Archive | January, 2011

Islam in Brussels

31 Jan

Olivier Servaix, sociologist at Université catholique de Louvain, said in an interview to La Libre Belgique last week that Brussels, would have a Muslim majority in 15-20 years, due to the community’s high birth-rate. According to Servaix, a third of the population of Brussels is Muslim. Since 2001, Mohammed is the most popular name for new-born boys.

Mahfoud Romdhani, a local parliamentarian, says that this projection should be taken carefully, since not all immigrants from Muslim countries are Muslim, or practicing Muslims.

Though this might be true, the youth are showing a return to Islam, and about 75% of Muslims consider themselves practicing today.

Molenbeek is one of the most Muslim suburbs of Brussels. Philippe Moureaux, the mayor of Molenbeek has done much to reach to his Muslim constituency, such as creating a council of mosques subsidized by the municipality, or opening the municipality slaughterhouse during the Eid al-Adha.

Servias says that currently it is peaceful, but there might come a day of social explosion, and somebody might also try to capitalize on the high unemployment in Brussels, over 20%, which affects mainly the Muslim population.

Jean-Francois Bastin (65), a Belgian convert to Islam who now calls himself Abu Abdullah Abdulaziz Bastin, founded the Party of Young Muslims (PJM, Parti Jeunes Musulmans) in 2004. Bastin believes that immigrants should stop feeling colonized and that it’s now time for Belgium to adapt. He wants more visible mosques, calls to prayer, schools and retirement homes. The party received less than 5,000 votes in the previous local elections in its two districts, Molenbeek and Anderlecht.

Source:Islam in Europe

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Unrest in Egypt

30 Jan

Sometimes i really wish i followed up with the news so i’d know what is going on in the world.

Only a while ago i heard about the unrest in Cairo due to the political situation. When we were there, uncle talked to us a little about the government and how Egypt used to be in the past and how it has changed so much because of leaders in the country.

Around 30 minutes ago, i heard on the malay channel on the radio that a few Al-Azhar students are back and they said the unrest was not in all areas but mainly in tahrir and perhaps downtown area. I remember our bus arrived at Tahrir when we returned to Cairo from Siwa. Its a really crowded area especially at night.

From BBC news, i gathered a little more information about the situation in Cairo. Many people are being killed, the army have been called down, a curfew has been made, the police is arresting people…

From Al-jazeera English:

I cant really believe this is happening! We were just there around a month ago and things were well and peaceful. We visited the museum so full of amazing and well-preserved ancient artefacts. It will never be the same again.

From CNN blog:

Egypt’s information ministry announced the shutdown of the Al Jazeera channel in Egypt and the withdrawal of its media license to operate in the country, state-run Nile TV reported Sunday.

– A body was found in front of the country’s interior ministry Sunday morning, but there was no police presence nearby. Meanwhile, military tanks and hundreds of protesters were out on Cairo’s Tahrir Square. No violence was spotted in that area.

– Vandals ripped off the heads off two mummies and tossed relics onto the ground in Cairo’s Egyptian Museum, said Zahi Hawass, secretary-general of Egypt’s Supreme Council of Antiquities. The vandals were arrested and jailed, Hawass said. The museum has stepped up security and is now guarded by Egypt’s army, he said.

– Four people admitted to looting in the Cairo area, according to state-run Nile TV, which aired their confessions.

– People who were trying to protect their property said they are worried about criminal gangs armed with samurai swords, clubs or rifles. Every time a motorcycles drove by, people rushed out to make sure such criminals didn’t stop.

– Ahmed Rehab of the Council of American Islamic Relations said police were absent on Cairo streets. “People are walking around with baseball bats and knives,” Rehab said early Sunday. “We didn’t get any sleep all night.”

– In Alexandria, the scene at hospitals was chaotic. The facilities were short-staffed, and injured protesters said they were not being treated quickly enough.

– At least 31 people have been killed in protests in Alexandria, hospital authorities told CNN Saturday. Earlier, the state-run Nile TV earlier reported that at least 38 people died in the country’s unrest. It was unclear whether the Alexandria deaths were part of that toll.

