The Blog-Health-o-Meter™ reads Minty-Fresh™.

Crunchy numbers

A Boeing 747-400 passenger jet can hold 416 passengers. This blog was viewed about 2,600 times in 2010. That’s about 6 full 747s.

In 2010, there were 12 new posts, growing the total archive of this blog to 135 posts.

The busiest day of the year was November 15th with 30 views. The most popular post that day was The Hajj – A Journey of a Lifetime& The Pilgrimage To Makkah by:Al-Hajj Malik El-Shabazz (Malcolm X).

Where did they come from?

The top referring sites in 2010 were en.search.wordpress.com, facebook.com, mycrazyreader.info, student-loan-consilidation.com, and en.wordpress.com.

Some visitors came searching, mostly for al hajj, imydp, name of allah, alhambra mosaic conservation picture, and new discoveries in mathematics.

Attractions in 2010

These are the posts and pages that got the most views in 2010.

The Hajj – A Journey of a Lifetime& The Pilgrimage To Makkah by:Al-Hajj Malik El-Shabazz (Malcolm X) December 2007

New Discoveries in the Islamic Complex of Mathematics, Architecture and Art June 2010

A Short Story of Eid. September 2008

Memorize the word of your Lord February 2010

IMYDP PROSPECTUS:Our Vision and Mission May 2008

“Four of them ( Zil-Qadah, Zil-Hijjah, Muharram and Rajab) are sacred.”

(Surah At-Tawbah:36)

“The best of fasts besides the month of Ramadhan is the fasting of Allah’s month of Muharram.”

(Muslim)

This is stated in a Hadeeth reported by Hazrat Aisha (Radhiyallahu-Anha):

“that the Holy Prophet Sallallahu-Alayhi-Wasallam) ordered the observance of the fast of Aashora.  However, when the fast of Ramadhan became compulsory, then whosoever wished, kept this fast and whosoever desired did not observe this fast.”

(Bukhari)

But, nevertheless the Prophet (Sallallahu-Alayhi-Wasallam) continued to fast this day and encouraged his Companions to do the same.

The Prophet (Sallallahu-Alayhi-Wasallam) has exhorted and encouraged his Ummah to fast on this day. He said:

“This fast[Aahura] is a compensation for the (minor) sins of the past year.”

(Muslim)

Hazrat Ibn Abbas (Radhiyallahu-Anhu) said:

“When Rasulullah (Sallallahu-Alayhi-Wasallam) observed the fast of the day of Aashora and ordered (his Companions) to fast, they said: `O Rasulullah! It is a day revered (glorified) by the Jews and Christians.’    Thereupon Rasulullah said: “The coming year, if Allah wills (I remain alive), I will for surely fast on the ninth (also).”

(Muslim)

“Observe the fast of Aashora and oppose the Jews.  Fast a day before it or a day after.”

(Baihaqi)

“One who generously spends on his family on the day of Aashora, Allah will increase (his provision) for the whole year.” (Baihaqi)

May Allah guide us all upon the Straight Path and save us from every act which brings His displeasure.

The first ten days of Dhu’l-Hijjah:

Days of virtue and righteous deeds

Praise be to Allaah Who has created Time and has made some times better than others, some months and days and nights better than others, when rewards are multiplied many times, as a mercy towards His slaves. This encourages them to do more righteous deeds and makes them more eager to worship Him, so that the Muslim renews his efforts to gain a greater share of reward, prepare himself for death and supply himself in readiness for the Day of Judgement.

This season of worship brings many benefits, such as the opportunity to correct one’s faults and make up for any shortcomings or anything that one might have missed. Every one of these special occasions involves some kind of worship through which the slaves may draw closer to Allaah, and some kind of blessing though which Allaah bestows His favour and mercy upon whomsoever He will. The happy person is the one who makes the most of these special months, days and hours and draws nearer to his Lord during these times through acts of worship; he will most likely be touched by the blessing of Allaah and will feel the joy of knowing that he is safe from the flames of Hell. (Ibn Rajab, al-Lataa’if, p.8)

The Muslim must understand the value of his life, increase his worship of Allaah and persist in doing good deeds until the moment of death. Allaah says (interpretation of the meaning):

“And worship your Lord until there comes unto you the certainty.” [al-Hijr 15:99] The mufassireen (commentators) said: “‘The certainty’ means death.”

Among the special seasons of worship are the first ten days of Dhu’l-Hijjah, which Allaah has preferred over all the other days of the year. Ibn ‘Abbaas (may Allaah be pleased with him and his father) reported that the Prophet (peace and blessings of Allaah be upon him) said: “There are no days in which righteous deeds are more beloved to Allaah than these ten days.” The people asked, “Not even jihaad for the sake of Allaah?” He said, “Not even jihaad for the sake of Allaah, except in the case of a man who went out to fight giving himself and his wealth up for the cause, and came back with nothing.” (Reported by al-Bukhaari, 2/457).

Ibn ‘Abbaas (may Allaah be pleased with him and his father) also reported that the Prophet (peace and blessings of Allaah be upon him) said: “There is no deed more precious in the sight of Allaah, nor greater in reward, than a good deed done during the ten days of Sacrifice.” He was asked, “Not even jihaad for the sake of Allaah?” He said, “Not even jihaad for the sake of Allaah, except in the case of a man who went out to fight giving himself and his wealth up for the cause, and came back with nothing.” (Reported by al-Daarimi, 1/357; its isnaad is hasan as stated in al-Irwaa’, 3/398).

These texts and others indicate that these ten days are better than all the other days of the year, with no exceptions, not even the last ten days of Ramadaan. But the last ten nights of Ramadaan are better, because they include Laylat al-Qadr (“the Night of Power”), which is better than a thousand months. Thus the various reports may be reconciled. (See Tafseer Ibn Katheer, 5/412).

You should know, my brother in Islaam, that the virtue of these ten days is based on many things:

Allaah swears an oath by them, and swearing an oath by something is indicative of its importance and great benefit. Allaah says (interpretation of the meaning): “By the dawn; by the ten nights” [al-Fajr 89:1-2]. Ibn ‘Abbaas, Ibn al-Zubayr, Mujaahid and others of the earlier and later generations said that this refers to the first ten days of Dhu’l-Hijjah. Ibn Katheer said: “This is the correct opinion.” (Tafseer Ibn Katheer, 8/413)
The Prophet (peace and blessings of Allaah be upon him) testified that these are the best days of this world, as we have already quoted above from saheeh ahaadeeth.
The Prophet (peace and blessings of Allaah be upon him) encouraged people to do righteous deeds because of the virtue of this season for people throughout the world, and also because of the virtue of the place – for the Hujjaaj (pilgrims) to the Sacred House of Allaah.
The Prophet (peace and blessings of Allaah be upon him) commanded us to recite a lot of Tasbeeh (“Subhan-Allaah”), Tahmeed (“Al-hamdu Lillaah”) and Takbeer (“Allaahu akbar”) during this time. ‘Abdullaah ibn ‘Umar (may Allaah be pleased with him and his father) reported that the Prophet (peace and blessings of Allaah be upon him) said: “There are no days greater in the sight of Allaah and in which righteous deeds are more beloved to Him than these ten days, so during this time recite a great deal of Tahleel (“La ilaaha ill-Allaah”), Takbeer and Tahmeed.” (Reported by Ahmad, 7/224; Ahmad Shaakir stated that it is saheeh).
These ten days include Yawm ‘Arafaah (the Day of ‘Arafaah), on which Allaah perfected His Religion. Fasting on this day will expiate for the sins of two years. These days also include Yawm al-Nahar (the Day of Sacrifice), the greatest day of the entire year and the greatest day of Hajj, which combines acts of worship in a way unlike any other day.
These ten days include the days of sacrifice and of Hajj.Question: What must the Muslim avoid during these ten days if he wants to offer a sacrifice?

The Sunnah indicates that the one who wants to offer a sacrifice must stop cutting his hair and nails and removing anything from his skin, from the beginning of the ten days until after he has offered his sacrifice, because the Prophet (peace and blessings of Allaah be upon him) said: “When you see the new moon of Dhu’l-Hijjah, if any one of you wants to offer a sacrifice, then he should stop cutting his hair and nails until he has offered his sacrifice.” According to another report he said: “He should not remove (literally, touch) anything from his hair or skin.” (reported by Muslim with four isnaads, 13/146)

The Prophet’s instruction here makes one thing obligatory and his prohibition makes another haraam, according to the soundest opinion, because these commands and prohibitions are unconditional and unavoidable. However, if a person does any of these things deliberately, he must seek Allaah’s forgiveness but is not required to offer (an extra) sacrifice in expiation; his sacrifice will be acceptable. Whoever needs to remove some hair, nails, etc. because it is harming him, such as having a broken nail or a wound in a site where there is hair, should do so, and there is nothing wrong with that. The state of ihraam is so important that it is permitted to cut one’s hair if leaving it will cause harm. There is nothing wrong with men or women washing their heads during the first ten days of Dhu’l-Hijjah, because the Prophet (peace and blessings of Allaah be upon him) only forbade cutting the hair, not washing it.

