Arab contributions to mathematics and the introduction of the Zero
J Morgan
Regional, Science, 4/22/1998
Arab contributions to human civilization are noteworthy. In arithmetic
the style of writing digits from right to left is an evidence of its
Arab origin. For instance, the numeral for five hundred in English
should be written as 005, not as 500 according to English's
left-to-right reading style.
Another invention that revolutionized mathematics was the introduction
of the number zero by Muhammad Bin Ahmad in 967 AD. Zero was introduced
in the West as late as the beginning of the thirteenth century. Modern
society takes the invention of the zero for granted, yet the Zero is a
non-trivial concept, that allowed major mathematical breakthroughs.
Arab civilizations also made a great contribution to fractions and to
the principle of errors, which is employed to solve Algebra problems
arithmetically.
Concerning Algebra, al-Khawarzmi is credited with the first treatise. He
solved Algebra equations of the first and second degree (known as
quadratic equations, and are are prevelant in science and engineering)
and also introduced the geometrical method of solving these equations.
He also recognized that quadratic equations have two roots. His method
was continued by Thabet Bin Qura, the translator of Ptolemy's works who
developed Algebra and first realized application in geometry. By the
11th century the Arabs had founded, developed and perfected geometrical
algebra and could solve equations of the third and fourth degree.
Another outstanding Arab mathematician is Abul Wafa who created and
successfully developed a branch of geometry which consists of problems
leading to equations in Algebra of a higher degree than the second. He
made a number of valuable contributions to polyhedral theory.
Al-Karaki, of the 11th century is considered to be one of the greatest
Arab mathematicians. He composed one arithmetic book and another on
Algebra. In the two books, he developed an approximate method of finding
square roots, a theory of indices, a theory of mathematical induction
and a theory of intermediate quadratic equations.
Arabs have excelled in geometry, starting with the transition of Euclid
and conic section of Apolonios and they preserved the genuine works of
these two Greek masters for the modern world, by the 9th century AD. and
then started making new discoveries in this domain.
In his book translated by Roger Bacon, Ibn al-Haitham wrote a book on
geometrical optics, dealing with problems that would be difficult to
solve even now.
It is also at the hand of the Arabs that the geometry of conic sections
was developed to a great extent.
However, Arab achievements in this field were crowned by the discovery
made by Abu Jafar Muhammad Ibn Muhammad Ibn al-Hassan, known as
Nassereddine al-Tusi. Al-Tusi separated trigonometry from astronomy.
This contribution recognizes and explains weakness in Euclid's theory of
parallels, and thereby may thus be credited as founder of non-Euclidian
geometry.
http://www.arabicnews.com/ansub/Daily/Day/980422/1998042208.html
dsharavi
> Arab contributions to mathematics and the introduction of the Zero
> Regional, Science, 4/22/1998
> Arab contributions to human civilization are noteworthy.
The Impending Collapse of Arab Civilization
Lieutenant Colonel James G. Lacey, U.S. Army Reserve
U.S. Naval Institute Proceedings, September 2005
[...]
Interestingly, on the Arab League's website there is a paper that
details all of the contributions made by Arab civilization. It is a
long and impressive list, which unfortunately marks 1406 as the last
year a significant contribution was made. That makes next year the
600th anniversary of the beginning of a prolonged stagnation, which
began a dive into the abyss with the end of the Ottoman Empire. Final
collapse has been staved off only by the cash coming in from a sea of
oil and because of a few bright spots of modernity that have resisted
the general failure.
Statistics tell an ugly story about the state of Arab civilization.
According to the U.N.'s Arab Human Development Report:
There are 18 computers per 1000 citizens compared to a global average
of 78.3.
Only 1.6% of the population has Internet access.
Less than one book a year is translated into Arabic per million
people, compared to over 1000 per million for developed countries.
Arabs publish only 1.1% of books globally, despite making up over 5%
of global population, with religious books dominating the market.
Average R&D expenditures on a per capita basis is one-sixth of Cuba's
and less than one-fifteenth of Japan's.
The Arab world is embarking upon the new century burdened by 60
million illiterate adults (the majority are women) and a declining
education system, which is failing to properly prepare regional youth
for the challenges of a globalized economy. Educational quality is
also being eroded by the growing pervasiveness of religion at all
levels of the system. In Saudi Arabia over a quarter of all university
degrees are in Islamic studies. In many other nations primary
education is accomplished through Saudi-financed madrassas, which have
filled the void left by government's abdication of its duty to educate
the young.