After reading a few other sources that i understand the gravity of what is going on there now. I really hope aunty and uncle are doing ok there. Ameen.

There are a number of videos and latest updates about what is going on there now on this site.

my little nephew

29 Jan

How love can turn to hate so easily? I read it somewhere but i cant remember. Do you believe it to be true? I couldnt quite understand.

Post partum depression, mothers who fall into depression after the birth of their child. Really sad, i can only imagine.

I am not a mother yet so i wouldnt know right. Of course i can only hope it doesnt befall me, Insyallah.

Sometimes when baby-sitting my little nephew, i experience a myriad of emotions. All crashing and merging together making me all confused.

I’d be resting but the moment i hear through the door that he is awake, i would creep into the living room to just look at him and i know he will smile when he sees company. Doesnt like being alone much. His toothless million dollars smile does something to me. Even though i had no intention of staying, i would find myself sitting next to his bear-baby bed to just watch him make the ‘cat-sound’ and squeal while he tugs involuntarily at his matching baby blue pajamas.

Sometimes, he would tug at them to expose his little bulging tummy and bring his miniature fist into his waiting mouth. Hungry or not, his fist is the favourite thing he places into his mouth. You can stuff the pacifier into his mouth but no he would push it out only to replace its space with his knuckles.

It’ll only be a few minutes before he would start crying slowly at first and then fiercely, till his chubby face turns crimson, if no one gives him some attention. Sometimes i would just squeeze the smiley face which would emit a squeky sound to attract his attention and he will momentarily stop crying. Play a little before his seeks attention again…

The thing about babies is you never know for sure what they want and many first time mothers would just have to practice trial and error. For a non-experienced person like me, when a baby is left in my care, all i want to do is put him to sleep. Even if that is what he wants, he would still cry because he isnt comfortable. One have just got to make eduated guesses as to what is the problem. My brother suggested empathy would help one remain patient when clueless as to what a baby is crying for. Is it really possible? 

Choices are:

he is hungry

he needs a nappy change

he is sleepy

he is just irritated

he wants to burp

he just wants his mummy

So after trying everthing out and he is still awake, by that time, he would be sleepy so making him sleep would be fast and oh boy, would i be relieved. I can stare at him and he looks like an angel, its not that i think he is otherwise but i didnt think i would be happy just staring at him sleeping soundly.

I think to myself, hasnt he grown so fast? He was just a little thing a while ago and now, he is outgrowing his clothes and tub. Amazing isnt it, God’s creation. Subhanallah.

Sometimes i get so frustrated with you because i dont know what you want, please forgive me. I guess that makes me different from a mother.

Arabic science episodes

28 Jan

I enjoyed them so very much, there are 3 episodes. If you watch it on youtube, one episode consist of 6 parts, 10 minutes each. He would go to Cairo, Damascus, Cordoba, Tehran and Baghdad to look at the discoveries of ancient Islamic Scholars.

does everything have to do with the elections?

26 Jan

The sensitive nature of this topic calls for extra careful measures thus it might not be very clear but i would try my best to get the message across.

X said that when s/he wanted the RC’s to help out in some event, they didnt ever so willingly. However, after the elections and political party A (i guess related to the RC’s) lost to political party B (independent party), the RC’s didnt want to help with the event anymore because they ‘wanted to show the residents this is what will happen if they vote for the political party B.

Even though i expect things like that here, it still came as a surprise. Social services can be affected by the politics thus one must be aware of what is going on in the political arena too 🙂

Recently, while reading about property prices, i came across:

“There’s no denying that the recent measures are an election move to placate the public to show that the government is doing something,” says an analyst who wishes to remain anonymous.

Minister Mah confirmed this recently during an interview with the TODAY newspaper.

“If you ask me whether it has got anything to do with the elections, the answer is yes. Everything has got to do with the elections,” he was quoted as saying.

Source: Fit to post

Life is so different now, without me realising it has evolved and now my concerns are so different.

Property prices definitely affect alot of Singaporeans, including myself. While others search for other avenues, others just choose to wait and see. Perhaps the cooling measures might take effect but we have to be patient.

