Abu Ja'far Muhammad ibn Musa al-Khwãrizmi 800 A.D. - 847 A.D. Magdalena Mulvihill History of Mathematics

BIOGRAPHY FACTS Born around 780 In Khorasan province of Persia (now in Uzbekistan) and died in Baghdad around 850, no exact dates are known. His name indicates that he was "Muhammed, son of Moses, father of Jafar, from Khwarizm. (Qutrubbull?) Lived in the epicenter of an Islamic empire that stretched from the Mediterranean to India. (near Baghdad) He was an orthodox Muslim (in his youth- adherent of the old Zoroastrian religion.)

MORE FACTS The rulers of the Abbasid dynasty (Caliph al-Ma’mun), founded an academy in Baghdad called the House of Wisdom where the learned men including al-Khwarizmi collected and translated all the scientific works that they could get hold of. Under the rule of al Wathig he was send to investigate the tomb of the Seven Sleepers at Ephesus. Al Khwarizmi was summoned to al Wathig sickbed to predict (cast a horoscope) how long he will live. (50 yr vs. 10 days)

Did you know… He accomplished most of his work in the period between 813 and 833 All of Al-Khwarizimi's works were written in Arabic. The statue of al-Khwarizmi is at the Mirkabir University of Technology in Tehran, Iran. Al-Khwarizmi was one of the earliest and most influential Muslim mathematicians. HE WAS THE FATHER OF ALGEBRA Modern statue of al-Khwarizmi at Khiva, in Ouzbekistan. Photo Alain Juhel.

According to Victor Katz… History of mathematics, brief edition “ The most important contributions of the Islamic mathematicians lie in the are of algebra. They took the material already developed by the Babylonians, combined it with the classical Greek heritage of geometry, and produced a new algebra, which they proceeded to extend. ” The Compendious Book on Calculation by Completion and Balancing It was translated into Latin in the Middle Ages and holds an eminent place in the history of mathematics.

Getting the work done Algebra The Treatise on Hindu numerals Astronomy Geography The Treatise on the Jewish calendar Chronicle

The Treatise on Hindu numerals al Khwarizmi's work on Hindu numerals did not survive in Arabic but has reached us in Latin translation Title “Treatise on calculation with Hindu numerals” or “ Book of addition and subtraction by the method of calculation of the Hindu” It expands the use of numerals 1 to 9 and 0 Place value system Explains various applications It deals with sexagesimal fractions Extractions of the square root The changing face of numerals: Brahmi numerals from India (top); Arabic-Indic numerals, developed and popularised by al-Khwarizmi;

Astronomical work Zij al-sindhind Based ultimately on a Sanskrit astronomical work It is just an another revision of the Zij al-sindhind Important because it’s the first total Arabic astronomical work to survive ( Latin only) Zij al-sindhind – “set of astronomical tables” This translation was the basis of astronomical works by al-Fazari and Ya’gub ibn Tariq in the late eight century Constructed table of sines base 150 (common Hindu parameter) , in extended tables base 60 is used ( more usual in Islamic sine table) Consists of instructions for computation and use of the tables Tables of eclipses, solar declination, and right ascention Various trigonometrical tables Tables closely resemble standard form that Ptolemy used, it is highly likely that they influenced al- Khwarizmi’s tables but basic parameters are derived from Hindu astronomy

Geography Kitab surat al-ard – “Book of the Form of the Earth” It is clear that there is some relationship between this work and Ptolemy’s Geography ( ex. same or systematically different coordinates, by 10, 15,20, minutes; the same places) Almost entirely consist of lists of longitudes and latitudes of cities and localities Cities Mountains Coordinates of extreme points and longitudes Seas Salient points of coastlines and description of their outline Islands Coordinates of their centers, length and breadth Central points of various geographical regions Rivers Salient points and the towns on the

Hubert Dauntich's reconstruction of al-Khwarizmi's map.

Jewish calendar Istikhraj ta’rikh al-yahud – “Extraction of the Jewish Era” Well informed and accurate work Important as evidence for the antiquity of the present Jewish calendar A very short treatise describes the Jewish calendar, the 19-year intercalation cycle Rules for determining on what day of the week the first day of the month Tishri shall fall Calculates interval between Jewish era and the Seleucid era Gives rules for determining the mean longitude of the sun and moon using Jewish calendar

Other work “Book on construction of astrolabe” and “Book on construction of astrolabe” Determination of sun’s altitude Of the ascendant and of ones terrestrial latitude “Chronicle” Did not survive but several historians quote it as an authority for events in the Islamic period Scientific achievements were at best mediocre, but uncommonly influential The other works did not achieve success of such magnitude as Algebra

ALGEBRA the practical manual, not a theoretical one The compendious book on calculation by completion and balancing Al-jabr – can be translated as “restoring or compliting” and refers to the operation of transporting a subtracted quantity from one side of an equation to the other side, where it becomes an added quantity. Al-magubala – can be translated as “comparing or balancing” and refers to a reduction of a positive term by subtracting equal amounts from both sides of the equation. Ex. 3x+2=4-2x al-jabr 3x+2x+2=4 5x +2 -2 =4 -2 al-magubala 5x=2 First part of the book is the work of elementary practical mathematics, it provides what is easiest and most useful in arithmetic Cases that men were concern about: partition lawsuits, inheritance, trade, measuring of land or digging canals

ALGEBRA The quantities he dealt with were generally of three kinds. Al-Khwarizmi reduced them to six standard forms of linear and quadratic equations. The square (of the unknown) The root of the square (the unknown itself) The absolute numbers (the constants in the equation) Such elaboration of six-fold classifications is necessary because Islamic mathematicians did not recognize the existence of negative numbers or zero as a coefficient.

ALGEBRA Squares are equal to roots ax2 =bx Square are equal to numbers ax2 =c Roots are equal to numbers bx =c Squares and roots are equal to numbers ax2 + bx = c Square and numbers are equal to roots ax2 + c = bx Roots and numbers are equal to squares bx + c = ax2 where a, b, c are positive integers

LITERAL TRANSLATION “A quantity :I multiplied a third of it and a dirham(a unit) by a fourth of it and a dirham: it becomes twenty. It’s computation is that you multiply a third of something by a fourth of something: it comes to a half of a sixth of a square. And you multiply a dirham by a third of something; and multiply a dirham by a fourth of something to get a fourth of something; and a dirham by a dirham to get a dirham. Thus its total, a half of a sixth of a square and a third of something and a quarter of something and a dirham, is equal to twenty dirhams.” (x/3+1)(x/4+1)=20 X2/12 +x/3 +x/4 +1=20

Algebra Second part of the book has a short section on business transactions Expounds the “rule of three” How to determine the fourth member in a proportion sum where two quantities and one price, or two prices and one quantity, are given. Third part concerns practical mensuration Rules for finding the are of various plane figures, including circle Finding the volume of a number of solids, including cone, pyramid, and truncated pyramid.

ALGEBRA AL-KITAB AL MUKHTASAR FI HISAB AL-JABR WA’LMUQABALA Or In algebra Al-Khwarizmi explains how to reduce any given problem to one of these standard forms. This is done by the use of al-jabr and al-muqabula combined with other arithmetical operations. That’s where the title of his book came from. AL-KITAB AL MUKHTASAR FI HISAB AL-JABR WA’LMUQABALA Or The Compendious Book on Calculation by Completion and Balancing

Recources The dictionary of scientific biography www.gap-system.org/~history/Biographies/Al-Khwarizmi.html www.en.wikipedia.org/wiki www.cosmosmagazine.com (the science of everything) Credit: Science and Islam, Icon Books Ltd