The wisdom behind this prohibition of the one who wants to offer a sacrifice from cutting his hair etc., is so that he may resemble those in ihraam in some aspects of the rituals performed, and so that he may draw closer to Allaah by offering the sacrifice. So he leaves his hair and nails alone until the time when he has offered his sacrifice, in the hope that Allaah will save him in his entirety from the Fire. And Allaah knows best.

If a person has cut his hair or nails during the first ten days of Dhu’l-Hijjah because he was not planning to offer a sacrifice, then he decides later, during the ten days, to offer a sacrifice, then he must refrain from cutting his hair and nails from the moment he makes this decision.

Some women may delegate their brothers or sons to make the sacrifice on their behalf, then cut their hair during these ten days. This is not correct, because the ruling applies to the one who is offering the sacrifice, whether or not he (or she) delegates someone else to carry out the actual deed. The prohibition does not apply to the person delegated, only to the person who is making the sacrifice, as is indicated in the hadeeth. The person who is sacrificing on behalf of someone else, for whatever reason, does not have to adhere to this prohibition.

This prohibition appears to apply only to the one who is offering the sacrifice, not to his wife and children, unless any of them is offering a sacrifice in his or her own right, because the Prophet (peace and blessings of Allaah be upon him) used to sacrifice “on behalf of the family of Muhammad,” but there are no reports that say he forbade them to cut their hair or nails at that time.

If a person was planning to offer a sacrifice, then he decides to go and perform Hajj, he should not cut his hair or nails if he wants to enter ihraam, because the Sunnah is only to cut hair and nails when necessary. But if he is performing Tamattu’ [whereby he performs ‘Umrah, comes out of ihraam and enters ihraam anew for Hajj], he should trim his hair at the end of his ‘Umrah because this is part of the ritual.

The things that are described above as being prohibited for the person who is planning to offer a sacrifice are reported in the hadeeth quoted above; the person is not forbidden to wear perfume, have marital relations, wear sewn garments, etc.

Concerning the types of worship to be performed during these ten days: one must understand that these days are a great blessing from Allaah to His slave, which is appreciated properly by the actively righteous. It is the Muslim’s duty to appreciate this blessing and make the most of the opportunity, by devoting these ten days to paying more attention to striving hard in worship. Among His blessings to His slaves, Allaah has given us many ways in which to do good and worship Him, so that the Muslim may be constantly active and consistent in his worship of his Lord.

Among the good deeds which the Muslim should strive to do during the first ten days of Dhu’l-Hijjah are:

Fasting. It is Sunnah to fast on the ninth day of Dhu’l-Hijjah, because the Prophet (peace and blessings of Allaah be upon him) urged us to do good deeds during this time, and fasting is one of the best of deeds. Allaah has chosen fasting for Himself, as is stated in the hadeeth qudsi: “Allaah says: ‘All the deeds of the son of Adam are for him, except for fasting, which is for Me and I am the One Who will reward him for it.’” (Reported by al-Bukhaari, 1805).

The Prophet (peace and blessings of Allaah be upon him) used to fast on the ninth of Dhu’l-Hijjah. Hunaydah ibn Khaalid reported from his wife that some of the wives of the Prophet (peace and blessings of Allaah be upon him) said: “The Prophet (peace and blessings of Allaah be upon him) used to fast on the ninth of Dhu’l-Hijjah, on the day of ‘Aashooraa’, on three days of each month, and on the first two Mondays and Thursdays of each month.” (Reported by al-Nisaa’i, 4/205 and by Abu Dawud; classified by al-Albaani as saheeh in Saheeh Abi Dawud, 2/462).
Takbeer. It is Sunnah to say Takbeer (“Allaahu akbar”), Tahmeed (“Al-hamdu Lillaah”), Tahleel (“La ilaha ill-Allaah”) and Tasbeeh (“Subhaan Allaah”) during the first ten days of Dhu’l-Hijjah, and to say it loudly in the mosque, the home, the street and every place where it is permitted to remember Allaah and mention His name out loud, as an act of worship and as a proclamation of the greatness of Allaah, may He be exalted.Men should recite these phrases out loud, and women should recite them quietly.

Allaah says (interpretation of the meaning):

“That they might witness things that are of benefit to them (i.e., reward of Hajj in the Hereafter, and also some worldly gain from trade, etc.), and mention the name of Allaah on appointed days, over the beast of cattle that He has provided for them (for sacrifice)…” [al-Hajj 22:28]

The majority of scholars agree that the “appointed days” are the first ten days of Dhu’l-Hijjah, because of the words of Ibn ‘Abbaas (may Allaah be pleased with him and his father): “The ‘appointed days’ are the first ten days (of Dhu’l-Hijjah).”

The Takbeer may include the words “Allaahu akbar, Allaahu akbar, la ilaaha ill-Allaah; wa Allaahu akbar wa Lillaahi’l-hamd (Allaah is Most Great, Allaah is Most Great, there is no god but Allaah; Allaah is Most Great and to Allaah be praise),” as well as other phrases.

Takbeer at this time is an aspect of the Sunnah that has been forgotten, especially during the early part of this period, so much so that one hardly ever hears Takbeer, except from a few people. This Takbeer should be pronounced loudly, in order to revive the Sunnah and as a reminder to the negligent. There is sound evidence that Ibn ‘Umar and Abu Hurayrah (may Allaah be pleased with them) used to go out in the marketplace during the first ten days of Dhu’l-Hijjah, reciting Takbeer, and the people would recite Takbeer when they heard them. The idea behind reminding the people to recite Takbeer is that each one should recite it individually, not in unison, as there is no basis in Sharee’ah for doing this.

Reviving aspects of the Sunnah that have been virtually forgotten is a deed that will bring an immense reward, as is indicated by the words of the Prophet (peace and blessings of Allaah be upon him): “Whoever revives an aspect of my Sunnah that is forgotten after my death, he will have a reward equivalent to that of the people who follow him, without it detracting in the least from their reward.” (Reported by al-Tirmidhi, 7/443; this is a hasan hadeeth because of corroborating asaaneed).

Performing Hajj and ‘Umrah. One of the best deeds that one can do during these ten days is to perform Hajj to the Sacred House of Allaah. The one whom Allaah helps to go on Hajj to His House and to perform all the rituals properly is included in the words of the Prophet (peace and blessings of Allaah be upon him): “An accepted Hajj brings no less a reward than Paradise.”
Doing more good deeds in general, because good deeds are beloved by Allaah and will bring a great reward from Him. Whoever is not able to go to Hajj should occupy himself at this blessed time by worshipping Allaah, praying (salaat), reading Qur’an, remembering Allaah, making supplication (du’aa’), giving charity, honouring his parents, upholding the ties of kinship, enjoining what is good and forbidding what is evil, and other good deeds and acts of worship.
Sacrifice. One of the good deeds that will bring a person closer to Allaah during these ten days is offering a sacrifice, by choosing a high-quality animal and fattening it, spending money for the sake of Allaah. (more information to follow, in sha Allaah).
Sincere repentance. One of the most important things to do during these ten days is to repent sincerely to Allaah and to give up all kinds of disobedience and sin. Repentance means coming back to Allaah and foregoing all the deeds, open and secret, that He dislikes, out of regret for what has passed, giving it up immediately and being determined never to return to it, but to adhere firmly to the Truth by doing what Allaah loves.If a Muslim commits a sin, he must hasten to repent at once, without delay, firstly because he does not know when he will die, and secondly because one evil deed leads to another.

Repentance at special times is very important because in most cases people’s thoughts turn towards worship at these times, and they are keen to do good, which leads to them recognizing their sins and feeling regret for the past. Repentance is obligatory at all times, but when the Muslim combines sincere repentance with good deeds during the days of most virtue, this is a sign of success, in sha Allaah. Allaah says (interpretation of the meaning): “But as for him who repented, believed and did righteous deeds, then he will be among those who are successful.” [al-Qasas 28:67]

The Muslim should make sure that he does not miss any of these important occasion, because time is passing quickly. Let him prepare himself by doing good deeds which will bring him reward when he is most in need of it, for no matter how much reward he earns, he will find it is less than he needs; the time of departure is at hand, the journey is frightening, delusions are widespread, and the road is long, but Allaah is ever watchful, and to Him will we return and render account. As the Qur’aan says (interpretation of the meaning):

“So whosoever does good equal to the weight of an atom, shall see it,

And whosoever does evil equal to the weight of an atom, shall see it.”