In the movie, HumTum (me and you) the message which the leading actor kept saying throughout the movie was,” Life is a long while.” Is it? And who guranteed you a long while? I feel that my youth is only beginning but it seem to be moving so fast. I look forward to the weekend, and in the blink of an eye, it is over. The question plays in my mind, over and over; is this it? is life supposed to be like that? *gee i sound like im a mid life crisis, only am i not too young to be in such a crisis and too old to be in an identity crisis*

p.s. im quite looking forward to the elections because it is the first time i would be able to exercise my rights to vote.

At first Sight by Nicholas Sparks

25 Jan

I decided this deserves a post on its own and will of course be stored in the Library as well.

I was sceptical when i first saw the book lying on the shelf in the library, not having much time i grabbed it and breezed past the borrowing machine.

Without much hesitation, I started on it almost immediately. I honestly didnt know what to expect as it is not an author known to me though his name does ring a bell. Yea, i found out later that he wrote amongst other books, The Notebook and A Walk to Remember which were adapted by motion pictures.

File:Posternotebook.jpg  Definitely well-written, unlike other romance novels i’ve read. Jude Devereux for instance signature were romantic stories mostly in the old English times or in the countryside.

As for Sandra Brown,  quite different still but the focus is on the romance.

Nicholas Sparks though, made me wonder what would the story be about, the pregnancy? their life after marriage? the wedding plans? some supernatural mystery? Halfway through it, i wondered what else since they seem to be at the happily-ever-after stage already.

I totally didnt expect the last bit which i would say was not what one wants to read but in contrast, it is the harsh reality of life- it is not always happily ever after is it?

I liked the setting too, Boone Creek. Reminded me of Bon temps from True Blood, the country house in Forrest Gump and other movies. It is the quiet life i seek, the life of stillness and peace while enjoying the company of loved ones. I know it might take a lot of getting used for a born and bred city dweller.

Am i just being unappreciative? maybe. and of course the grass is always greener on the other side, isnt it?

History of Trigonometry

24 Jan

It is not all islamic, the people of the past translated into their own language what have been found out from years before their time and developed on it.

As for trigonometry, it started to be known in India for many centuries before someone from Baghdad got hold of the knowledge from the Indians and translated it to Arabic. Similarly for philosophy and astrology, it was translated from the greeks and developed on and sometimes to correct the incorrect notions and theories.

It is a three part article from nrich.maths.org.

part one (read the full version here) Below is a summarized version.

part two : Eudoxus to Ptolemy’s times and the passing of knowledge.

By this time, mathematicians and astronomers had developed a complex mathematically based science, had a wide range of geometrical techniques whereby they measured the Earth, estimated the distances of the Moon and the Sun, developed a theory of the movement of the planets, and precisely catalogued hundreds of stars. A substantial body of geometrically based mathematics had been developed and scholars made commentaries on the works of Euclid, Apollonius, Archimedes, and others. In the next centuries, Diophantos wrote his Arithmetica, which was to inspire Fermat centuries later, Pappus recorded much of the earlier learning for later generations, and contacts along the trade routes began to be made with people in India and China. In September 622 Mohammed made his famous escape from persecution in Mecca to safety in Medina, and within two hundred years, the Arab culture had established an empire from India through the Middle East and North Africa and into Spain.

part three :

The next part of the story can be found here. It tells how from the 10th century CE Arab scholars collected all kinds of knowledge from ‘even as far as China’. They consolidated the techniques of astronomy, and established trigonometry as a distinct branch of mathematics. During the 12th and 13th centuries many of the Arab works were translated into Latin and the ideas passed into the hands of European scholars. Further contributions were made and new material added, and by 1464, when Regiomontanus had read the available material in Greek and Latin, he completed his major work, On Triangles of Every Kind where trigonometry was set out as a series of logically connected theorems, in the style of Euclid.

1. Ancient Instruments and Measuring the Stars

The most ancient device found in all early civilisations, is a “shadow stick”. The shadow cast from a shadow stick was used to observe the motion of the Sun and thus to tell time. Today we call this instrument a Gnomon. The name gnomon comes from the Greek and refers to any L-shaped instrument, originally used to draw a right angle.

