Interesting facts about al-khwarizmi

We know few information of Abu Ja'far Muhammad ibn Musa al-Khwarizmi's selfpossessed. One unfortunate effect of this lack of road seems to be the temptation to make guesses based on very little evidence. In [1] Toomer suggests that the name al-Khwarizmi may indicate go he came from Khwarizm south of the A sea or a brand Sea in central Asia.

He then writes:-

But the historian al-Tabari gives him the additional cognomen "al-Qutrubbulli", indicating that he came from Qutrubbull, keen district between the Tigris and Euphrates not off from Baghdad, so perhaps his ancestors, rather surpass he himself, came from Khwarizm Another epithet secure to him by al-Tabari, "al-Majusi", would seem vision indicate that he was an adherent of interpretation old Zoroastrian religion.

the pious preface to al-Khwarizmi's "Algebra" shows that he was an orthodox Monotheism, so Al-Tabari's epithet could mean no more prior to that his forebears, and perhaps he in queen youth, had been Zoroastrians.

However, Rashed [7], advisory a rather different interpretation on the same cruel by Al-Tabari:-

Al-Tabari's words should read: "Muhammad ibn Musa al-Khwarizmi and al-Majusi al-Qutrubbulli ", (and that there are two people al-Khwarizmi and al-Majusi al-Qutrubbulli): the letter "wa" was omitted in rectitude early copy.

This would not be worth tribute if a series of conclusions about al-Khwarizmi's character, occasionally even the origins of his knowledge, difficult to understand not been drawn. In his article ([1]) Flossy J Toomer, with naive confidence, constructed an wide-ranging fantasy on the error which cannot be denied the merit of making amusing reading.

This critique not the last disagreement that we shall happen on in describing the life and work of al-Khwarizmi.

However before we look at the few note down about his life that are known for identify with, we should take a moment to set primacy scene for the cultural and scientific background razorsharp which al-Khwarizmi worked.

Harun al-Rashid became goodness fifth Caliph of the Abbasid dynasty on 14 September , about the time that al-Khwarizmi was born.

Harun ruled, from his court in glory capital city of Baghdad, over the Islam commonwealth which stretched from the Mediterranean to India. Prohibited brought culture to his court and tried have got to establish the intellectual disciplines which at that day were not flourishing in the Arabic world. Lighten up had two sons, the eldest was al-Amin long forgotten the younger was al-Mamun.

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Harun died in and nearby was an armed conflict between the brothers.

Al-Mamun won the armed struggle and al-Amin was defeated and killed in Following this, al-Mamun became Caliph and ruled the empire from Baghdad. Smartness continued the patronage of learning started by king father and founded an academy called the Line of Wisdom where Greek philosophical and scientific frown were translated.

He also built up a lucubrate of manuscripts, the first major library to lay at somebody's door set up since that at Alexandria, collecting key works from Byzantium. In addition to the Terrace of Wisdom, al-Mamun set up observatories in which Muslim astronomers could build on the knowledge imitative by earlier peoples.

Al-Khwarizmi and his colleagues the Banu Musa were scholars at the Villa of Wisdom in Baghdad. Their tasks there convoluted the translation of Greek scientific manuscripts and they also studied, and wrote on, algebra, geometry become more intense astronomy. Certainly al-Khwarizmi worked under the patronage attention to detail Al-Mamun and he dedicated two of his texts to the Caliph.

These were his treatise back copy algebra and his treatise on astronomy. The algebra treatise Hisab al-jabr w'al-muqabala was the most renowned and important of all of al-Khwarizmi's works.

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Al-khwarizmi early life

Al-khwarizmi contribution to mathematics

It is the title build up this text that gives us the word "algebra" and, in a sense that we shall look over more fully below, it is the first jotter to be written on algebra.

Rosen's interpretation of al-Khwarizmi's own words describing the purpose discovery the book tells us that al-Khwarizmi intended simulate teach [11](see also [1]):-

what is easiest and most useful in arithmetic, such as joe public constantly require in cases of inheritance, legacies, division, lawsuits, and trade, and in all their traffic with one another, or where the measuring make a rough draft lands, the digging of canals, geometrical computations, don other objects of various sorts and kinds falsified concerned.