In economic terms we have already commented that the combined weight
of the Arab states is less than that of Spain. Strip oil out of
Mideast exports and the entire region exports less than Finland.
According to the transnational Organization for Economic Cooperation
and Development (OECD), regional economic growth is burdened by
declining rates of investment in fixed capital structure, an inability
to attract substantial foreign direct investment, and declining
productivity - the economic trinity of disaster.
Economic stagnation coupled with rapid population growth is reducing
living standards throughout the region, both comparatively and in real
terms. In the heady days of the late 1970s oil boom, annual per-capita
GDP growth of over 5% fueled high levels of expectations. GDP
per-capita grew from $1,845 to $2,300. Today, after adjusting for
inflation, it stands at $1,500, reflecting an overall decline in
living standards over 30 years. Only sub-Saharan Africa has done
worse. If oil wealth is subtracted from the calculations the economic
picture for the mass of Arab citizens becomes dire.
Things are indeed bad in the Arab world and will get much worse.
This statement should not be read as mere opinion. While predictions
of the future are usually fraught with peril, those based on
demographics are, barring some unforeseen plague or truly catastrophic
war, uncannily accurate. Using even the most optimistic
assumption-that fertility rates drop by fifty percent in a
generation-the respected Population Resource Center, based in
Princeton, New Jersey, expects Arab populations to grow from 280
million to almost 460 million by 2020 and to over 600 million a
generation later. On the face of it the Arab world is staring
political and economic disaster in the face. Arab governments and
institutions are already failing to meet basic human needs in many
Arab countries. It is hard to imagine how they will cope with the
stress of such a massive population increase.
The percentage of the population under age 15 is double that of
Western Europe and those under age 24 make up 50% to 65% of Middle
East countries-an astonishingly young population. This youth bulge is
already beginning to rock the foundations of Islamic society. Upheaval
and revolution are the likely results of a massive number of youth
confronted by stagnating or collapsing economies as they enter
adulthood.
A youth bulge has always correlated strongly with increased levels of
violence within a society, from terrorism to war. Massive youth
violence is predictably more likely when lack of economic opportunity
stunts ambitions for a satisfying job, a good marriage, and a home. A
2004 study by The World Bank calls this combination of a youth bulge
coupled with poor economic performance an "explosive combination." In
socially and politically repressive societies, found throughout the
Middle East, there are very few outlets for pent-up frustrations
except for violence or immersion into religion-a combustible mixture.
In the Middle East, it is evident that terrorism and especially
suicide operations are a phenomenon closely associated with youth.
Youthful involvement in terrorism can be viewed as the extreme end of
a broader youthful attraction to violence more generally.
Additionally, this attraction is being reinforced within a generation
that is being radicalized by an environment featuring high levels of
violence, radical religious ideology, and growing anti-Americanism.
One serious question that requires an answer is why youth are
attracted to Islamic organizations, which to Western eyes appear to be
extremely repressive to many of the aspirations and desires of typical
young men and women? In a 2003 Brookings Institution paper, Graham
Fuller, a senior resident consultant at the RAND Corporation, provides
this answer:
. . . the religious activism of Islamism in the Muslim world is not
politically conservative at all: it calls for change to the status quo
that is broadly hated. Much of the youthful spirit of rebellion
against the status quo can thus be readily harnessed by the Islamist
movement, both violent and non-violent. They provide a channel for the
expression of discontent, blessed and legitimized by powerful
religious tradition that incorporates nationalist impulses as well. It
is noteworthy that Islamism serves as a vehicle of protest everywhere
except where it is in power, such as Iran and Sudan. It is the status
quo that is the major target of anger. (Author's emphasis) A youth
bulge is always destabilizing, but it can often be managed if a
society is able to properly educate its youth and provide them with
adequate economic opportunities at the end of the education process.
Arab nations are failing in both areas.
As I see it, the overarching cause of civilizational collapse is that
culture and institutions of that civilization can no longer adapt to
external stresses. This assertion is grounded in my interpretation of
the writings of Will Durant, Story of Civilization, John Roberts' The
Rise of the West, and Fernand Braudel's A History of Civilizations.
The tyrants and dictators who have long ruled the Arab world have
proven unable to implement the changes required to reverse the trends
of collapse. Unable to reverse economic and societal ills, and
unresponsive to the mass of the Arab population, these rulers
instituted polices of strong internal oppression, which further closed
off Arab society from the adoption of new ideas and methods.