Mason's Square

GNomon 1 Gnomon 2Sundial

For more about sundials go to Leo’s article – Brief History of Time Measurement.

Hindu construction for E-W line

Egyptian Merkhet

The Merkhet is one of the oldest known astronomical instruments. It was developed around 600 BCE and uses a plumb line to obtain a true vertical, as in the picture. The other object is the rib of a palm leaf, split at one end to make a thin slit for a sight. Babylonian and Egyptian astronomers were able to measure the altitude and lateral displacement of heavenly objects from a particular direction by using a Merkhet, thus giving the earliest ideas of turning, or angle.

Wall carving of Egyptians using a Merkhet

The Egyptians divided the 360 degrees of the ecliptic into 36 sections of 10 degrees each. [see Note 1 below]. This division was known before 2300 BCE. Each ten degree section (called a decan from the Greek for ten) contained a constellation of stars lined up along the ecliptic. Since the Earth makes a full rotation in 24 hours, the stars in a new decan will rise above the horizon about every 40 minutes. The system of decans was used for determining the night hours and the seasons.
Egyptian Decan Star Chart
The divisions in the top part of the chart represent decans. The chart was read from right to left and the pictures represent Mars (the boat and the bull), Orion with the three stars including the Sun and Moon, Sirius, Jupiter, Saturn, Mercury and Venus. The lower section contains pictures of star gods or demons. They represent some of the most important days of the year. The chart is largely symbolic and functional but does contain pictures of some significant groups of stars.

2. Babylonian Astronomers

lUnar table

As you can see, Neugebauer published the sexagesimal values for twelve measurements of the position of the Moon taken from a clay tablet dated 133/132 BCE.

3. The Hindu Sulbasutras

The Sulbasutras are the only early sources of Hindu mathematical knowledge and originally come from the Vedic period (during the second millennium BCE). The earliest written texts we have from this oral tradition date from about 800 BCE. The Sulbasutras are the instructions for constructing various geometrical shapes to make ‘fire-altars’ using the “Peg and Cord” technique. Each ‘fire-altar’ was a different shape and associated with unique gifts from the Gods.

The Vedic people knew how to find the cardinal directions (NSEW). The Sulbasutras gave procedures for the construction of the altars by starting with a line marking the E-W direction (sun rises in east and sinks in the west), thus the E-W direction had special religious significance.

4. Chinese Astronomy

The Chinese were the most accurate observers of celestial phenomena before the Arabs. “Oracle Bones” with star names engraved on them dating back to the Chinese Bronze Age (about 2,000 BCE) have been found, and very old star maps have been found on pottery, engraved on stones, and painted on the walls of caves.

Surviving records of astronomical observations made by two astronomers Shi Shen and Gan De date from the 4th century BCE.

Shi Shen wrote a book on astronomy, and made a star map and a star catalogue. In 364 BCE Gan De made the first recorded observation of sunspots, and the moons of Jupiter and they both made accurate observations of the five major planets. Their observations were based on the principle of the stars rotating about the pole (equivalent to the earth rotating on its axis).

A famous map due to Su Song (1020-1101) and drawn on paper in 1092 represents the whole sky with the positions of some 1,350 stars.

Chinese Star Map

The equator is represented by the horizontal straight line running through the star chart, while the ecliptic curves above it.

Some elements of Indian astronomy reached China with the expansion of Buddhism (25-220 CE). Later, during the period (618-907 CE) a number of Indian astronomers came to live in China and Islamic astronomers collaborated closely with their Chinese counterparts particularly during (1271-1368).

Islamic Scholar: Nasir Al-Din Al-Tusi

23 Jan

   

(1201-1274 C.E.)

Nasir al-Din was one of the greatest scientists, philosaphers, mathematicians, astronomers, theologians and physicians of the time and was a prolific writer. He made significant contributions to a large number of subjects, and it is indeed difficult to present his work in a few words. He wrote one or several treatises on different sciences and subjects including those on geometry, algebra, arithmetic, trigonometry, medicine, metaphysics, logic, ethics and theology. In addition he wrote poetry in Persian.

One of al-Tusi’s most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. As stated in [1]:-

This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.