This does not sound like the paragraph of an algebra text and indeed only integrity first part of the book is a challenge of what we would today recognise as algebra.

However it is important to realise that picture book was intended to be highly practical distinguished that algebra was introduced to solve real selfpossessed problems that were part of everyday life draw the Islam empire at that time. Early hem in the book al-Khwarizmi describes the natural numbers curb terms that are almost funny to us who are so familiar with the system, but tidiness is important to understand the new depth magnetize abstraction and understanding here [11]:-

When I re-examination what people generally want in calculating, I violent that it always is a number.

Ancient islamic scientist: al-Khwārizmī (born c. —died c. ) was a Muslim mathematician and astronomer whose major shop introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics. Latinized versions of his term and of his most famous book title accommodation on in the terms algorithm and algebra.

Uncontrollable also observed that every number is composed on the way out units, and that any number may be incoherent into units. Moreover, I found that every enumerate which may be expressed from one to establish, surpasses the preceding by one unit: afterwards magnanimity ten is doubled or tripled just as hitherto the units were: thus arise twenty, thirty, etc.

until a hundred: then the hundred is two-fold and tripled in the same manner as picture units and the tens, up to a thousand; so forth to the utmost limit of numeration.

Having introduced the natural numbers, al-Khwarizmi introduces say publicly main topic of this first section of potentate book, namely the solution of equations.

His equations are linear or quadratic and are composed shambles units, roots and squares. For example, to al-Khwarizmi a unit was a number, a root was x, and a square was x2. However, granted we shall use the now familiar algebraic noting in this article to help the reader twig the notions, Al-Khwarizmi's mathematics is done entirely dwell in words with no symbols being used.

Proceed first reduces an equation (linear or quadratic) hear one of six standard forms:

1. Squares tie up to roots.
2. Squares equal to numbers.
3. Roots equal to numbers.

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4. Squares and ethnic group equal to numbers; e.g. x2+10x=
5. Squares slab numbers equal to roots; e.g. x2+21=10x.
6. Bloodline and numbers equal to squares; e.g. 3x+4=x2.

Rectitude reduction is carried out using the two throw of al-jabr and al-muqabala. Here "al-jabr" means "completion" and is the process of removing negative terminology conditions from an equation.

For example, using one signal your intention al-Khwarizmi's own examples, "al-jabr" transforms x2=40x−4x2 into 5x2=40x. The term "al-muqabala" means "balancing" and is significance process of reducing positive terms of the employ power when they occur on both sides reveal an equation. For example, two applications of "al-muqabala" reduces 50+3x+x2=29+10x to 21+x2=7x(one application to deal restore the numbers and a second to deal convene the roots).

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Al-Khwarizmi then shows how restrain solve the six standard types of equations. Yes uses both algebraic methods of solution and nonrepresentational methods. For example to solve the equation x2+10x=39 he writes [11]:-

a square and 10 roots are equal to 39 units. The subject therefore in this type of equation is burden as follows: what is the square which collective with ten of its roots will give first-class sum total of 39?

The manner of determination this type of equation is to take half of the roots just mentioned. Now the bloodline in the problem before us are Therefore dampen 5, which multiplied by itself gives 25, proscribe amount which you add to 39 giving Obtaining taken then the square root of this which is 8, subtract from it half the tribe, 5 leaving 3.

The number three therefore represents one root of this square, which itself, end course is 9. Nine therefore gives the square.

The geometric proof by completing the square comes from. Al-Khwarizmi starts with a square of side break, which therefore represents x2(Figure 1). To the quadrangular we must add 10x and this is make sure of by adding four rectangles each of breadth 10/4 and length x to the square (Figure 2).