[al-Zalzalah 99:7-8]

There is much to be gained, so make the most of the opportunity afforded by these invaluable and irreplaceable ten days. Hasten to do good works, before death strikes, before one can regret one’s negligence and failure to act, before one is asked to return to a place where no prayers will be answered, before death intervenes between the hopeful one and the things he hopes for, before you are trapped with your deeds in the grave.

O you whose hard heart is as dark as the night, is it not time that your heart was filled with light and became soft? Expose yourself to the gentle breeze of your Lord’s mercy during these ten days, for Allaah will cause this breeze to touch whomever He wills, and whoever is touched by it will be happy on the Day of Judgement. May Allaah bless our Prophet Muhammad and all his Family and Companions.

Fasting

It is haraam to fast on the days of Eid because of the hadeeth of Abu Sa’eed al-Khudri (may Allaah be pleased with him), who said that the Messenger of Allaah (peace and blessings of Allaah be upon him) forbade fasting on the day of Fitr and the day of Sacrifice (Adhaa). [Muslim, 827]

Ghusl (taking a bath)

One of the manners of Eid is to take a bath before going out to the prayer. It is reported in a saheeh report in al-Muwatta’ and elsewhere that ‘Abd-Allaah ibn ‘Umar used to take a bath on the day of al-Fitr before coming to the prayer-place. [al-Muwatta’ 428]

It was reported that Sa’eed ibn Jubayr said: “Three things are sunnah on Eid: to walk (to the prayer-place), to take a bath and to eat before coming out.” This is what Sa’eed ibn Jubayr said, and he may have learned this from some of the Sahaabah.

Al-Nawawi (may Allaah have mercy on him) mentioned that the scholars were agreed that it is mustahabb to take a bath before the Eid prayer.

The reason why it is mustahabb to take a bath before Friday prayer and other public gatherings also applies in the case of Eid, only more so.

Eating before coming out

One should not come out to the prayer-place on Eid al-Fitr before eating some dates, because of the hadeeth narrated by al-Bukhaari from Anas ibn Maalik who said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) would not go out on the morning of Eid al-Fitr until he had eaten some dates… and he would eat an odd number.” [al-Bukhaari, 953]

It is mustahabb to eat before coming out because this confirms that we are not allowed to fast on this day, and demonstrates that the fast is now over. Ibn Hajar (may Allaah have mercy on him) explained that this is to prevent people extending the fast and it also means obeying the commandment of Allaah. [Fath, 2/446]. If a person does not have any dates, he can eat anything permissible for breakfast. On Eid al-Adhaa, on the other hand, it is mustahabb not to eat until after the prayer, when one should eat from the meat of one’s sacrifice.

Takbeer on the day of Eid

This is one of the greatest sunnahs of this day, because of the words of Allaah (interpretation of the meaning): “… (He [Allaah] wants that you) must complete the same number (of days), and that you must magnify Allaah (say Takbeer – ‘Allaahu akbar’) for having guided you so that you may be grateful to Him.” [al-Baqarah 2:185]

Al-Waleed ibn Muslim said: “I asked al-Oozaa’i and Maalik ibn Anas about saying Takbeer aloud on Eid. They said, ‘Yes, ‘Abd-Allaah ibn ‘Umar used to say it aloud on the day of Fitr until the imaam came out.’”

Abu ‘Abd al-Rahmaan al-Salami said: “On Eid al-Fitr they would say it louder than on Eid al-Adhaa.” Wakee’ said, “i.e., the takbeer.” [Irwaa’, 3/122]

Al-Daaraqutni and others reported that when Ibn ‘Umar came out on Eid al-Fitr and Eid al-Adhaa, he would strive hard in making Takbeer until he reached the prayer-place, then he would continue making Takbeer until the imaam came.

Ibn Abi Shaybah reported with a saheeh isnaad that al-Zuhri said: “The people used to make Takbeer on Eid when they came out of their houses until they reached the prayer-place and until the imaam came out. When the imaam came out, they fell silent, until the imaam said Takbeer, then they said Takbeer.” [Irwaa’, 2/121]

The time for making Takbeer on Eid al-Fitr starts from the night of Eid until the time when the imaam comes in to lead the prayer.

The wording of the Takbeer

Ibn Abi Shaybah reported in al-Musannaf that Ibn Mas’ood (may Allaah be pleased with him) used to say Takbeer on the days of Tashreeq as follows:

Allaahu akbar, Allaahu akbar, laa ilaaha ill-Allaah, wa Allaahu akbar, Allaahu akbar wa Lillaahi’l-hamd

(Allaah is Most Great… there is no god but Allaah, Allaah is Most Great, and to Allaah be praise).” Ibn Abi Shaybah reported it elsewhere with the same isnaad, but with the phrase “Allaahu akbar” repeated three times.

Al-Muhaamili also reported that Ibn Mas’ood used to say:

Allaahu akbaru kabeeran, Allaahu akbaru kabeeran, Allaahu akbar wa ajall, Allaahu akbar wa Lillaahi’l-hamd

(Allaah is Most Great of All, Allaah is Most Great of all, Allaah is most Great and Most Glorious, and to Allaah be praise).” [al-Irwaa’, 3/126]

Congratulating one another

People may exchange congratulations and good greetings on Eid, no matter what form the words take. For example they may say to one another, “Taqabbal Allaahu minnaa wa minkum (May Allaah accept [the fast and worship] from us and from you” or “Eid mubarak” and other similar permissible greetings.

Jubayr ibn Nufayr said: “At the time of the Prophet (peace and blessings of Allaah be upon him), when people met one another on the day of Eid, they would say, ‘Taqabbal Allaahu minnaa wa minka (May Allaah accept from us and from you).’” [Ibn Hajar. Its isnaad is hasan. Fath, 2/446]

There is no doubt that congratulating others in this way is one of the noblest kinds of good manners and one of the highest social qualities among Muslims.

At the very least, one can return Eid greetings when they are given to you, and remain silent if nothing is said, as Imaam Ahmad (may Allaah have mercy on him) said: “If someone congratulates me, I return the greeting, but I do not initiate it.”

Looking one’s best for Eid

‘Abd-Allaah ibn ‘Umar (may Allaah be pleased with him) said: “‘Umar picked up a jubbah (long outer garment) made of silk that was for sale in the market, brought it to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said, “O Messenger of Allaah, buy this and wear it for Eid and when the delegations come.” The Messenger of Allaah (peace and blessings of Allaah be upon him) said, “This is the clothing of the one who has no share of the Hereafter…” [al-Bukhaari, 948]

The Prophet (peace and blessings of Allaah be upon him) approved of ‘Umar’s idea of looking one’s best, but he rejected and denounced the idea of buying this jubbah because it was made of silk.

Jaabir (may Allaah be pleased with him) said: “The Prophet (peace and blessings of Allaah be upon him) had a jubbah that he would wear on Eid and on Fridays.” [Saheeh Ibn Khuzaymah, 1765]

Al-Bayhaqi reported that Ibn Umar used to wear his best clothes on Eid, so men should wear the best clothes they have when they go out for Eid.

Women, on the other hand, should avoid adornment when they go out for Eid, because they are prohibited from showing their adornment in front of non-mahrem men. A woman who wants to go out is forbidden to wear perfume or to show off in a tempting way in front of men, because she is only going out for the purpose of worship. Do you think that it is right for a believing woman to disobey the One Whom she is going out to worship and go against His commands by wearing attention-grabbing tight and brightly coloured clothes or by putting on perfume and so on?

Ruling on listening to the Eid khutbah

Ibn Qudaamah (may Allaah have mercy on him) said in his book al-Kaafi (p. 234):

“When the imaam has said the salaam (at the end of the prayer), he should give a khutbah in two parts, like the two Friday khutbahs, because the Prophet (peace and blessings of Allaah be upon him) did this. (The Eid khutbah) differs from the Friday khutbahs in four ways … the fourth of which is: that it is sunnah and it is not obligatory to listen to it, because it was reported that ‘Abd-Allaah ibn al-Saa’ib said: “I attended Eid with the Messenger of Allaah (peace and blessings of Allaah be upon him), and when he had finished the prayer, he said: “We are going to give a khutbah, so whoever wishes to sit (and listen) to the khutbah, let him sit down, and whoever wants to leave, let him go.’”

Al-Nawawi (may Allaah have mercy on him) said in his book al-Majmoo’ Sharh al-Muhadhdhab, p. 23: “It is mustahabb for people to listen to the khutbah, although the khutbah and listening to it are not essential conditions of the Eid prayer. But al-Shaafa’i said: ‘If someone does not listen to the khutbah of Eid, at the time of an eclipse, when prayers for rain are offered, or during Hajj, or he speaks during one of these khutbahs, or leaves, I would not like this, but he does not have to repeat the prayer.”

