Posts Tagged ‘Arabic mathematics’

Mathematical structures in mediaeval Islamic art

March 22, 2010

Bismillah. With thanks to Dr. Sabbir Rahman & Abu Ammar Mangoranca for these.

Assalamu `alaikum,

I was delighted to read the following short article, which clearly demonstrates how far ahead of their time Muslim geometers were:

http://www.sciencenews.org/view/generic/id/8270/title/Math_Trek_Ancient_Islamic_Penrose_Tiles

Aperiodic Penrose Tilings are a very modern development yet,”The Darb-i Imam shrine was particularly remarkable because it showed girih tile patterns at two different scales, so that large girih tiles were broken up into smaller girih tiles. In principle, by repeatedly scaling up the tiling in this way, they could have covered an arbitrarily large wall with a Penrose tiling.”

Indeed, as the Wikipedia article on Penrose tilings should make clear, their development and discovery is highly non-trivial, and not something which is likely to be come upon purely by chance:

http://en.wikipedia.org/wiki/Penrose_tiling

The connection of Penrose tilings with the golden ratio is also quite fascinating. Note that the golden ratio has featured in Islamic architecture from the earliest times:

http://www.springerlink.com/content/rv6q10p8x320580l/

http://en.wikipedia.org/wiki/Mosque_of_Oqba

This is a link to the technical paper associated with the first article:

http://www.physics.harvard.edu/~plu/publications/Science_315_1106_2007.pdf

Wassalam,
Sabbir

Salaam:

The research of Dr Peter J. Lu on the Islamic art patterns is also described and with more illustrations at

http://www.saudiaramcoworld.com/issue/200905/the.tiles.of.infinity.htm.

Although this decorative art is found in medieval Muslim structures, especially mosques, the mathematical foundation of these patterns, or girih tiles, is only discovered in the West after 5 centuries.

Abu Ammar Mangorangca

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Arabic Arithmetic – the Abjad Numerical System

June 7, 2009

With the Name of Allah

Ever wondered what all that Arabic numerology is based on?  Here is a brief introduction to the Abjad numerical system.

Arabic Arithmetic – the Abjad Numerical System

Here’s another interesting example and puzzle, given with precisely the same wording by both Ibn Kathir (in al-Bidayah wa l-Nihayah, his history of the world) and Suyuti (in his Tarikh al-Khulafa’ or History of the Caliphs, Mu’assasah al-Kutub al-Thaqafiyyah, Beirut, 2nd ed., 1417/1996, p. 394 under the section on Al-Nasir li Din Allah who lived 553-622 and ruled 575-622, his reign including the reconquest of Jerusalem by Saladin in 583/1187).  The verbatim reproduction by Suyuti suggests that he took this from Ibn Kathir:

One of the strange matters [connected to the reconquest of Jerusalem] is that Ibn Barrajan mentioned in tafsir of “Alif Lam Mim: The Romans have been conquered” [Qur’an, 30:1-2] that Jerusalem would remain in the hands of the Crusaders (al-Rum) until the year 583, when they would be vanquished.  Jerusalem would be conquered and remain a Land of Islam until the end of time.  He derived all this from the arithmetic of the ayah, and it is precisely what happened.

Abu Shamah said: What Ibn Barrajan mentioned is a wondrous coincidence, for he died ages before the event, his death having occurred in the year 536.

(End of quote from Ibn Kathir & Suyuti)

Now, Ibn Barrajan’s arithmetic is puzzling.  Here are the Abjad values of the first two ayahs of Surah al-Rum:

1. Alif Lam Mim: 71

2. Ghulibat al-Rum: 1432, 277

The question is, how did he arrive at the year of the reconquest of Jerusalem?

The only way I can get anything to work is to use ayah 2 only, plus the Surah number (30) and the ayah number:

1432 – 277 + 30 + 2 = 1187, the CE date of the reconquest of Jerusalem which can be converted to the equivalent Hijri year.

Note that the subtraction at the beginning might be justified from the words that literally translate as “Conquered – The Romans.”

Would anyone like to comment on the following questions and notes?

(1) Was this indeed Ibn Barrajan’s arithmetic?

(2) Is there another explanation, perhaps involving a different version of the Abjad numbering (there were two different schemes in use historically: Eastern & Western) ?

(3) Did Ibn Barrajan really make this prediction, or was it interpolated into his manuscript after the event?

(4) The prediction as stated was fulfilled and remained true for almost eight centuries, but is no longer true ever since the Israeli occupation of Jerusalem in 1967.

(5) In the end, this is no more than a mathematical distraction, for the Qur’an is primarily a collection of Signs and Guidance for humanity in our journeys towards God.

Another example of numerology

Ibn Kathir quotes from the early authority Abu l-‘Aliyah that the mysterious letters may denote lifetimes of nations: “Alif is one year; Lam is thirty years; Mim is forty years.”[1]

He also quotes a narration that he dismisses as not authentic, to the effect that some Jews at the time of the Prophet (peace be upon him) speculated that the Prophet’s followers would rule for periods denoted by the mysterious letters.  The narration specifically mentions the following groups of letters: ALM, ALMS, ALR and ALMR, for which the numerical equivalents add up to 734 years of rule.  Ibn Kathir then remarks, “If this method is correct, one would have to add up the values of all fourteen of these letters, which would equate to a large figure.  If you calculate taking into account repetition [of groups of letters at the beginning of different surahs], the value will be even greater, and Allah knows best.”[2]


[1] Ibn Kathir, Tafsir, Maktabah Dar al-Fayha’, Damascus/Beirut, 1413/1992 (4 vols.), vol. 1, p. 39 under Qur’an 2:1

[2] Ibn Kathir, Tafsir, Maktabah Dar al-Fayha’, Damascus/Beirut, 1413/1992 (4 vols.), vol. 1, p. 41 under Qur’an 2:1.  Note that Ibn Kathir miscalculates the value of ALMS, forgetting the L, so he gives the total as 704.  The results of the calculations he suggests at the end are 1757 and 3385 years respectively, as detailed in this table: Numerical Values of the Mysterious Letters of the Quran