Populations that were unable to influence their governments found that
some methods of expression were still allowed within the context of
Islam. Working within this framework radicals found that they could
shelter their activities within a religious infrastructure, while at
the same time religious leaders realized that they were gaining enough
strength to make a grasp for secular power. This was a struggle that
went on in the West for a thousand years after the fall of Rome until
finally won by secular authority during what is now called the Age of
Reason.
Still, Islam is not the root cause of collapse. For instance, it has
not stood in the way of economic advancement and societal adaptation
in Asia. It is more accurate to say that fundamental failure of Arab
culture is causing people to begin looking backwards at the golden age
of their civilization. Two things ring out to them from those past
centuries: Arabs were powerful when they were united and when their
faith was new, vital, and fundamental.
A lot of the evidence that Huntington presents for his theory of
civilizational war makes more sense when viewed through the prism of
the collapse of Arab civilization. Global maneuvering that Huntington
interprets as preparations for a new round of world conflict are in
reality the spontaneous adjustments that other societies are making in
reaction to the collapse of a neighboring civilization. By accepting
that we are facing the collapse of Arab civilization we can, for the
first time, create a grand strategic concept for success. We no longer
have to engage in a war against terrorism, which is a method of
fighting and not an enemy. Additionally, we now have a strategic
explanation for what is going on that does not make Islam the culprit.
Hence we do not have to fight a religious war to win.
The grand strategic concept that provides the best chance of success
is the one that served us so well in the Cold War-containment. No
matter what else we do we must position ourselves to contain the
effects of the complete collapse of Arab civilization. Already 10
percent of the French population is from Muslim North Africa. Europe's
ability to assimilate a larger flood of economic refugees is
questionable. And mass migration is just one effect a total collapse
will have. Containment will mean adopting and maintaining difficult
policy choices, which include:
Working closely with the European nations to defend their southern
border against the mass migration of tens of millions of destitute
Arabs as well as armed confrontations with failing Arab states.
Renewing our close ties with Turkey and making that nation a bulwark
against the effects of collapse.
Working to help modernize and integrate the Russian military into an
enhanced European defense structure.
Ensuring China is a partner in this containment effort.
Propping up weak border states that are already dealing with the
spillover effects of Arab collapse-such as Pakistan and the new
Caucasus states. Assisting the Iranian popular will to establish a
government not based on a religious oligarchy. The Persian people may
form an eastern bulwark against collapse.
Plan for the security of critical resources even during possible
upheavals and regional turmoil.
Spillover effects such as terrorist groups already evident in places
like Indonesia and the Philippines must be eradicated or reversed. We
need to be clear that this is not a failure of Islam. In this regard
we must help Muslims outside of the Arab world find their own
interpretations of their faith and not fall prey to those being
espoused by the Arab world-Wahhabism.
None of the above policy prescriptions will be easy, nor can they be
achieved overnight. Most of them require the support of other nations,
which may be problematic. Many of these nations have not recognized
the risks they face from Arab collapse and see no reason to take
preemptive measures. It is easy to say that we need to work closely
with Europe to secure its southern border. In reality, that task will
be devilishly hard, not least because the Europeans appear very
reluctant to take any measures to protect themselves that might give
even a whiff of intolerance. Furthermore, American diplomacy, as of
recent decades, has not shown it is up to accomplishing many of the
recommended tasks. For instance, all attempts to engage Iran since the
fall of the Shah have been a debacle. Unfortunately, as the Iranian
nuclear crisis unfolds there is no indication we have gotten any
better at it. Do we have the wherewithal to engender a democratic
society in Iran and then to engage its support in our common
interests? Can we deal with an increasingly autocratic and threatening
Russia? Can we manage China's emergence as a superpower so that it can
be peacefully integrated into the global political system? The answers
to these questions are still unknown. However, because containment of
a civilizational collapse cannot be done by the United States alone
finding the right answers is critical.
By accepting that we need to contain the effects of a failing Arab
civilization we are then free to adopt one of three basic approaches:
Attempt to accelerate the collapse and pick up the pieces, akin to
letting an alcoholic hit bottom.
To contain the effects, but not to interfere with the fall for good or
bad. Reverse the tide when and where we can.
For a number of ethical and practical reasons the third choice is the
one that should and is most likely to be adopted, keeping in mind that
resisting the macro-forces of historical change will not be easy.
