[lit-ideas] Re: The de-islamization of Europe
- From: "John McCreery" <john.mccreery@xxxxxxxxx>
- To: lit-ideas@xxxxxxxxxxxxx
- Date: Sun, 21 Jan 2007 10:41:07 +0900
On 1/21/07, Eric <eyost1132@xxxxxxxxxxxxx> wrote:
>>Thus Islamic mathematicians invented algebra.
{Wrong answer buzzer sounds] No, they gave a name to it. Archimedes used
algebra in several of his engineering marvels.
A somewhat fuller historical sketch indicates that algebra, like most
enduring advances in human thought, has many different parents.
[See http://www.geocities.com/mathfair2002/school/alg/alg0.htm]
--------------
The History of Algebra
Algebra provides a generalization of arithmetic by using symbols,
usually letters, to represent numbers. For example, it is obviously
true that
2 + 3 = 3 + 2
This arithmetic statement can be generalized using algebra to
x + y = y + x
where x and y can be any number. Algebra has been studied for many
centuries. Babylonian, and ancient Chinese and Egyptian mathematicians
proposed and solved problems in words, that is, using "rhetorical
algebra". However, it was not until the 3rd century that algebraic
problems began to be considered in a form similar to those studied
today.
In the 3rd century, the Greek mathematician Diophantus of Alexandria
wrote his book Arithmetica. Of the 13 parts originally written, only
six still survive, but they provide the earliest record of an attempt
to use symbols to represent unknown quantities. Diophantus did not
consider general methods in Arithmetica, but instead solved a large
number of practical problems.
Several Indian mathematicians carried out important work in the field
of algebra in the 6th and 7th centuries. These include Aryabhatta,
whose book entitled Aryabhatta included work on linear and quadratic
equations, and Brahmagupta, who presented a general solution for a
quadratic equation.
The next major development in the history of algebra was the book
al-Kitab al-muhtasar fi hisab al-jabr wa'l-muqabala ("Compendium on
calculation by completion and balancing"), written by the Arabic
mathematician Al-Khwarizmi in the 9th century. The word algebra is
derived from al-jabr, or "completion". This book developed methods for
solving six different types of quadratic equations, and contained the
first systematic consideration of the subject separately from number
theory.
In about 1100, the Persian mathematician Omar Khayyam wrote a treatise
on algebra based on Euclid's methods. In it he identified 25 types of
equations and made the first formal distinction between arithmetic and
algebra. Some time later during the 12th century, Al-Khwarizmi's works
were translated and became available to Western scholars. In the 13th
century Leonardo Fibonacci wrote some important and influential books
on algebra. Other highly influential works were those of the Italian
mathematician Luca Pacioli (1445-1517), and of the English
mathematician Robert Recorde (1510-1558).
Rules for solving cubic equations were discovered about 1515 by
Scipione del Ferro (c. 1465-1526), and for the quartic equation by
Ludovico Ferrari (1522-1565) about 1545. In 1824 Niels Henrik Abel
(1802-1829) finally proved that, in general, it is not possible to
give general rules of this kind for solving equations of the fifth
degree or higher.
Further contributions to the symbols used in algebra were made in the
late 16th century and the 17th century by Fran輟is Vi鑼e (1540-1603) and
Ren� Descartes, among others.
Complex and negative roots were a later discovery, and took some time
to become accepted. In 1799, Karl Friedrich Gauss proved the
fundamental theorem of algebra, which had been proposed as early as
1629.
In the 19th and 20th centuries algebra has become much more abstract
and has grown to include much more than the theory of equations.
Modern developments in algebra include group theory and the study of
matrices.
--
John McCreery
The Word Works, Ltd., Yokohama, JAPAN
Tel. +81-45-314-9324
http://www.wordworks.jp/
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