This work also contains the famous sine formula for plane triangles:

a/sin A = b/sin B = c/sin C.

Another mathematical contribution was al-Tusi’s manuscript, dated 1265, concerning the calculation of n-th roots of an integer; see [6] for details of a copy of this manuscript made in 1413. This work by al-Tusi is almost certainly not original but rather it is his version of methods developed by al-Karaji‘s school. In the manuscript al-Tusi determined the coefficients of the expansion of a binomial to any power giving the binomial formula and the Pascal triangle relations between binomial coefficients.

We should mention briefly other fields in which al-Tusi contributed. He wrote a famous work on minerals which contains an interesting theory of colour based on mixtures of black and white, and included chapters on jewels and perfumes. He also wrote on medicine, but his medical works are among his least important. Much more important were al-Tusi’s contributions to philosophy and ethics. In particular in philosophy he asked important questions on the nature of space.

A <a href="http://reference.findtarget.com/search/Persia/">Persia</a>n (<a href="http://reference.findtarget.com/search/Iran/">Iran</a>ian) astrolabe from 1208 As the chief scientist at the observatory established under his supervision at Maragha, he made significant contributions to astronomy. The observatory was equipped with the best possible instruments, including those collected by the Mongol armies from Baghdad and other Islamic centres. The instruments included astrolabes, representations of constellations, epicycles, shapes of spheres, etc. He himself invented an instrument ‘turquet’ that contained two planes. After the devoted work of 12 years at the observatory and with the assistance of his group, he produced new astronomical tables called Al-Zij-Ilkhani dedicated to Ilkhan (Halagu Khan). Although Tusi had contemplated completing the tables in 30 years, the time required for the completion of planetary cycles, but he had to complete them in 12 years on orders from Halagu Khan. The tables were largely based on original observa- tions, but also drew upon the then existing knowledge on the subject. The Zij Ilkhani became the most popular tables among astronomers and remained so till the 15th century. Nasir al-Din pointed out several serious shortcomings in Ptolemy’s astronomy and foreshadowed the later dissatisfaction with the system that culminated in the Copernican reforms.

Tusi’s influence has been significant in the development of science, notably in mathematics and astronomy. His books were widely consulted for centuries and he has been held in high repute for his rich contributions.

Sources: ummah.com & history

Islamic Scholar: Al-Haytham

22 Jan

 

A devout Muslim, Ibn al-Haitham believed that human beings are flawed and only God is perfect. To discover the truth about nature, Ibn a-Haitham reasoned, one had to eliminate human opinion and allow the universe to speak for itself through physical experiments. “The seeker after truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them,” the first scientist wrote, “but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration.”

In his massive study of light and vision, Kitâb al-Manâzir (Book of Optics ), Ibn al-Haytham submitted every hypothesis to a physical test or mathematical proof. To test his hypothesis that “lights and colors do not blend in the air,” for example, Ibn al-Haytham devised the world’s first camera obscura, observed what happened when light rays intersected at its aperture, and recorded the results. Throughout his investigations, Ibn al-Haytham followed all the steps of the scientific method.

Kitab al-Manazir was translated into Latin as De aspectibus and attributed to Alhazen in the late thirteenth century in Spain. Copies of the book circulated throughout Europe. Roger Bacon, who sometimes is credited as the first scientist, wrote a summary of Kitab al-Manazir entitled Perspectiva (Optics) some two hundred years after the death of the scholar known as Alhazen.

Ibn al-Haytham conducted many of his experiments investigating the properties of light during a ten-year period when he was stripped of his possessions and imprisoned as a madman in Cairo. How Ibn al-Haytham came to be in Egypt, why he was judged insane, and how his discoveries launched the scientific revolution are just some of the questions Bradley Steffens answers in Ibn al-Haytham: First Scientist, the world’s first biography of the Muslim polymath.

Source.

Ibn al-Haytham’s writings are too extensive for us to be able to cover even a reasonable amount. He seems to have written around 92 works of which, remarkably, over 55 have survived. The main topics on which he wrote were optics, including a theory of light and a theory of vision, astronomy, and mathematics, including geometry and number theory. We will give at least an indication of his contributions to these areas.