By adopting the third option we can craft policies to improve economic
conditions and help specific regions within the Arab world adapt to
encroaching modernity. The United States must be able to spot shining
lights in the Arab world and work to protect them even as we help to
expand their influence. Discarding the theories of two men as eminent
as Samuel Huntington and Bernard Lewis is not a matter to take
lightly. History may even prove both men right and my analysis to be
well off the mark. However, the almost blind acceptance now being
given to these men's ideas is a dangerous trend. As military leaders
build the strategic plans and policies that will guide our forces for
a generation or more it is best to be skeptical of all underlying
assumptions. This article is designed to strike at the foundation of
the two most widely accepted arguments in the current forum of ideas.
If they are correct and sturdy then my position will not topple them.
In fact, like Kennan's X article they will be made stronger by having
to defend themselves against criticism. If they are weak, then it is
best to discard them now.
Lieutenant Colonel Lacey is a Washington-based writer focusing on
defense and international affairs issues. He was embedded with the
101st Airborne Division during the war in Iraq. He served on active
duty for a number of years and later edited journals on international
finance.
Deborah
The Cynic
"J Morgan" <John...@email.non> wrote in message
news:uIudndkc1_L7kJ_X...@giganews.com...
Wrong! Get the true account http://www.answers.com/topic/0-number . I have
reproduced an extract below.
History of zero
The Mesoamerican Long Count calendar developed in south-central Mexico
required the use of zero as a place-holder within its vigesimal (base-20)
positional numeral system. Many different glyphs, including this partial
quatrefoil--were used as a zero symbol for these Long Count dates, the
earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36
BCE.[13] Since the eight earliest Long Count dates appear outside the Maya
homeland,[14] it is assumed that the use of zero in the Americas predated
the Maya and was possibly the invention of the Olmecs. Many of the earliest
Long Count dates were found within the Olmec heartland, although the Olmec
civilization ended by the 4th century BCE, several centuries before the
earliest known Long Count dates.
Although zero became an integral part of Maya numerals, it did not influence
Old World numeral systems.
The use of a blank on a counting board to represent 0 dated back in India to
4th century BCE.[15]
In China, counting rods were used for calculation since the 4th century BCE.
Chinese mathematicians understood negative numbers and zero, though they had
no symbol for the latter,[16] until the work of Song Dynasty mathematician
Qin Jiushao in 1247 established a symbol for zero in China.[17] The Nine
Chapters on the Mathematical Art, which was mainly composed in the 1st
century CE, stated "[when subtracting] subtract same signed numbers, add
differently signed numbers, subtract a positive number from zero to make a
negative number, and subtract a negative number from zero to make a positive
number."[18]
By 130, Ptolemy, influenced by Hipparchus and the Babylonians, was using a
symbol for zero (a small circle with a long overbar) within a sexagesimal
numeral system otherwise using alphabetic Greek numerals. Because it was
used alone, not just as a placeholder, this Hellenistic zero was perhaps the
first documented use of a number zero in the Old World. However, the
positions were usually limited to the fractional part of a number (called
minutes, seconds, thirds, fourths, etc.)-they were not used for the integral
part of a number. In later Byzantine manuscripts of Ptolemy's Syntaxis
Mathematica (also known as the Almagest), the Hellenistic zero had morphed
into the Greek letter omicron (otherwise meaning 70).
Another zero was used in tables alongside Roman numerals by 525 (first known
use by Dionysius Exiguus), but as a word, nulla meaning "nothing," not as a
symbol. When division produced zero as a remainder, nihil, also meaning
"nothing," was used. These medieval zeros were used by all future medieval
computists (calculators of Easter). An isolated use of the initial, N, was
used in a table of Roman numerals by Bede or a colleague about 725, a zero
symbol.
In 498 CE, Indian mathematician and astronomer Aryabhata stated that
"Sthanam sthanam dasa gunam" or place to place in ten times in value, which
may be the origin of the modern decimal-based place value notation.[19]
The oldest known text to use a decimal place-value system, including a zero,
is the Jain text from India entitled the Lokavibh�ga, dated 458 CE. This
text uses Sanskrit numeral words for the digits, with words such as the
Sanskrit word for void for zero (see also the section Etymology above).[20]
The first known use of special glyphs for the decimal digits that includes
the indubitable appearance of a symbol for the digit zero, a small circle,
appears on a stone inscription found at the Chaturbhuja Temple at Gwalior in
India, dated 876 CE.[21][22] There are many documents on copper plates, with
the same small o in them, dated back as far as the sixth century CE, but
their authenticity may be doubted.[7]
The Indian numerals and the positional number system were introduced to the
Islamic civilization by Al-Khwarizmi.[citation needed] Al-Khwarizmi's book
on arithmetic synthesized Greek and Hindu knowledge and also contained his
own fundamental contribution to mathematics and science including an
explanation of the use of zero.