In al-Sharh al-Mumti’ ‘ala Zaad al-Mustanfi’ by Ibn ‘Uthaymeen, 5/192, it says:

One of the scholars said: “It is not obligatory to listen to the Eid khutbahs, because if it was obligatory to attend and listen to them it would be haraam to leave. But as it is permissible to leave, it is not obligatory to listen.”

Nevertheless, if talking disturbs those who are listening, it is haraam to talk because of this disturbance, not because of not listening. On this basis, if a person has a book with him during the imam’s Eid khutbah, it is permissible for him to read it, because this does not disturb anyone. But according to the madhhab followed by this author, it is obligatory to listen to the khutbah if one is present.

To go out one by one route and come back by another

Jaabir ibn ‘Abd-Allaah (may Allaah be pleased with him) reported that the Prophet (peace and blessings of Allaah be upon him) used to vary his routes on the day of Eid. [al-Bukhaari, 986]

We ask Allaah to accept our worship and our repentance. May Allaah bless our Prophet Muhammad (may Allaah be pleased with him).

Culled from: http://www.islamawareness.net/Eid/eidrulings.html

by Salim T S Al-Hassani*

Note of the editor

This essay is a revised and expanded version of a lecture presented at the 28th Annual Conference on the History of Arabic Sciences organised by the Institute for the History of Arabic Sciences, Aleppo University, Aleppo, Syria, in 25-27 April 2007. It was submitted for publication in the proceedings of the conference.

***

Table of contents

1. Introduction
2. Geometry at the basis of Islamic architectural decoration
3. The ‘Muqarnas’ Project
4. Conflicting Views on Mathematical Islamic Art
4.1. Dr Zohor Idrisi’s View
4.2. Professor George Saliba’s View
5. The Work of Alpay Özdural
6. Conclusion
7. Bibliography and Resources

***

1. Introduction

“Sophisticated geometry in Islamic architecture”, “Geometry meets artistry in medieval tile work”, “Geometry meets Arts in Islamic tiles”. These were some of the headlines we saw in February 2007 in the main news agencies and science dispatches giving coverage to an exciting discovery published by two American scholars, Peter J. Lu and Paul J. Steinhardt (respectively from the Department of Physics at Princeton and Harvard universities).^[1] The discovery is “that medieval Islamic artists produced intricate decorative patterns using geometrical techniques that were not understood by Western mathematics until the second half of the 20th century”. The combinations of ornate stars and polygons that have adorned mosques and palaces since the 15th century were created using a set of just five template tiles, which could generate patterns with a kind of symmetry that eluded formal mathematical description for another 500 years. The authors suggest that the Islamic artisans who created these typical girih^[2] designs had an intuitive understanding of highly complex mathematical concepts. They also suggest that these could be proof of a major role of mathematics in medieval Islamic art or it could have been just a way for artisans to construct their art more easily.

Girih designs feature arrays of tessellating polygons of multiple shapes, and are often overlaid with a zigzag network of lines. It had been assumed that straightedge rulers and compasses were used to create them — an exceptionally difficult process as each shape must be precisely drawn. From the 15th century, however, some of these designs are symmetrical in a way known today as “quasi-crystalline”. Such forms have either fivefold or tenfold rotational symmetry — meaning they can be rotated to either five or ten positions that look the same — and their patterns can be infinitely extended without repetition. The principles behind quasi-crystalline symmetry were calculated by the Oxford mathematician Roger Penrose in the 1970s, but it is now clear that Islamic artists were creating them more than five centuries earlier.

The present paper reviews this discovery and discusses related literature on the subject of mathematics and arts in Muslim heritage. In particular, it accounts the related works of:

1. Alpay Özdural who showed how such geometrical patterns were used to solve cubic algebraic equations and also used the manuscript of Abu’l-Wafa and other mathematical Islamic mathematical treatises as evidence that mathematicians instructed artisans,
2. Gülru Necipoglu who discussed geometry, muqarnas and the contribution of the mathematical sciences and
3. George Saliba who presented critical arguments against some of the derived conclusions.
4. Zohor Idrisi who belives that ongoing work on Islamic tiles lacks the essential historical context that is required to inform the reader of how and when these mathematical techniques developed.

It is hoped that this review paper will bring to life the debate on the subject of Mathematics and Islamic Art and Architecture.

2. Geometry at the basis of Islamic architectural decoration

A study of medieval Islamic art has shown that some of its geometric patterns use principles established only centuries later by modern mathematicians. In particular, recent research has provided the ground for the astonishing claim that 15th century Muslim architects and artists used techniques inspired by what mathematicians nowadays call “quasicrystalline geometry”. This indicates intuitive understanding of complex mathematical formulae, even if the artisans had not worked out the underlying theory.

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Figure 1: A computer reconstruction of the quasicrystalline patterns of the Darb-i Imam shrine (Isfahan, Iran), which was built in 1453 (Science Magazine, vol. 315, n° 1106, 2007).

The discovery was published in the journal Science in February 2007 by Paul J. Steinhardt and Peter J. Lu.^[3] The research shows that an important breakthrough had occurred in Islamic mathematics and design by 1200. The core of the discovery claims that Muslim architects of central Asia made tilings that reflected mathematics, they were so sophisticated that they were only figured out in the last decades of our age.

The similarity between ancient Islamic designs and contemporary quasicrystalline geometry lies in the fact that both use symmetrical polygonal shapes to create patterns that can be extended indefinitely. Until now, the conventional view was that the complicated star-and-polygon patterns of Islamic design were conceived as zigzagging lines drafted using straightedge rulers and compasses.

With this discovery, one can conclude that the combinations of ornate stars and polygons that have adorned mosques and palaces since the 15th century were created using a set of just five template tiles, which could generate patterns with a kind of symmetry that eluded formal mathematical description for another 500 years.

The discovery suggests that the Islamic artisans who created these typical girih designs had an intuitive understanding of highly complex mathematical concepts. “We can’t say for sure what it means,” says Lu, a graduate student in physics at Harvard’s Graduate School of Arts and Sciences. “It could be proof of a major role of mathematics in medieval Islamic art or it could have been just a way for artisans to construct their art more easily. It would be incredible if it were all coincidence, though. At the very least, it shows us a culture that we often don’t credit enough was far more advanced than we ever thought before.” ^[4]

Fig. 2A. Large image	Fig. 2B. Large image
Figure 2A & 2B: Girih tile reconstruction of the strapwork pattern on an interior archway in the Sultan’s Lodge in the Green Mosque in Bursa, Turkey. Adapted from Science Magazine, vol. 315, n° 1106, 2007) and Hamish Johnston, “Islamic quasicrystals’ predate Penrose tiles“, Physicsworld.com, Feb 22, 2007

Girih designs feature arrays of tessellating polygons of multiple shapes, and are often overlaid with a zigzag network of lines. It had been assumed that straightedge rulers and compasses were used to create them — an exceptionally difficult process as each shape must be precisely drawn. From the 15th century, however, some of these designs are symmetrical in a way known today as “quasi-crystalline”. Such forms have either fivefold or tenfold rotational symmetry — meaning they can be rotated to either five or ten positions that look the same — and their patterns can be infinitely extended without repetition. The principles behind quasi-crystalline symmetry were calculated by the Oxford mathematician Roger Penrose in the 1970s, but it is now clear that Islamic artists were creating them more than 500 years earlier.

Peter Lu, one of the authors of this discovery, began wondering whether there were quasi-crystalline forms in Islamic art after seeing decagonal artworks in Uzbekistan, while he was there for professional reasons. On returning to Harvard, he started searching the university’s vast library of Islamic art for quasi-crystalline designs. He found several, as well as architectural scrolls that contained the outlines of five polygon templates — a ten-sided decagon, a hexagon, a pentagon, a rhombus and a bow-tie shape — that can be combined and overlaid to create such patterns.

In keeping with the Islamic tradition of not depicting images of people or animals, many religious buildings were decorated with geometric star-and-polygon patterns, often overlaid with a zigzag network of lines. Lu and Steinhardt show in their study published in the journal Science that by the 13th century Islamic artisans had begun producing patterns using a small set of decorated, polygonal tiles which they call “girih” tiles.

Large image

Figure 3: Periodicgirih pattern from the Seljuk Mama Hatun Mausoleum in Tercan, Turkey (~1200 CE), with girih-tile reconstruction overlaid at bottom.

Art historians have until now assumed that the intricate tile work had been created using straight edges and compasses, but the study suggests that Muslim artisans were using a basic toolkit of girih tiles made up of shapes such as the decagon, pentagon, diamond and hexagon.