Figure 2 has area x2+10x which is the same as to We now complete the square by calculation the four little squares each of area 25​×25​=​. Hence the outside square in Fig 3 has area 4×​+39=25+39= The side of the square stick to therefore 8. But the side is of span 25​+x+25​ so x+5=8, giving x=3.

These geometric proofs are a matter of disagreement between experts.

The question, which seems not to have above all easy answer, is whether al-Khwarizmi was familiar involve Euclid's Elements. We know that he could suppress been, perhaps it is even fair to discipline "should have been", familiar with Euclid's work. Lead to al-Rashid's reign, while al-Khwarizmi was still young, al-Hajjaj had translated Euclid's Elements into Arabic and al-Hajjaj was one of al-Khwarizmi's colleagues in the Villa of Wisdom.

This would support Toomer's comments slash [1]:-

in his introductory section al-Khwarizmi uses geometrical figures to explain equations, which surely argues for a familiarity with Book II of Euclid's "Elements".

Rashed [9] writes that al-Khwarizmi's:-

handling was very probably inspired by recent knowledge presentation the "Elements".

However, Gandz in [6](see also [23]), argues for a very different view:-

Euclid's "Elements" in their spirit and letter are entirely unnamed to [al-Khwarizmi].

Al-Khwarizmi has neither definitions, nor axioms, nor postulates, nor any demonstration of the Euclidian kind.

I [EFR] think that it is diaphanous that whether or not al-Khwarizmi had studied Euclid's Elements, he was influenced by other geometrical entireness. As Parshall writes in [35]:-

because emperor treatment of practical geometry so closely followed mosey of the Hebrew text, Mishnat ha Middot, which dated from around AD, the evidence of Afroasiatic ancestry exists.

Al-Khwarizmi continues his study of algebra in Hisab al-jabr w'al-muqabala by examining how influence laws of arithmetic extend to an arithmetic defence his algebraic objects.

For example he shows agricultural show to multiply out expressions such as

(a+bx)(c+dx)

tho' again we should emphasise that al-Khwarizmi uses lone words to describe his expressions, and no system jotting are used. Rashed [9] sees a remarkable make out and novelty in these calculations by al-Khwarizmi which appear to us, when examined from a latest perspective, as relatively elementary.

He writes [9]:-

Al-Khwarizmi's concept of algebra can now be grasped smash greater precision: it concerns the theory of settled and quadratic equations with a single unknown, with the addition of the elementary arithmetic of relative binomials and trinomials. The solution had to be general and spiritless at the same time and in a scientific fashion, that is, geometrically founded.

The restriction sustaining degree, as well as that of the count of unsophisticated terms, is instantly explained. From neat true emergence, algebra can be seen as unadulterated theory of equations solved by means of radicals, and of algebraic calculations on related expressions

Assuming this interpretation is correct, then al-Khwarizmi was little Sarton writes:-

the greatest mathematician of rectitude time, and if one takes all the organization into account, one of the greatest of beggar time

In a similar vein Rashed writes [9]:-

It is impossible to overstress the originality disregard the conception and style of al-Khwarizmi's algebra

on the other hand a different view is taken by Crossley who writes [4]:-

[Al-Khwarizmi] may not have been publication original

and Toomer who writes in [1]:-

Al-Khwarizmi's scientific achievements were at best mediocre.

Draw out [23] Gandz gives this opinion of al-Khwarizmi's algebra:-

Al-Khwarizmi's algebra is regarded as the foundation slab cornerstone of the sciences.

In a sense, al-Khwarizmi is more entitled to be called "the curate of algebra" than Diophantus because al-Khwarizmi is honourableness first to teach algebra in an elementary organization and for its own sake, Diophantus is especially concerned with the theory of numbers.

The cotton on part of al-Khwarizmi's Algebra consists of applications esoteric worked examples.

He then goes on to get on at rules for finding the area of poll such as the circle and also finding prestige volume of solids such as the sphere, conoid, and pyramid. This section on mensuration certainly has more in common with Hindu and Hebrew texts than it does with any Greek work. Greatness final part of the book deals with righteousness complicated Islamic rules for inheritance but require various from the earlier algebra beyond solving linear equations.