A seven volume work on optics, Kitab al-Manazir, is considered by many to be ibn al-Haytham’s most important contribution. It was translated into Latin as Opticae thesaurus Alhazeni in 1270. The previous major work on optics had been Ptolemy‘s Almagest and although ibn al-Haytham’s work did not have an influence to equal that of Ptolemy‘s, nevertheless it must be regarded as the next major contribution to the field. The work begins with an introduction in which ibn al-Haytham says that he will begin “the inquiry into the principles and premises”. His methods will involve “criticising premises and exercising caution in drawing conclusions” while he aimed “to employ justice, not follow prejudice, and to take care in all that we judge and criticise that we seek the truth and not be swayed by opinions”.

Also in Book I, ibn al-Haytham makes it clear that his investigation of light will be based on experimental evidence rather than on abstract theory. He notes that light is the same irrespective of the source and gives the examples of sunlight, light from a fire, or light reflected from a mirror which are all of the same nature. He gives the first correct explanation of vision, showing that light is reflected from an object into the eye. Most of the rest of Book I is devoted to the structure of the eye but here his explanations are necessarily in error since he does not have the concept of a lens which is necessary to understand the way the eye functions. His studies of optics did led him, however, to propose the use of a camera obscura, and he was the first person to mention it.

Book II of the Optics discusses visual perception while Book III examines conditions necessary for good vision and how errors in vision are caused. From a mathematical point of view Book IV is one of the most important since it discusses the theory of reflection. Ibn al-Haytham gave [1]:-

… experimental proof of the specular reflection of accidental as well as essential light, a complete formulation of the laws of reflection, and a description of the construction and use of a copper instrument for measuring reflections from plane, spherical, cylindrical, and conical mirrors, whether convex or concave.

Alhazen’s problem, quoted near the beginning of this article, appears in Book V. Although we have quoted the problem for spherical mirrors, ibn al-Haytham also considered cylindrical and conical mirrors. The paper [36] gives a detailed description of six geometrical lemmas used by ibn al-Haytham in solving this problem. Huygens reformulated the problem as:-

To find the point of reflection on the surface of a spherical mirror, convex or concave, given the two points related to one another as eye and visible object.

Huygens found a good solution which Vincenzo Riccati and then Saladini simplified and improved.

Book VI of the Optics examines errors in vision due to reflection while the final book, Book VII, examines refraction [1]:-

Ibn al-Haytham does not give the impression that he was seeking a law which he failed to discover; but his “explanation” of refraction certainly forms part of the history of the formulation of the refraction law. The explanation is based on the idea that light is a movement which admits a variable speed (being less in denser bodies)

Ibn al-Haytham’s study of refraction led him to propose that the atmosphere had a finite depth of about 15 km. He explained twilight by refraction of sunlight once the Sun was less than 19° below the horizon.

Abu al-Qasim ibn Madan was an astronomer who proposed questions to ibn al-Haytham, raising doubts about some of Ptolemy‘s explanations of physical phenomena. Ibn al-Haytham wrote a treatise Solution of doubts in which he gives his answers to these questions. They are discussed in [43] where the questions are given in the following form:-

What should we think of Ptolemy‘s account in “Almagest” I.3 concerning the visible enlargement of celestial magnitudes (the stars and their mutual distances) on the horizon? Is the explanation apparently implied by this account correct, and if so, under what physical conditions? How should we understand the analogy Ptolemy draws in the same place between this celestial phenomenon and the apparent magnification of objects seen in water? …

There are strange contrasts in ibn al-Haytham’s work relating to Ptolemy. In Al-Shukuk ala Batlamyus (Doubts concerning Ptolemy), ibn al-Haytham is critical of Ptolemy‘s ideas yet in a popular work the Configuration, intended for the layman, ibn al-Haytham completely accepts Ptolemy‘s views without question. This is a very different approach to that taken in his Optics as the quotations given above from the introduction indicate.

One of the mathematical problems which ibn al-Haytham attacked was the problem of squaring the circle. He wrote a work on the area of lunes, crescents formed from two intersecting circles, (see for example [10]) and then wrote the first of two treatises on squaring the circle using lunes (see [14]). However he seems to have realised that he could not solve the problem, for his promised second treatise on the topic never appeared. Whether ibn al-Haytham suspected that the problem was insoluble or whether he only realised that he could not solve it, in an interesting question which will never be answered.