“Straight edges and compasses work fine for the recurring symmetries of the simplest patterns we see, but it probably required far more powerful tools to fully explain the elaborate tiling with decagonal [10-sided] symmetry,” P. J. Lu said, quoted by the journal The Independent on 25 February 2007. He adds that “individually placing and drafting hundreds of decagons with a straight edge would have been exceedingly cumbersome. It’s more likely these artisans used particular tiles that we’ve found by decomposing the artwork”.^[5]

The scientists found that by 1453, Islamic architects had created overlapping patterns with girih tiles at two sites to produce near-perfect quasi-crystalline patterns that did not repeat themselves. “The fact that we can explain so many sets of tiling, from such a wide range of architectural structures throughout the Islamic world with the same set of tiles, makes this an incredibly interesting universal picture,” P. J. Lu said.^[6]

With this result, despite the debate that surrounded it in scholarly circles, we can see that very important discoveries in the Islamic scientific tradition are still to come, and that with the continuing research in different sources, including those of material remains of Muslim civilisation, the picture of our knowledge may be enriched and even changed dramatically.

3. The ‘Muqarnas’ Project

As a background to the present day research on Islamic architecture as a conjunction of mathematics, arts and practical knowledge, we can mention the ongoing work on the Muqarnas. A Muqarnas is a type of corbel used as a decorative device in traditional Islamic architecture. The term is the Arabic word for stalactite vault, an architectural ornament developed around the middle of the 10th century in north eastern Iran and almost simultaneously, but apparently independently, in central North Africa. A Muqarnas is a three-dimensional architectural decoration composed of niche like elements arranged in tiers. The two-dimensional projection of a Muqarnas vault consists of a small variety of simple geometrical elements. Excellent examples can be found in the Alhambra in Granada, and in the mausoleum of Sultan Qaitbay in Cairo.^[7]

Fig. 4A. Large image	Fig. 4B. Large image
Figures 4: The iwans that surround the courtyard of Masjid-i-Jame in Isfahan consist of three Muqarnas, each giving different impressions: (4A) the southern Muqarnas, occupying a frontal position facing the courtyard, has an apex made up of 8 segments, suggesting a primitive strength; (4B)the eastern Muqarnas, with its 11-segmented apex, is complex and not aesthetically pleasing. (4C) the western Muqarnas has a 5-segment apex, and displays an elegant form such as that seen in Hakuho sculptures.(Source).

Fig. 4C. Large image

The singular beauty of the Muqarnas has been reported by travellers throughout history. Their descriptions, however, are no more than brief introductions, and many details remain unclear. In his work on such architectural ornaments, Shiro Takahashi created exact drawings of many varieties of Muqarnas, classifying them into types in an attempt to clarify the formative styles of Muqarnas.^[8]

On the other hand, scholars from Heidelberg University in Germany, led by Yvonne Dold-Samplonius, designed The Muqaras Project aimed at the study of Muqarnas tradition in Islamic architecture. The project is entitled: Mathematical Concepts and Computer Graphics for the Reconstruction of Stalactite Vaults – Muqarnas – in Islamic Architecture.^[9]

The focus in this project is laid on two main points. One is that, from the late 11th century on, all Muslim lands adopted and developed the Muqarnas, which was widely used in constructions. The second and far more important point is that, from the moment of its first appearance, the Muqarnas acquired four characteristic attributes, whose evolution and characteristics form its history: it was three-dimensional and therefore provided volume wherever it was used, the nature and depth of the volume being left to the discretion of the maker; it could be used both as an architectonic form, because of its relationship to vaults, and as an applied ornament, because its depth could be controlled; it had no intrinsic limits, since not one of its elements is a finite unit of composition and there is no logical or mathematical limitation to the scale of any one composition; and it was a three-dimensional unit which could be resolved into a two-dimensional outline.

Fig. 5A. Large image	Fig. 5B. Large image	Fig. 5C. Large image
Figures 5: Muqarnas drawings in The Topkapi Scroll, the best preserved example of its kind, displaying geometry and ornament of Islamic architecture: (5A) Vault fragment with black-dotted polygonal grid lines, triangular one-twentieth repeat unit of a decagonal vault, and fan-shaped radial Muqarnas quarter vault; (5B) Fan-shaped radial muqarnas quarter vault, and shell-shaped radial muqarnas quarter vault; (5C) Fan-shaped radial muqarnas quarter vault, rhombodial one-eight repeat unit of an octagonal fan-shaped radial muqarnas quarter vault, fan-shaped radial muqarnas quarter vault, and rectangular repeat unit of stellate Muqarnas fragment. (Source).

The work of the group is based on the analysis made by Yvonne Dold-Samplonius of the mathematical work of the 15th century Timurid mathematician Ghiyath al-Din Mas’ud al-Kashi (ca. 1380-1429). Al-Kashi defines the Muqarnas as:

“The muqarnas is a ceiling like a staircase with facets and a flat roof. Every facet intersects the adjacent one at either a right angle, or half a right angle, or their sum, or another combination of these two. The two facets can be thought of as standing on a plane parallel to the horizon. Above them is built either a flat surface, not parallel to the horizon, or two surfaces, either flat or curved, that constitute their roof. Both facets together with their roof are called one cell. Adjacent cells, which have their bases on one and the same surface parallel to the horizon, are called one tier.” ^[10]

Building on the classification of different varieties of Muqarnas by al-Kashi, the project analyses the intermediate elements which connect the roofs of adjacent cells. In this sense, al-Kashi distinguishes four types of Muqarnas: The Simple Muqarnas and the Clay-plastered Muqarnas, both with plane facets and roofs, as well as the Curved Muqarnas, or Arch, and the Shirazi, in which the roofs of the cells and the intermediate elements are curved. The plane projection of a simple element (either cell or intermediate element) is a basic geometrical form , namely a square, half-square (cut along the diagonal), rhombus, half-rhombus (isosceles triangle with as base the shorter diagonal of the rhombus), almond (deltoid), jug (quarter octagon), and large biped (complement to a jug), and small biped (complement to an almond). Also rectangles occur.

The elements are constructed according to the same unit of measure, so they fit together in a wide variety of combinations. Al-Kashi uses in his computation the module of the Muqarnas, defined as the base of the largest facet (the side of the square) as a basis for all proportions.

The Muqarnas is used in large domes, in smaller cupola, in niches, on arches, and as an almost flat decorative frieze. In each instance the module as well as the depth of the composition is different and adapts to the size of the area involved or to the required purpose. The Muqarnas is at the same time a linear system and an organization of masses.^[11]

Fig. 6A. Large image	Fig.6B. Large image
Figures 6: South octagon vault of the Takht-i Suleyman (Throne of Salomon), the ruins of which are situated ca. 30 km North of Takab, N.W. of Tehran. Takht-i Suleyman was a palace built in the 13th century by the Ilkhanid ruler Abaqa (1265-1281). In the ruins of the western part of the palace a plate has been found, which was recognized as a construction plan for a Muqarnas vault. In analogy to this plan, the scholars of The Muqarnas Project at Heidelberg University in Germany proposed a possible plan to reconstruct the much simpler south octagon vault. (Source).

Fig. 6C. Large image

Departing from the existence of a lot of ground plans of existing Muqarnas, some of these 3D-vaults are still in good shape, others broke down and have to be reconstructed from their plans; but even in many cases such plans do not exist any more. The Muqarnas Project mentioned above intends to convert existing Muqarnas plans into the computer in such a way that their properties can be analyzed (what kind of elements occur, which elements can be connected and how, what are the possible heights of the succeeding tiers, what about regional differences, cultural differences, differences in time, and so forth). In addition, the inherent aim to such an investigation is to build a computer program that is able to answer these questions on Muqarnas plans automatically. The obvious material to start with, according to the scholars of this project, are the Illkhanid Muqarnas plans.^[12] These plans can be compared with existing architecture and thus show limitations in computer possibilities.

In the second stage, the scholars are inclined to apply these methods on plans which are not known to have been realized, such as those recorded in the Topkapi Scroll. With all this knowledge in hand, it will be possible to apply these methods for different purposes, such as reconstructing Muqarnas vaults in ruins (like for instance in Varamin, Iran), or to produce short videos tapes on Muqarnas to be used for teaching.^[13]

4. Conflicting Views on Mathematical Islamic Art

The subject of the influence of mathematicians on the artisans is a hotly debated subject which requires scholarly resolution. Recently, the author of this article consulted colleagues on this subject and in particular asked their views on the recent discoveries of Lu and Steinhardt. I give below the views of two contemporary scholars, Dr Zohor Idrisi and Prof. George Saliba. In addition, I account briefly of the tantalizing work achieved by the late Alpay Özdural.

