most importantly if they want to critically examine the physical world in the light of Qur'an and Sunnah, then they must study mathematics. It is only by using some high-powered math (such as Analysis (Calculus)) can Muslims make some serious and scholarly contribution in these very important fields. Otherwise, all of their arguments would sound very pleasant to the ear, but would lack theoretical foundations. As a result, when it would come to practical implementations, they would lack sufficient basis. It is mathematical tools that can provide such strong bases. I would urge the present day Muslim scholars to pay due attention in this very neglected field. If we, the Muslims want to be smart in this very complex world, we have to be smart mathematically and make a proper integration between mathematics and Islamic principles based on Qur'an and Sunnah.

  27. Ishrat Chowdhury from Mississauga, Ontario, Canada


    I am confused. Which direction I should follow during salat time? Would please let me know ?


    --Ishrat Azim Chowdhury.