Al-Khwarizmi was a Persian mathematician who spent most of his life in Baghdad. He lived during the reign of Caliph al-Ma’mum of the Abbasid caliphate.

Al-Khwarizmi is considered the ‘father of algebra’. In 825 AD, Al-Khwarizmi wrote his first book in Arabic to explain the Hindu system. It was titled Al-Khwarizmi on the Hindu Art of Calculating. The book introduced the use of the Hindu numerals 1-9, the number zero, and the place value system still in use today.

Around 830 AD he wrote another important book on algebra, Kitab al-mukhtasar fi hisab al-jabr wa’l-muqabaa (The Compendious Book in Calculation by Completion and Balancing) became the starting point of algebra in the Islamic world and it also gave its title to serve the western name for the subject.

It was the first book on the systematic solution of linear and quadratic equations and is sometimes referred to by the shortened title Algebra. The book regarded as the foundation and cornerstone of mathematics.

## The origin of the word ‘Algorithm’

The word “algorithm” itself is quite interesting; at first glance, it may look as though someone intended to write “logarithm” but jumbled up the first four letters. The word did not appear in Webster’s New World Dictionary as late as 1957; we find only the older form “algorism” with its ancient meaning, i.e., the process of doing arithmetic using Arabic numerals. In the middle ages, abacists computed on the abacus and algorists computed by algorism. Following the middle ages, the origin of this word was in doubt, and early linguists attempted to guess at its derivation by making combinations like algiros [painful] + arithmos [number]; others said no, the word comes from “King Algor of Castile.” Finally, historians of mathematics found the true origin of the word algorism: it comes from the name of a famous Persian textbook author, Abu Ja’far Mohammed ibn Mûsâ al’Khowârizmî (c. 825)-literally, “Father of Ja’far, Mohhamed, son of Moses, a native of Khowârizm.” Khowârizm is today the small Soviet city of Khiva. Al’Khowârizmî wrote the celebrated book Kitab al jabr w’al’muqabala (“Rules of restoration and reduction”); another word, “algebra,” stems from the title of his book, although the book wasn’t really very algebraic.

Gradually the form and meaning of “algorism” became corrupted; as explained by the Oxford English Dictionary, the word was “erroneously refashioned” by “learned confusion” with the word arithmetic. The change from “algorism” to “algorithm” is not hard to understand in view of the fact that people had forgotten the original derivation of the word. An early German mathematical dictionary, Vollstandiges Mathematisches Lexicon (Leipzig, 1747), gives the following definition for the word Algorithmus: “Under this designation are combined the notions of the four types of arithmetic calculations, namely addition, multiplication, subtraction, and division.” The Latin phrase algorithms infinitesimals was at that time used to denote “ways of calculation with infinitely small quantities, as invented by Leibnitz.”

Al-Khwarizmi emphasized that he wrote his algebra book to serve the practical needs of the people concerning matters of inheritance, legacies, partition, lawsuits, and commerce.

Abu Abdullah Mohammad Ibn Musa al’Khowârizmî was a mathematician, astronomer, and geographer. He was perhaps one of the greatest mathematicians who ever lived, as, in fact, he was the founder of several branches and basic concepts of mathematics. He influenced mathematical thought to a greater extent than any other medieval writer. His work on algebra was outstanding, as he not only initiated the subject in a systematic form but he also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra. The very name Algebra has been derived from his famous book Al’Jabr wa’al’Muqabilah. His arithmetic synthesized Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science.

He treated (probably for the first time) the handling of the elementary arithmetic operations with respect to the Hindu-Arabic decimal numerals. About 750 A.D., the Hindu principles of decimal arithmetic were brought to Persia, as several important works were translated into Arabic. Not long after this, al’Khowârizmî wrote his Arabic textbook on the subject. His work was a strong influence on Leonardo Pisano (Fibonacci), whose book on arithmetic (1202 A.D.) played a major role in the spreading of Hindu-Arabic numerals into Europe.

