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 Springs of Islamic civilization

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PostSubject: Springs of Islamic civilization   Mon 5 Oct - 21:15

Al-Khwarizmi

The
springs which fed Islamic civilization sprang from many lands. Symptomatic of
this is the fact that the family of its greatest early scientist, the Central
Asian scholar Muhammad ibnMusa al-Khwarizmi, came from the old and high
civilization that had grown up inthe region of Khwarizm. This is the ancient
name for the region around Urgenchin the U.S.S.R., a city near the delta of the
Amu Dar'ya (Oxus) River on the Aral Sea.

Al-Khwarizmi served the Caliph al-Ma'mun in the House of Wisdom and is
connected to a later caliph, al - Wathiq (842 - 847), by the following story
told by the historian al - Tabari. It seems that when al-Wathiq was stricken by
a serious illness he asked al-Khwarizmi to tell from his horoscope whether or
not he would survive. Al- Khwarizmi assured him he would live another fifty
years, but al-Wathiq died in ten days. Perhaps al-Tabari tells this story to
show that even great scientists can make errors, but perhaps he told it as an
example of al-Khwarizmi's political astuteness. The hazards of bearing bad news
to a king, who might mistake the bearer for the cause, are well known.

Al-Khwarizmi's principal contributions to the sciences lay in the four areas of
arithmetic, algebra, geography and astronomy. In arithmetic and astronomy he
introduced Hindu methods to the Islamic world, while his exposition of algebra
was of prime importance in the development of that science in Islam. Finally,
his achievements in geography earn him a place among the ancient masters of
that discipline.

His arithmetical work The Book of Addition and Subtraction According to the
Hindu Calculation
introduced the very useful decimal positional system that
the Hindus had developed by the sixth century A.D., along with the ten ciphers
which make that system, the one we use today, so convenient. His book was the
first Arabic arithmetic to be translated into Latin, and its influence on
Western mathematics is illustrated by the derivation of the word algorithm.
This word is in constant use today in computing science and mathematics to
denote any definite procedure for calculating something, and it originated in
the corruption of the name al- Khwarizmi to the Latin version algorismi.

Al-Khwarizmi's book had an equally important effect on Islamic mathematics, for
it provided Islamic mathematicians with a tool that was in constant - though
not universal - use from the early ninth century onward. From the oldest
surviving Arabic arithmetic, Ahmad al-Uqlidisi's Book of Chapters, written
ca. A.D.950, to the encyclopedic treatise of 1427 by Jamshid al-Kashi, The
Calculators' Key,
decimal arithmetic was an important system of calculation
in Islam. By the mid-tenth century Ahmad b. Ibrahim al-Uqlidisi solved some
problems by the use of decimal fractions in his book on Hindu arithmetic, so
that in a little over a century al- Khwarizmi's treatise had led to the
invention of decimal fractions. These too were used by such Islamic
mathematicians as al-Samaw'al ben Yahya al-Maghribi in the twelfth century to
find roots of numbers and by al-Kashi in the fifteenth century to express the
ratio of the circumference of a cirlce to its radius as 6.2831853071795865, a
result correct to sixteen decimal places.




Arithmetic
was only one area in which al- Khwarizmimade important contributions to
Islamic mathematics. His other famous work, written before his Arithmetic, is
his Kitab al-jabr wa l-muqabala (The Book of Restoring and Balancing),
which is dedicated to al-Ma'mun. This book became the starting point of the
subject of algebra for Islamic mathematicians, and it also gave its title to
serve as the Western name for the subject, for algebra comes from the
Arabic al-jabr. In this book a variety of influences are evident,
including Babylonian and Hindu methods that lead to solutions of what we would
call quadratic equations and Greek concerns with classification of problems
into different types and geometrical proofs of the validity of the methods
involved.

The synthesis of Oriental procedures with Greek proofs is typical of Islam, as
is the application of a science to religious law, in this case the thorny
problems posed by Islamic inheritance law. A large part of the book is devoted to
such problems, and here again al- Khwarizmi's example became the model for
later Islamic writers. Thus, after the time of al- Khwarizmi, Abu Kamil, known
as "The Egyptian Reckoner", also wrote on the application of algebra
to inheritance problems.