In number theory al-Haytham solved problems involving congruences using what is now called Wilson‘s theorem:

if p is prime then 1 + (p – 1) ! is divisible by p .

In Opuscula ibn al-Haytham considers the solution of a system of congruences. In his own words (using the translation in [7]):-

To find a number such that if we divide by two, one remains; if we divide by three, one remains; if we divide by four, one remains; if we divide by five, one remains; if we divide by six, one remains; if we divide by seven, there is no remainder.

Ibn al-Haytham gives two methods of solution:-

The problem is indeterminate, that is it admits of many solutions. There are two methods to find them. One of them is the canonical method: we multiply the numbers mentioned that divide the number sought by each other; we add one to the product; this is the number sought.

Here ibn al-Haytham gives a general method of solution which, in the special case, gives the solution (7 – 1)! + 1. Using Wilson‘s theorem, this is divisible by 7 and it clearly leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6. Ibn al-Haytham’s second method gives all the solutions to systems of congruences of the type stated (which of course is a special case of the Chinese Remainder Theorem).

Another contribution by ibn al-Haytham to number theory was his work on perfect numbers. Euclid, in the Elements, had proved:

If, for some k > 1, 2k – 1 is prime then 2k-1(2k – 1) is a perfect number.

The converse of this result, namely that every even perfect number is of the form 2k-1(2k – 1) where 2k – 1 is prime, was proved by Euler. Rashed ([7], [8] or [27]) claims that ibn al-Haytham was the first to state this converse (although the statement does not appear explicitly in ibn al-Haytham’s work). Rashed examines ibn al-Haytham’s attempt to prove it in Analysis and synthesis which, as Rashed points out, is not entirely successful [7]:-

But this partial failure should not eclipse the essential: a deliberate attempt to characterise the set of perfect numbers.

Ibn al-Haytham’s main purpose in Analysis and synthesis is to study the methods mathematicians use to solve problems. The ancient Greeks used analysis to solve geometric problems but ibn al-Haytham sees it as a more general mathematical method which can be applied to other problems such as those in algebra. In this work ibn al-Haytham realises that analysis was not an algorithm which could automatically be applied using given rules but he realises that the method requires intuition. See [18] and [26] for more details.

Article by: J J O’Connor and E F Robertson

Source.

Using math in physics and astronomy, Ibn Al-Haytham wrote treaties on the light of the Moon, in which he argues that the moon shines like a self luminous object, though its light is borrowed from the Sun.

He wrote on the Halo and Rainbow, on Spherical Burning Mirrors, on Paraboloidal Burning Mirrors, and on the Shape of an eclipse, which examines the camera obscura phenomena.

Camera Obscura
Karmal al-Din al-Farisi
Istanbul, Fourteenth Century

source.

one of the few movies we watch in the cinema

21 Jan

Honestly, i didnt really like the movie very much. Q said it was an ok movie. What was a little different from any other chick-flick was that she has a disease and that make a whole lot of difference. Honestly, having a sick spouse is normal but having a sick gf seems a little too much trouble. Oh well, all’s sweet in the name of love, right? or not…

I think im getting sick of chick-flicks, like at last because of its predictability and stupidty? Perhaps too strong a word but really, boy meets girl, boy woos girl, girl play hard to get, they go on their first date and end up in the bedroom, they fall in love after having sex a few times. The movie cant end like that, there must be a climax to imitate real life so they will create a reason for boy to leave girl or the other way only to chase the other down and live happily ever after.

There werent any other movies which i’d like to watch and we had free tickets. AND i get to eat popcorn! weeee! How i missed eating them.

While walking there, we saw this place which sells pop corn and oh the aroma of popcorn gets to me every single time! However it was quite costly and we dont know of its halal. Q would prefer to think of it as not halal for his own benefit 😉

It is called Garrett Popcorn and we saw it along Citylink Mall.

Below is the popcorn from the cinema, which we got for free! Yay!