4.1. Dr Zohor Idrisi’s View

Dr. Idrisi considers that we should not jump too quickly into claiming the ground breaking character of the ongoing work on tiling, tessellating and crystallography. This subject is far removed from Greek style elementary geometry. For mathematicians, the work on tiling is a real nightmare as it is a highly specialised field that industry has been researching ever since the 1970s with the work of Penrose.^[14]

Scholars, such as Branko Grünbau^[15] (from the University of Washington in Seattle), had worked intensively on the subject of tiling before P. J. Lu and P. J. Setinheardt published their article recently. Surprisingly though, Grünbaum’s work is coloured by the view point he expresses being that the Muslims did not understand the mathematics of their artistic work. It is interesting to note that several of the press reviews accounting of P. J. Lu and P. J. Setinheardt’s discovery are similar to those expressed by Grünbaum.

This is why Dr. Idrisi stresses that without doubt this discovery is a fascinating one for a mathematician, but the ongoing work on Islamic tiles lacks the essential historical context that is required to inform the reader of how and when these mathematical techniques developed.

4.2. Professor George Saliba’s View

Referring to the breakthrough the Harvard/Princeton scientists that already stormed the public media, Professor Saliba^[16] wrote:

“I have seen several references to that, and of course in all instances the question of the relationship between the artisans and the mathematicians is brought up.

Thanks for looking into this relationship a little closer, and for finding out that I had already written something about it quite some time ago, and for referring to the article in which I discuss this relationship in Islamic civilization.^[17] I hope this article is read carefully as it should constitute a good warning to those who jump to conclusions way too quickly. History does not work in that fashion, and I for one do not believe, nor can I defend a statement that says that artisans have achieved a breakthrough in the 15th century, or even earlier as some accounts now speculate, that bespoke of quasi-crystalline symmetries when the very concept of crystalline structures and their geometry was not known as far as I can tell. In my article… I warn that we should stick to the exhibitable evidence, preferably textual, before we jump to conclusions on how to interpret artistic designs, no matter how tempting the process of “discovering” breakthroughs is. The warning should be heeded especially when we are always accused of tooting our own horns way too loudly, and thus loosing credibility in the process. And that is why I stick to exhibitable evidence. Not speculation.

Of what I have read so far, the authors of the “discovery” of the breakthrough do not even claim that there was an exhibitable connection between the artisans’ work and the geometry of quasi-crystalline symmetries, and admit that they are speculating, and I agree with them that Islamic civilization never received its fair share of credit. But that does not mean that artisans achieved a breakthrough, the description that gets repeated in the press all over the place, when the very concept of the structures of crystalline symmetries had not even been conceived.

One of the participants in the discussion that I have read is a physicist down at Duke, and he even uses such terms as “almost” got it, but never says that the said symmetries were actually or precisely duplicated. I pay a much closer attention to this innocuous “almost”, just as much as Abu al-Wafa’ al-Buzjani did when he evaluated the artisans’ work of his time. They also “almost” got it.

I withhold comments on the subject until I find the textual evidence I argued for in my article.”

5. The Work of Alpay Özdural

In the work of another scholar, the research on the Islamic complex of mathematics, architecture and art was conducted in another direction. Indeed, recently, Alpay Özdural, a scholar from the Eastern Mediterranean University in North Cyprus, carried on investigations the results of which he published in a series of articles.^[18] Unfortunately, the early passing away on 22 February 2003 of this brilliant scholar has put an end to this wave of promising research.

Large image

Figure 7: Constructions 37 (left) and 42 (right) reconstructed by Alpay Özdural from the anonymous work On Interlocks of Similar or Corresponding Figures (Fi tadakhul al-ashkal al-mutashabiha aw al-mutawafiqa) (ca. 1300).

In one of his articles, Özdural draws conclusions from the analysis of two mathematical sources, On the Geometric Constructions Necessary for the Artisan (Kitab fima yahtaju ilayhi al-saani’ min al-a’mal al-handasiya) by Abu ‘l-Waf al-Buzjani (ca. 940-998), and an anonymous work, On Interlocks of Similar or Corresponding Figures (Fi tadakhul al-ashkal al-mutashabiha aw al-mutawafiqa) (ca. 1300).^[19] These sources provide us with insight into the collaboration between mathematicians and artisans in the Islamic world. Studying this connection, the author presents a series of quotations from these two sources, which show that mathematicians taught geometry to artisans by means of cut-and-paste methods and of geometrical figures that had the potential of being used for ornamental purposes.

Large image

Figure 8: Decorative brickwork on the northern iwan of the Esfahan’s Great Mosque showing clockwise and counterclockwise swastikas in one of the circumferential bands. (Source).

Alpay Özdural points out in particular that the anonymous work on ornamental geometry, On interlocks of similar or complementary figures, appears to be compiled by a scribe at a series of meetings between mathematicians and artisans. Some of those constructions display the highest advancements attained by Muslim mathematicians thus represent the intimate link between theory and praxis that created the intriguing and awe-inspiring ornamental patterns. For instance, three of these are in fact the solutions to problems that require cubic equations. In those times mathematicians solved the cubic equations by means of conic sections; but such solutions were only for demonstration purposes with no practical application. These three constructions in Interlocks of Figures, which records the collaboration of mathematicians and artisans, are the cases of “moving geometry,” that is to say, mechanical procedures that are equivalent to the solutions for cubic equations.^[20]

The first construction is about “a right-angled triangle such that if [a length equal to the shortest side] is cut from the hypotenuse of the triangle towards the shortest side and a perpendicular is erected at the point of cutting, it cuts off the intermediate side at a point where [the distance] from it to the right angle is equal to the perpendicular itself”. The solution is achieved by trial-and-error, i.e., by moving a straightedge around a pivotal point until the required position is reached. It actually corresponds to solving the cubic equationx³ + 2x² – 2x – 2 = 0 giving a real positive value of x=1.17 approximately.

The second construction concerns again the same right triangle; but in this case joining two such triangles facing opposite directions completes the rectangular repeat unit of the ornamental pattern in question. This time the moving instrument was a prototype of the T-square. It revolves around the centre of a circle so that the solution is achieved by the intersection of two implied hyperbolas, which is equivalent to equation x³ – 3x² – x + 1 = 0. The T-square, which appears to be introduced at that particular meeting, was meant to facilitate drawing patterns that involve conic sections. After the invention of this simple drafting instrument, we can interpret by hindsight that transmission of knowledge by way of architectural drawings-mostly ground plans based on square grids-gained impetus.

The third construction consists of four right-angled triangles rotating around a central square so as to form an ornamental pattern. The special property of this triangle is that “the altitude plus the shortest side is equal to the hypotenuse.” Omar Khayyam (1048-1122), the celebrated poet-mathematician, had written a treatise on this triangle and offered the solution of equation x³ – 20x² + 20x – 2000 = 0 by means of conic sections. The solution in Interlocks of Figures was achieved again with the aid of the T-square. In this case, its sliding movement translates the solution of equation x³ – 4x² + 6x – 2 = 0 into the intersection of a circle and a parabola, by way of focus-directrix property. The triangle that Omar Khayyam had discovered has other properties; it embodies what the Greeks called “the musical proportion.” A mathematical analysis of the North Dome Chamber (constructed in 1088-89 CE) of the Great Mosque of Isfahan, reveals that its proportions were generated wholly by Omar Khayyam’s triangle, thus exemplifying the active involvement of prominent mathematicians in the great accomplishments of Islamic architecture.

6. Conclusion

In this short paper, our aim was to review some important results of the ongoing research on the connections of mathematics, architecture and art in Muslim heritage. It is obvious that this survey is far from covering the subject as it deserves. Our hope is that, by drawing the attention to these ongoing debates in scholarly circles, in particular Arab scholars, artists, mathematicians and architects will take a serious interest in this very exciting subject.