It was only centuries later, in the 12th century, that the Indian numeral
system was introduced to the Western world through Latin translations of his
Arithmetic.
Doc Martian
LOL!!
^^
/**/
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/_ /
/_ /
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/_ /
/' _ /
/'_ /
,/_ /
/_ /
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/ /
/'_'/' '/'__'7,
/'/ / / /" /_\
('( ' ')
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I'm sure you'ss like it!
( Don't forget to suck your finger after ramming it in your ass )
LOL!
Cheers!
Doc
�Do�g�T
theorems), LONG before bumhammad shagged his first lettle girl.
dsharavi
> Regional, Science, 4/22/1998
> Arab contributions to human civilization are noteworthy.
The last contribution seems to have been in the late 14thC. Since
then, their chief contribution to civilization has been global
terrorism.
> In arithmetic
> the style of writing digits from right to left is an evidence of its
> Arab origin.
Digits written in “Arabic numerals” are written left to right. The
numerals were themselves invented by Hindu mathematicians in the 3rdC
BCE, and transmitted to Europe via North African mathematicians.
>For instance, the numeral for five hundred in English
> should be written as 005, not as 500 according to English's
> left-to-right reading style.
> Another invention that revolutionized mathematics was the introduction
> of the number zero by Muhammad Bin Ahmad in 967 AD.
Mesoamericans used zero as early as 36 BCE. Ancient Greeks debated the
status of zero as a number, and Greek mathematicians were the first to
use zero as a number in the early 2ndC CE. The Persian Al-Khwarizmi
introduced the Hindu numeral system to the Islamic world via his 9thC
syntheses of Greek and Hindu knowledge. Translations of his work
spread the Indian numeral system, and Al-Khwarizmi's contributions to
the use of zero, to the Western world.
>Zero was introduced
> in the West as late as the beginning of the thirteenth century. Modern
> society takes the invention of the zero for granted, yet the Zero is a
> non-trivial concept, that allowed major mathematical breakthroughs.
The West was debating the concept, and Greeks were using zero as a
number, in the early 2ndC CE, centuries before Islam was invented.
> Arab civilizations also made a great contribution to fractions and to
> the principle of errors, which is employed to solve Algebra problems
> arithmetically.
Fractions were used in the Indus Valley (2800 BCE), Egypt (1,000 BCE),
Greece (c600 BCE), and others before Islam. Jamshid al-Kashi claimed
to have discovered decimal fractions in the 15thC, but he was wrong.
Al-Hassar, a Mogrebi Muslim, developed the modern mathematical
notation for fractions in the late 12thC, and Leonardo Fibonacci oin
the early 13thC. (Fibonacci studied under prominent Muslim
mathematicians of the time)
> Concerning Algebra, al-Khawarzmi is credited with the first treatise.
Al-Khwarzmi was Persian, from a Zorastrian family converted to Islam.
Had made major contributions to mathematics, astronomy, astrology,
geography and cartography.
>His method
> was continued by Thabet Bin Qura, the translator of Ptolemy's works who
> developed Algebra and first realized application in geometry.
Thabit ibn Qurra al-Harrani was from northern Mesopotamia, who
belonged to the Sabian sect of the star-worshipping Hermeticist sect,
a protected minority under the early Abbasids.
>By the
> 11th century the Arabs had founded, developed and perfected geometrical
> algebra and could solve equations of the third and fourth degree.
“The concinnity of geometry and algebra dates as far back at least to
Euclid's Elements in the 3rd century B.C.[2] It was not, however,
until 1844 that algebra would be used in a systematic way to describe
the geometrical properties and transformations of a space. In that
year, Hermann Grassmann introduced the idea of a geometrical algebra
in full generality as a certain calculus (analogous to the
propositional calculus) which encoded all of the geometrical
information of a space.”
http://en.wikipedia.org/wiki/Geometrical_algebra#History
> Another outstanding Arab mathematician is Abul Wafa who created and
> successfully developed a branch of geometry which consists of problems
> leading to equations in Algebra of a higher degree than the second.