Finally, we must comment on al- Khwarizmi's contribution to the science of
cartography. He was part of the team of astronomers employed by al-Ma'mun to
measure the length of one degree along a meridian. Since the time of
Aristotle(who wrote in the middle third of the fourth century B.C.), men had
known that the earth was spherical and, hence, that multiplication of an
accurate value for the length of one degree by 360 would lead to a good
estimate for the size of the earth. In the century after Aristotle the scientist
Eratosthenes of Alexandria, who was the first scientist to be appointed
Librarian of the famous library in that city, used this idea with his knowledge
of mathematical astronomy to obtain an estimate of 250,000 stades for the
circumference of the earth. This was later shortened by an unknown author to
180,000 stades, a figure far too small but adopted by the astronomer, Klaudios
Ptolemaios (Ptolemy) in his Geography.

We know that the Hellenistic stade is approximately 600 feet but this was not
known to the caliph al-Ma'mun. As al-Biruni says in his Coordinates of
Cities,
al-Ma'mun "read in some Greek books that one degree of
themeridian is equivalent to 500 stadia..... However, he found that its actual
length [i.e. the stade's] was not sufficiently known to the translators to
enable them to identify it with local standards of length." Thus
al-Ma'munordered a new survey to be made on the large, level plain of Sinjar
some 70miles west of Mosul,
and two surveying parties participated. Starting from a common location one
party traveled due north and the other due south. In the words of al-Biruni:


Each party observed the meridian altitude of the sun until they
found that the change in its meridian altitude had amounted to one degree,
apart from the change due to variation in the declination. While proceeding on
their paths, they measured the distances they had traversed, and planted arrows
at different stages of their paths (to mark their courses). While on their way
back, they verified, by a second survey, their former estimates of the lengths
of the courses they had followed, until both parties met at the place whence
they had departed. They found that one degree of a terrestrial meridian is
equivalent to fifty-six miles. He (Habash) claimed that he had heard Khalid
dictating that number to Judge Yahya b. Aktham. So he heard of that achievement
from Khalid himself.


Again one
sees an Islamic side to this project in the involvement if a jurist, for the
law was the Islamic religious law and in this case the jurist (qadi in
Arabic) was the chief justice of Basra,
Yahya b. Aktham. Al-Biruni goes on to say that a second result was also
obtained by the survey, namely 56 2/3miles/degree, and in fact al-Biruni uses
this value in his own computations later on.


Al- Khwarizmi's
contribution went beyond this to assist in the construction of a map of the
known world, a project that would require solving three problems that combined
theory and practice. The first problem was mainly theoretical and required
mastery of the methods, such as those explained by Ptolemy in the mid-second
century A.D., for mapping a portion of the surface of a sphere (the earth) onto
a plane. The second was to use astronomical observations and computations to
find the latitude and longitude of important places on the earth's surface. The
difficulties involved here are both theoretical and practical. The third
problem was to supplement these observations by reports of travelers (always
more numerous and usually less reliable then astronomers ) on journey-times
from one place to another. Among al-Khwarizmi's achievements in his
geographical work The Image of the Earth were his correction of
Ptolemy's exaggerated length of the Mediterranean Sea
and his much better description of the geography of Asia
and Africa. With such a map the caliph could
survey at a glance the extent and shape of the empire he controlled.

Thus it was that on his death al-Khwarizmi's legacy to Islamic society included
a way of representing numbers that led to easy methods of computing, even with
fractions, a science of algebra that could help settle problems of inheritance,
and map that showed the distribution of cities, seas and islands on the earth's
surface.




This article is excerpted from the book "Episodes in the
Mathematics of Medieval Islam" by J. L. Berggren.
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Habib

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PostSubject: Re: Springs of Islamic civilization   Sun 15 Aug - 14:04

All these facts are undiscussable yet neglected by the West
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Red1
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PostSubject: Re: Springs of Islamic civilization   Sun 22 Aug - 23:40

The right things were done


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Habib

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PostSubject: Re: Springs of Islamic civilization   Fri 8 Oct - 21:07

Quote :
Al- Khwarizmi's
contribution went beyond this to assist in the construction of a map of the
known world, a project that would require solving three problems that combined
theory and practice. The first problem was mainly theoretical and required
mastery of the methods, such as those explained by Ptolemy in the mid-second
century A.D., for mapping a portion of the surface of a sphere (the earth) onto
a plane. The second was to use astronomical observations and computations to
find the latitude and longitude of important places on the earth's surface. The
difficulties involved here are both theoretical and practical. The third
problem was to supplement these observations by reports of travelers (always
more numerous and usually less reliable then astronomers ) on journey-times
from one place to another. Among al-Khwarizmi's achievements in his
geographical work The Image of the Earth were his correction of
Ptolemy's exaggerated length of the Mediterranean Sea
and his much better description of the geography of Asia
and Africa. With such a map the caliph could
survey at a glance the extent and shape of the empire he controlled.

Sorry to post a reply again. I was attracted by the topic and wanted to point out this idea
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