7. Bibliography and Resources

• Ball, Philip, “Islamic tiles reveal sophisticated maths“. Published online 22 February 2007 | Nature| doi:10.1038/news070219-9.
• Baron, David,”Medieval Islamic Architecture Presages 20th-Century Mathematics“, Harvard University Gazette, February 22, 2007.
• Degeorge, Gerard, and Porter, Yves, The Art of the Islamic Tile. Paris: Flammarion, 2002.
• Hecht, Jeff,”Medieval Islamic tiling reveals mathematical savvy“, NewScientist.com, 22 February 2007.
• Henderson, Mark, “Amazing maths of the mosaic makers“, The Times (London), 23 February 2007.
• Highfield, Roger,”Islamic tilers may have led scientific field“, The Telegraph (London), 23/02/2007.
• Johnston, Hamish, “Islamic ‘Quasicrystals’ Predate Penrose tiles“, PhysicsWeb.org, 22 February 2007.
• Lu, Peter J., and Steinhardt, Paul J., “Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture,” Science vol. 315, n° 1106 (2007): click here to download the article (in PDF); updated information and services, including high-resolution figures, can be found here.
• Lu, Peter J., and Steinhardt, Paul J., “Supporting Online Material for Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture”: PDF version and further materials.
• Necipoglu, Gülru 1995. The Topkapi Scroll. Geometry and Ornament in Islamic Architecture. Santa Monica CA: The Getty Center for the History of Arts and the Humanities.
• Minkel, J. R., “Islamic Artisans Constructed Exotic Non-repeating Pattern 500 Years Before Mathematicians“, Scientific American online , February 22, 2007.
• Özdural, Alpay, “Omar Khayyam, Mathematicians and Conversazioni with Artisans.” Journal of the Society of Architectural Historians vol 54 (1995): pp. 54-71
• Özdural, Alpay, “On Interlocking Similar or Corresponding Figures and Ornamental Patterns of Cubic Equations.” Muqarnas vol. 13 (1996): pp. 191-211
• Özdural, Alpay, “A Mathematical Sonata for Architecture: Omar Khayyam and the Friday Mosque of Isfahan.” Technology and Culture vol. 39 (1998): pp. 699-715;
• Özdural, Alpay, “Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World.” Historia Mathematica vol. 27 (2000): pp. 171–201.
• Özdural, Alpay “The Use of Cubic Equations in Islamic Art and Architecture”, in Nexus IV: Architecture and Mathematics, edited by José Francisco Rodrigues and Kim Williams. Turin, Italy: Kim Williams Books, 2002.
• Rehmeyer, Julie J., “Ancient Islamic Penrose Tiles“, Sciencenews Online, February 24, 2007, vol. 171, No. 8.
• Saliba, George “Artisans and Mathematicians in Medieval Islam”, Journal of the American Oriental Society, Oct-Dec 1999, vol. 119, pp. 637-645
• Whipps, Heather, “Medieval Islamic Mosaics Used Modern Math“, LiveScience.com, 22 February 2007.

References

[1.] Peter J. Lu and Paul J. Steinhardt, “Decagonal and Quasi-crystalline Tilings in Medieval Islamic Architecture,” Science vol. 315, n° 1106 (2007). See the review FSTC, A Discovery in Architecture: 15th-Century Islamic Architecture Presages 20th-Century Mathematics (published online on www.MuslimHeritage.com in 26 February, 2007) where numerous links to the article published in Science and to supporting online material, as well as links to media coverage resources for interested readers, are provided.
[2.] Girih as defined by Gülrun Necipoglu The Topkapi Scroll: Geometry and Ornament in Islamic Architecture:, Santa Monica, 1995, pp. 92-93): “The girih [is] a highly codified mode of geometric patterning with a distinctive repertoire of algebraically definable elements… The girih mode, with its two- and three-dimensional formulations compiled in surveying examples of pattern scrolls, is characterized by its self-consciously limited vocabulary of familiar, almost emblematic, star-and-polygon compositions generated by invisible grid systems that eliminated a broad spectrum of alternative geometric designs”.
[3.] Ibid
[4.] David Baron, “Medieval Islamic Architecture Presages 20th-Century Mathematics“, Harvard University Gazette, February 22, 2007.
[5.] Steve Connor, “Islamic artists were 500 years ahead of Western scientists”, The Independent (London), Friday, February 23, 2007.
[6.] Ibid
[7.] See on Muqarnas Doris Behrens-Abouseif, “Mukarnas”, Encyclopaedia of Islam, vol. VII, Leiden-New York: E.J.Brill, 1993; Naoko Fukami, “Studies on Muqarnas-vaulting in the Islamic Architecture: 1) the Area of central Asia: Khorasan, Khoarzum and Turan, Journal of the Society of Architectural Historians of Japan No. 22 (1994): pp. 2-36; Naoko Fukami, “Studies on Muqarnas-vaulting in the Islamic Architecture: 2) the Area of Iran: Mazandaran, Azerbaijan, Tehran, Isfahan and Yazd-Fars-kerman”, Journal of the society of Architectural Historians of Japan No. 25 (1996): pp. 23-61; Naoko Fukami, “Studies on Muqarnas-vaulting in the Islamic Architecture: 3) the Areas of Anatolia, Syria and Iraq”, Journal of the society of Architectural Historians of Japan No. 27 (1997): pp. 2-46; Kamil Haydar, Al-’Amarah al-’Arabiyya al-Islamiyyah: al-Khasa’is al-takhtitiyya li-’l-muqarnasat [Arabic Islamic Architecture: Characteristics of Muqarnas], Beirut: Dar al-Fikr al-Lubnani, 1994. For a general bibliography and links, click here.
[8.] Shiro Takahashi, “Muqarnas: A Three-Dimentional Decoration of Islam Architecture“. See especially the “Muqarnas Database” comprising 617 ceiling plans and 1645 examples by Shiro Takahashi): for access, click here.
[9.] The group includes Silvia Harmsen, Susanne Krömker and Michael Winckler (Heidelberg University) and several international cooperation partners: Gülru Necipoglu Sackler (Museum Aga Khan Chair for the History of Architecture, Harvard), Mohammad Al-Assad (Center for the Study of the Built Environment, Amman), and Jan P. Hogendijk (Mathematical Institute, University of Utrecht): click here for more information. An important outcome of the research conducted by this group of scholars concerning al-Kashi’s contribution to architecture was issued as a video tape distributed by The American Mathematical Society: Qubba for al-Kâshî. Video Tape (Heidelberg: Institut für Wissenschaftliches Rechnen, Universität Heidelberg), 1996. Another video tape was produced later on by the same group: Yvonne Dold-Samplonius et al., Magic of Muqarnas: Stalactite Vaults in Islamic Architecture, Video, Duration 18 min, Format PAL or NTSC, May 2005.
[10.] Quoted in Yvonne Dold-Samplonius, “Practical Arabic Mathematics: Measuring the Muqarnas by al-Kashi”, Centaurus vol. 35 (1992), pp. 193-242; idem, “How al-Kashi Measures the Muqarnas: A Second Look”, in Mathematische Probleme im Mittelalter: Der lateinische und arabische Sprachbereich. Edited by Menso Folkerts (Wolfenbütteler Mittelalter-Studien, vol. 10), Wiesbaden: Harrassowitz Verlag, 1996, pp. 56-90.
[11.] On all these varieties of Muqarnas, click here to visit the survey provided by Shiro Takahashi on a large array of plans of, ordered by their geographic and historic relations.
[12.] These plans are reproduced in Ulrich Harb’s book: Ilkhanidische Stalaktitengewolbe Beitrage zu Entwurf und Bautechnik, Berlin: Dietrich Reimer Verlag, 1978.
[13.] See the Project website at Heidelberg University: Muqarnas Visualization in the Numerical Geometry Group.
[14.] Private communication on 25 February 2007.
[15.] See in particular for a first view on the work of this scholar: Branko Grünbaum, Zdenka Grünbaum, G. C. Shephard, “Symmetry in Moorish and Other Ornaments”, in Computers & Mathematics with Applications, Part B 12 (1986), no. 3-4, pp. 641-653; Branko Grünbaum, G. C. Shephard, “Interlace Patterns in Islamic and Moorish Art,” The Visual Mind, Leonardo Book Series, MIT Press, Cambridge, Mass., 1993, pp. 147-155.
[16.] Private communication on 7 March 2007.
[17.] George Saliba, “Artisans and Mathematicians in Medieval Islam”, Journal of the American Oriental Society, vol. 119 (1999), pp. 637-645. In this article, George Saliba reviews the book by Gülru Necipoglu, The Topkapi Scroll: Geometry and Ornament in Islamic Architecture. Getty’s Sketchbooks and Albums, vol. 1. Santa Monica, The Getty Center for the History of Art and the Humanities, 1995.
[18.] Alpay Özdural 1995. “Omar Khayyâm, Mathematicians and Conversazioni with Artisans” Journal of the Society of Architectural Historians vol 54: pp. 54-71 (establishes a connection between a triangle constructed by al-Khayyâm in his treatise of algebra and mosaic drawings); Alpay Özdural, “On Interlocking Similar or Corresponding Figures and Ornamental Patterns of Cubic Equations” Muqarnas (Leiden) vol. 13 (1996): pp. 191-211 (a partial analysis of an Iranian manuscript from the 13th-14th centuries including mosaic drawings that could not be drawn by compass and ruler); Alpay Özdural, “A Mathematical Sonata for Architecture: Omar Khayyam and the Friday Mosque of Isfahan.” Technology and Culture vol. 39 (1998): pp. 699-715; Alpay Özdural, “Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World.” Historia Mathematica vol. 27 (2000): pp. 171–201
[19.] This work can be dated to around 1300 because the mathematician, Abu Bakr al-Khalil al-Tajir al-Rasadi (ca. 1300), is cited twice as one of the participants of the discussions, and the text probably came from Tabr¯iz he capital city of the Ilkhanids, which was the scene of huge construction campaigns under the sponsorship of Gazan Khan and his vizier Rashid al-Din at the turn of the fourteenth century.
[20.] Özdural, Alpay “The Use of Cubic Equations in Islamic Art and Architecture”, in Nexus IV: Architecture and Mathematics, edited by José Francisco Rodrigues and Kim Williams. Turin, Italy: Kim Williams Books, 2002. Click here to read the online abstract.