Abul Wafa was another Persian mathematician. 'He devised a wall
quadrant for the accurate astronomy measurement of the declination of
stars. He also introduced the tangent function and improved methods of
calculating trigonometry tables'. The lunar crater Abul Wafa is named
after him.
> Al-Karaki, of the 11th century is considered to be one of the greatest
> Arab mathematicians. He composed one arithmetic book and another on
> Algebra. In the two books, he developed an approximate method of finding
> square roots, a theory of indices, a theory of mathematical induction
> and a theory of intermediate quadratic equations.
> Arabs have excelled in geometry, starting with the transition of Euclid
> and conic section of Apolonios and they preserved the genuine works of
> these two Greek masters for the modern world, by the 9th century AD. and
> then started making new discoveries in this domain.
“While most scientists in this period were Muslims and wrote in
Arabic, a great portion and many of the best known of the contributors
were of Persians origin[2][3] but there were also Berbers, Arabs,
Moors, Turks, and sometimes different religions (Muslims, Christians,
Jews, Sabians, Zoroastrians, irreligious). Arabic was the dominant
language—much like Latin in Medieval Europe, Arabic was used as the
chosen written language of most scholars throughout the Islamic
world.”
Deborah
Herman Rubin
dsharavi <dsh...@gmail.com> wrote:
>On May 6, 3:21 pm, J Morgan <JohnM...@email.non> wrote:
<> Arab contributions to mathematics and the introduction of the Zero
<> Regional, Science, 4/22/1998
<> Arab contributions to human civilization are noteworthy.
>The last contribution seems to have been in the late 14thC. Since
>then, their chief contribution to civilization has been global
>terrorism.
I am not going to criticize much in this posting, which
points out how the claimed Arabic contributions are not.
There are, however, a few points.
<> In arithmetic
<> the style of writing digits from right to left is an evidence of its
<> Arab origin.
>Digits written in =93Arabic numerals=94 are written left to right. The
>numerals were themselves invented by Hindu mathematicians in the 3rdC
>BCE, and transmitted to Europe via North African mathematicians.
It has been conjectured that the decimal system, with the
same characters multiplying every power of 10, came from
the Babylonian base 60 system, which came from the Sumerians
at least 4000 years ago.
Also, the Babylonians, and I believe the Sumerians before
them, had sexagesimal fractions. The Babylonians even had
a two-"sigit" value for the square root of 2.
>=93The concinnity of geometry and algebra dates as far back at least to
>Euclid's Elements in the 3rd century B.C.[2] It was not, however,
>until 1844 that algebra would be used in a systematic way to describe
>the geometrical properties and transformations of a space. In that
>year, Hermann Grassmann introduced the idea of a geometrical algebra
>in full generality as a certain calculus (analogous to the
>propositional calculus) which encoded all of the geometrical
>information of a space.=94
>http://en.wikipedia.org/wiki/Geometrical_algebra#History
<> Another outstanding Arab mathematician is Abul Wafa who created and
<> successfully developed a branch of geometry which consists of problems
<> leading to equations in Algebra of a higher degree than the second.
>Abul Wafa was another Persian mathematician. 'He devised a wall
>quadrant for the accurate astronomy measurement of the declination of
>stars. He also introduced the tangent function and improved methods of
>calculating trigonometry tables'. The lunar crater Abul Wafa is named
>after him.
<> Al-Karaki, of the 11th century is considered to be one of the greatest
<> Arab mathematicians. He composed one arithmetic book and another on
<> Algebra. In the two books, he developed an approximate method of finding
<> square roots, a theory of indices, a theory of mathematical induction
<> and a theory of intermediate quadratic equations.
<> Arabs have excelled in geometry, starting with the transition of Euclid
<> and conic section of Apolonios and they preserved the genuine works of
<> these two Greek masters for the modern world, by the 9th century AD. and
<> then started making new discoveries in this domain.
>=93While most scientists in this period were Muslims and wrote in
>Arabic, a great portion and many of the best known of the contributors
>were of Persians origin[2][3] but there were also Berbers, Arabs,
>Moors, Turks, and sometimes different religions (Muslims, Christians,
>Jews, Sabians, Zoroastrians, irreligious). Arabic was the dominant
>language=97much like Latin in Medieval Europe, Arabic was used as the
>chosen written language of most scholars throughout the Islamic
>world.=94
>Deborah
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
dsharavi
> <> Arab contributions to mathematics and the introduction of the Zero
> <> Regional, Science, 4/22/1998
> <> Arab contributions to human civilization are noteworthy.