The importance of Khowârizmî’s works was recognized in the twelfth century by the West, when Adelard de Bath (who has been called the first English scientist, 1080 – 1160), Gerard of Cremona (Italy, 1117 – 1187) and others translated his works into Latin where it was used by the Western scholars as to the principal mathematical textbook at European universities until the 16th century.

Al-Khwarizmi worked most of his life in the Baghdad House of Wisdom (Bayt al-Hikma), a library, translation institute, and place of learning that was a major intellectual center of the Islamic Golden Age.

His full name is Abu Abdallah Muhammad ibn Musa Al-Khwarizmi. The last-mentioned name (his nisba) refers to his birthplace, Khwarizm, modern Khiva, south of the Aral Sea. He was born around 780 in the town of Kath part of Khwarizm. Kath is now buried in the sand. He died around 850. He was summoned to Baghdad by Caliph Al-Ma’mun and appointed court astronomer. From the title of his work, Hisab Al-Jabr wal Muqabalah (Book of Calculations, Restoration and Reduction), Algebra (Al-Jabr) derived its name.

Al-Khwarizmi emphasized that he wrote his algebra book to serve the practical needs of the people concerning the matters of inheritance, legacies, partition, lawsuits and commerce. He considered his work as worship to God.

## Al Khwarizmi’s identity and the quadratic formula

Al Khwarizmi is often considered the father of algebra, due to an influential text he wrote, and his name is the origin of the term algorithm. His `completing-the-square’ technique lies at the heart of a beautiful formula that we call al Khwarizmi’s identity. The usual quadratic formula is a consequence.

here we will show you how:

– will see how the completing-the-square leads to al Khwarizmi’s identity

– how the quadratic formula follows from al Khwarizmi’s identity

– use the quadratic formula to factor quadratic polynomials.

This step is probably the algebraic highlight of the course and the most detailed steps. On this page is a very important derivation. Make sure you proceed slowly and carefully, please check all the steps by writing things out line by line, and then apply your understanding to work out the answers to the questions. This is how we learn mathematics.

Solving a quadratic equation using completing the square

Suppose we want to solve the quadratic equation

x^{2}−14−1887=0.

Half of the coefficient of x is −7, so we take the 1887 to the other side, and add the square of −7

to both sides. This gives

x^{2}−14+49=1887+49=1936.

Now we rewrite the left-hand side as a perfect square:

(x−7)^{2}=1936.

At this stage we have to “take the square root” of 1936

. What does this mean? It means finding a number with the property that 2=1936. In this case, such a number actually exists: it is =44. But otherwise, we would just write ±√1936

to represent an approximate square root and it’s negative. We can’t forget about the negative, since we want two solutions!

So in our case x−7=44 or −7=−44. Thus we do get two solutions, namely =51 or =−37.

more at https://www.futurelearn.com/courses/maths-linear-quadratic-relations/0/steps/117435

## Some other Contributions

### Improvements in Sundials

Sundial is an instrument that shows time with the help of the position of the Sun. The sun forms a shadow of the pointer on a plate which contains marks of the time period. The shadow of the pointer rotates on the marks when the sun changes its position. Al-Khwarizmi improved the design of sundials and made them a universal instrument for checking the time in any part of the world.

### Map Development

Al-Khwarizmi developed an accurate map of that time with the help of 70 geographers.

– The Soviet Union issued a stamp in 1983 on which an image of Al-Khwarizmi was engraved.

– The Amir Kabir University of Tehran in Iran has placed the statue of Al-Khwarizmi.

– Al-Khwarizmi became the head of Dar-ul-Hikmat (House of Wisdom) at the time of Muslim Caliph Mamun.

References:

http://www.disc-conference.org

https://muslimheritage.com

https://www.sapaviva.com

https://www.futurelearn.com

https://www.researchgate.net

https://science4fun.info

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