~ End ~

Back to the table of Context

*Professor Salim T S Al-Hassani, Professorial Fellow, Faculty of Humanities and Arts, University of Manchester; Chairman of Foundation for Science, Technology & Civilisation, (FSTC),UK.

by: Salim T. S. Al-Hassani, Thu 13 August, 2009

THE TRUE MUSLIMAH

All praise and blessings be to Allah,as befits His glory and the greatness of His power and majesty.Peace and blessings be upon our Prophet Muhammad(PBUH), the most noble of Prophets and Messengers whom Allah sent to bring life to arabs and mercy to the world.

The ideal    muslimah is a woman                  of  moral excellence true to her nature,not confused by alien and morally bankrupt ideas.She preserves her self-respect and dignity through her piety in obedience to Allah and His Messenger (PBUH).She is proud of the great position that islam has given her amongst humanity.She performs her duty knowing that her role is clearly defined and that even today her rights are greater than any other ideology provided.She is the role model that every true believer hopes to emulate.

One  of the  prominent features which distinguishes her as a muslim woman is her deep faith in Allah and her sincere conviction to what happens in the universe and whatever fate befalls human beings only happens through the will of Allah.She worships Allah and regularly prays five times a day as ordered by Allah and his Prophet with good intention.She fasts during the month of Ramadhan and performs all the five pillars of islam with obedience and humbleness.She accepts the will and decree of Allah and do away with evil and the forbidden.She feels a sense of responsibility for the members of her family and the society as a whole.She is a role model wherever she finds herself.May we be one of the beloved of                    Allah and among the best of women selected by Allah.May Allah guide us all with his mercy and blessings to the right and straigHt.PATH

Mariam Ali Muhammed

By: Mariam Ali Muhammed.

You are the one above millions

For your modesty and bashfulness

With loving and caring

You are the success of many

For with you they gain strength

Oh Woman of islam,woman of life

You gave them life with your qualities

Qualities that islam bestows on thy

Walking in shyness and humbleness

Full of mercy and kindness

Mercy which flows in abundance

Like the rain of life on earth

Oh Woman of islam,woman of faith

Your beauty fills the heart with passion

All embracing you with compassion

For you are the first school of life

Full of knowledge and understanding

With which you conquered ignorance

Victorious were you that you defeated many

Oh Woman of islam,Woman of faith

Stand firm for the world needs you

Stand firm for you are the world

Bringing all souls together

Under your umbrella of love

Oh Woman of islam,Woman of faith

Indeed you are the beauty of this world

courtesy,

Mariam Ali Muhammed.

Jawad Jafry | Wednesday, April 21st, 2004

The genocide lasted decades. Historians said that the world had never seen

murder and destruction on such a massive scale. Millions died and those left
alive often longed for death. People openly wondered whether the light of Islam
would be forever extinguished. But the course of history changed through some
of God’s most unassuming servants.

In the thirteenth century a tidal wave of devastation swept over the Muslim
world. City after city, region after region disintegrated amidst a storm of
iron and fire. The death toll was incredible.

Nishapur 1,747,000 dead
Baghdad 1,600,000 dead
Herat 1,600,000 dead
Samarkand 950,000 dead
Merv 700,000 dead
Aleppo 50,000 dead
Balkh completely destroyed
Khiva completely destroyed
Harran completely destroyed

Baghdad was often described as the jewel of the world. For six long weeks this
jewel cracked and shattered under the ferocious might of the Tartar hordes.
The rivers of the Tigris and Euphrates ran red with blood. Women who had observed
modest and chaste lives were savagely assaulted and raped. Five centuries of
knowledge accumulated from every literate civilization and contained in the
world’s largest libraries was reduced to ashes. Many of humanity’s
greatest centers of education, commerce and culture became nothing more than
killing fields.

The architect of this colossal avalanche of death was Genghis Khan. His barbaric
legions were triggered into a forty year bloodlust through the folly of the
Muslim ruler, Muhammad Khwarizm Shah. Once a powerful and mighty monarch, Khwarizm
Shah ordered the execution of Mongol caravans that came to trade within his
kingdom. When Genghis Khan sent a delegation of envoys to lodge a formal protest,
Khwarizm Shah executed most of them. These two inhuman acts were avenged at
the cost of millions of innocent lives.

The Tartar Holocaust began in 1218 CE six centuries after the death of the
Prophet Muhammad, peace be upon him. It moved westward from Mongolia across
Central Asia and the Persian Gulf, southward toward Delhi and northwest to Budapest
and Moscow. People as far away as Sweden shuddered at the thought of a Mongol
invasion. Muslims were so overawed by their power that one Mongol could kill
over a hundred Muslims and none would dare defend himself. In Arabic a proverb
sprang up which meant that if someone tells you the Mongols have suffered a
defeat don’t believe him.
On the eve of the Mongol invasion, the spiritual state of the Muslim world was
pathetic. Corruption, disunity, and materialism were rampant. Khwarizm Shah
was not the only example of insufferable leadership. The Abbasid Caliph, Al-Mustasim,
was reportedly pleased to hear of the collapse of Khwarizm Shah’s empire
because of his personal dislike for the monarch. Before the Mongols reached
Baghdad, the Caliph’s advisors had convinced him to seriously scale back the
army. The city was in no way prepared to withstand what lay in store for it.

And yet Islam did not die. Genghis Khan who proclaimed himself as the Scourge
of God, who delighted in the rape of conquered women could not exterminate the
Muslim ummah. Within a generation the tide had begun to turn in Islam’s
favour. Baghdad was destroyed by Genghis’ grandson Halaku but his great
grandson Berek became a Muslim. In fact, Berek withdrew his forces from Halaku’s
army after the fall of Baghdad which contributed to the first defeat the Mongols
suffered against the Muslims during the battle of Ayn Jalut in 1260. The aura
of the Mongols’ terrifying invincibility was broken. Three years later
Berek himself would defeat Halaku’s forces in the Caucus region. Those
who tried to destroy Islam became its protectors.

The role that ordinary Muslims played in this miraculous recovery cannot be
ignored. The entire ummah owes a debt of gratitude to those men and women who
never forgot the centrality of their faith or the importance of sharing it with
others. Berek or Baraka Khan was introduced to Islam by two unknown merchants.
Their efforts eventually led Islam to reach Russia and Eastern Europe.

If the Tartars are regarded as part of Islam’s universal brotherhood
today, one can thank the efforts of unsung heroes like Jamal Uddeen. The vast
Mongol empire was divided amongst the various descendants of Genghis. In certain
parts of the empire, the Mongols regarded Muslims as no better than animals
while Christianity or Buddhism were expected to become the official state religion.
But the sincerity of ordinary believers like Jamal was to outshine all else.

Jamal was a Persian who was travelling through the Middle Kingdom or Chaghatay
Khanate known for its animosity toward Muslims. With his small band of travellers
he mistakenly travelled through the game preserves of the Mongol Prince Tuqluq.
Jamal was arrested and brought before Tuqluq. In his anger the prince told Jamal
that a dog was worth more than a Persian. Jamal replied, “Yes. If we did
not have the true faith, we would indeed be worse than dogs.” Tuqluq was
struck by the reply. He inquired what Jamal meant by the true faith. When Jamal
explained the message of Islam Tuqluq was convinced. He asked Jamal for some
time to unite the fractured Middle Kingdom and then he would proclaim his faith.
Jamal returned home and later fell ill. As he was dying, he instructed his son
Rasheed to remind the prince of his promise when he became king. When Tuqluq
ascended the throne Rasheed set out to meet him. An ordinary person had little
access to royalty and after many efforts Rasheed risked his life to enact a
plan. He called out the adhan at fajr nearby the royal compound. He was brought
before the king and there he invited him to fulfill his promise. On that very
morning Tuqluq Timur Khan, king of the unified Middle Kingdom, became a Muslim.

Death and destruction are ravaging Baghdad once more. The innocent victims
of this injustice must not be forgotten. We owe it to them to follow in the
footsteps of the Last Prophet, in the footsteps of ordinary believers like Jamal
and Rasheed Uddeen and share Islam with each and every human being. The beauty
of our character and our sincere conduct need to be the beacons that attract
those around us to this Divinely prescribed system of life. True it is Allah
alone who guides; it is also true that Allah does not change the condition of
a people until they change what is within themselves. For us to do anything
less would be to disgrace those who are dying before our very eyes.

Historical Sources:
Saviours of the Islamic Spirit, Volume 1, by Abul Hasan Ali Nadwi
History of Islam, Volume 2, by Masudul Hasan
A Short History of the Saracens, by Amir Ali

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