>,dsharavi <dshr...@gmail.com> wrote:
> >The last contribution seems to have been in the late 14thC. Since
> >then, their chief contribution to civilization has been global
> >terrorism.
On May 8, 10:12 am, hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
> I am not going to criticize much in this posting, which
> points out how the claimed Arabic contributions are not.
Correct, in part. Arabs contributed a great deal; but much of what the
previous post claimed were Arab contributions, as you point out, were
not.
Perhaps I should have added that their contributions weren't produced
from thin air, and that they were based on the previous scholarship of
Christians, Jews, and pagans.
> There are, however, a few points.
>
> <> In arithmetic
> <> the style of writing digits from right to left is an evidence of its
> <> Arab origin.
> >Digits written in =93Arabic numerals=94 are written left to right. The
> >numerals were themselves invented by Hindu mathematicians in the 3rdC
> >BCE, and transmitted to Europe via North African mathematicians.
> It has been conjectured that the decimal system, with the
> same characters multiplying every power of 10, came from
> the Babylonian base 60 system, which came from the Sumerians
> at least 4000 years ago.
> Also, the Babylonians, and I believe the Sumerians before
> them, had sexagesimal fractions. The Babylonians even had
> a two-"sigit" value for the square root of 2.
This is true, but it seemed unnecessarily detailed, as well as
complicated, for the general tenor of these NGs to repeated it here.
But thanks.
Deborah
> >"The concinnity of geometry and algebra dates as far back at least to
> >Euclid's Elements in the 3rd century B.C.[2] It was not, however,
> >until 1844 that algebra would be used in a systematic way to describe
> >the geometrical properties and transformations of a space. In that
> >year, Hermann Grassmann introduced the idea of a geometrical algebra
> >in full generality as a certain calculus (analogous to the
> >propositional calculus) which encoded all of the geometrical
> >information of a space."
> >http://en.wikipedia.org/wiki/Geometrical_algebra#History
> <> Another outstanding Arab mathematician is Abul Wafa who created and
> <> successfully developed a branch of geometry which consists of problems
> <> leading to equations in Algebra of a higher degree than the second.
> >Abul Wafa was another Persian mathematician. 'He devised a wall
> >quadrant for the accurate astronomy measurement of the declination of
> >stars. He also introduced the tangent function and improved methods of
> >calculating trigonometry tables'. The lunar crater Abul Wafa is named
> >after him.
> <> Al-Karaki, of the 11th century is considered to be one of the greatest
> <> Arab mathematicians. He composed one arithmetic book and another on
> <> Algebra. In the two books, he developed an approximate method of finding
> <> square roots, a theory of indices, a theory of mathematical induction
> <> and a theory of intermediate quadratic equations.
> <> Arabs have excelled in geometry, starting with the transition of Euclid
> <> and conic section of Apolonios and they preserved the genuine works of
> <> these two Greek masters for the modern world, by the 9th century AD. and
> <> then started making new discoveries in this domain.
> >"While most scientists in this period were Muslims and wrote in
> >Arabic, a great portion and many of the best known of the contributors
> >were of Persians origin[2][3] but there were also Berbers, Arabs,
> >Moors, Turks, and sometimes different religions (Muslims, Christians,
> >Jews, Sabians, Zoroastrians, irreligious). Arabic was the dominant
> >language=97much like Latin in Medieval Europe, Arabic was used as the
> >chosen written language of most scholars throughout the Islamic
> >world."
> >Deborah
NefeshBarYochai
Muslim men needed to know about the zero, because they needed one
digit, in example the zero, to measure the average length of their
penises.
kahali...@gmail.com
I agree with that beacuse Muslims are ZERO so they wanted to invent
something that can best describe them.
Also, do you know Muslims were the first to say BLACK is also a color
like red or blue? Muslims are the first who claimed some stars emit
black light and some white light. There are more starts emitting black
color that is why the space looks black.
Ask your physics teacher if black is a color?
Alexander
Forget it. Yochai is till trying to find his Penis to measure it.
I would estimate that a real black hole is what you have in the space
usually reserved for what might have been your brain.