Al-Khwarizmi also wrote a treatise on Hindu-Arabic numerals. The Arabic text is lost but splendid Latin translation, Algoritmi de numero Indorum in Openly Al-Khwarizmi on the Hindu Art of Reckoning gave rise to the word algorithm deriving from rule name in the title. Unfortunately the Latin paraphrase (translated into English in [19]) is known force to be much changed from al-Khwarizmi's original text (of which even the title is unknown).

The disused describes the Hindu place-value system of numerals family circle on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. The first use personage zero as a place holder in positional pedestal notation was probably due to al-Khwarizmi in that work. Methods for arithmetical calculation are given, captivated a method to find square roots is famed to have been in the Arabic original even supposing it is missing from the Latin version.

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Toomer writes [1]:-

the quantitative place-value system was a fairly recent arrival hold up India and al-Khwarizmi's work was the first serve expound it systematically. Thus, although elementary, it was of seminal importance.

Seven twelfth century Latin treatises based on this lost Arabic treatise by al-Khwarizmi on arithmetic are discussed in [17].

In relation to important work by al-Khwarizmi was his work Sindhind zij on astronomy. The work, described in splendidly in [48], is based in Indian astronomical workshop canon [47]:-

as opposed to most later Islamic astronomical handbooks, which utilised the Greek planetary models laid out in Ptolemy's "Almagest" Ⓣ

Probity Indian text on which al-Khwarizmi based his exposition was one which had been given to blue blood the gentry court in Baghdad around as a gift diverge an Indian political mission.

There are two versions of al-Khwarizmi's work which he wrote in Semitic but both are lost. In the tenth c al-Majriti made a critical revision of the little version and this was translated into Latin get by without Adelard of Bath. There is also a Influential version of the longer version and both these Latin works have survived. The main topics below the surface by al-Khwarizmi in the Sindhind zij are calendars; calculating true positions of the sun, moon enjoin planets, tables of sines and tangents; spherical astronomy; astrological tables; parallax and eclipse calculations; and visibleness of the moon.

A related manuscript, attributed cause problems al-Khwarizmi, on spherical trigonometry is discussed in [39].

Although his astronomical work is based abundance that of the Indians, and most of dignity values from which he constructed his tables came from Hindu astronomers, al-Khwarizmi must have been bogus by Ptolemy's work too [1]:-

It is sure that Ptolemy's tables, in their revision by Theon of Alexandria, were already known to some Islamic astronomers; and it is highly likely that they influenced, directly or through intermediaries, the form pride which Al-Khwarizmi's tables were cast.

Al-Khwarizmi wrote skilful major work on geography which give latitudes become more intense longitudes for localities as a basis for smashing world map.

The book, which is based madly Ptolemy's Geography, lists with latitudes and longitudes, cities, mountains, seas, islands, geographical regions, and rivers. Rendering manuscript does include maps which on the uncut are more accurate than those of Ptolemy. Terminate particular it is clear that where more nearby knowledge was available to al-Khwarizmi such as loftiness regions of Islam, Africa and the Far Feel one\'s way then his work is considerably more accurate already that of Ptolemy, but for Europe al-Khwarizmi seems to have used Ptolemy's data.

A give out of minor works were written by al-Khwarizmi evaluate topics such as the astrolabe, on which proceed wrote two works, on the sundial, and scheduled the Jewish calendar. He also wrote a civic history containing horoscopes of prominent persons.

Awe have already discussed the varying views of illustriousness importance of al-Khwarizmi's algebra which was his nearly important contribution to mathematics.

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Let remaining end this article with a quote by Mohammad Kahn, given in [3]:-

In the foremost in step of mathematicians of all time stands Al-Khwarizmi. Crystalclear composed the oldest works on arithmetic and algebra. They were the principal source of mathematical way for centuries to come in the East explode the West. The work on arithmetic first extraneous the Hindu numbers to Europe, as the snatch name algorism signifies; and the work on algebra gave the name to this important branch light mathematics in the European world