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The IBM World Book Encyclopaedia raises the question as how
the Arabic Numerals originated (!?) as appeared in an article contributed by Nadine
L. Verderber, Ph.D., Prof. of Mathematics, Southern Illinois Univ., Edwardsville.
The article states, as such, "Scholars do not know how Arabic numerals originated."
"The Hindus developed the zero sometime after 600 AC."
Apparently the Arabic Numerals were originated based on the
concept of trigonometry. This explanation is easily justifiable in a time where
mathematics had flourished in various directions under the guardianship of the "House
of Wisdom" in Baghdad functioning as the centre of study and research in the Islamic
world of the 9th century. Creating appropriate mathematical symbols was,
in fact, part of the process to develop advanced mathematical techniques required
by the ever expanding needs for mathematical solutions to all forms of life. The
Islamic civilization expanded over three continents, Asia, Africa and Europe. Many
nations were part of this great empire. The need for finding mathematical solutions
were vital in every field: building engineering, astronomy, navigation, statistics
of population, wages and taxes, and so on. Under such circumstances the knowledge
of numbers and all related symbols had to be universally understood and adopted
by all people. By 3,000 BC, the people of the very same land, Mesopotamia, invented
the world's first writing system.
Their descendants, the Arabs, who had great experience in inventing
codes and scriptures, invented a singular symbol that is remarkably simple and universal.
Each Numeric Symbol represents “Angle”. Thus Symbol "1" represents "one angle,"
symbol "2" represents "two angles" and so on. A full illustration for symbols 1-9
is as shown here.
The forgotten brilliance The World Book Multimedia Encyclopaedia
has largely ignored the work of the Scientists during the Islamic and the Arabic
medieval era. The contributions of the Muslims and Arabs in the field of Mathematics
were very significant. The great Harvard historian of science, Professor George
Sarton wrote in his monumental Introduction to the History of Science[4]: "From
the second half of the 8th to the end of the 11th century,
Arabic was the scientific, the progressive language of mankind... When the West
was sufficiently mature to feel the need of deeper knowledge, it turned its attention,
first of all, not to the Greek sources, but to the Arabic ones." O'Connor and Robertson[2]
published various articles about the contribution of those forgotten brilliance.
Muhammad ibn Musa al-Khawarizmi, who flourished under the Abbasid
state at Baghdad through 813-833 AC, was a mathematician, astronomer and geographer.
He was perhaps one of the greatest mathematicians who ever lived. 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 "AI-Jabr wa-al-Muqabilah." Thus, he explained
the use of zero, a numeral of fundamental importance developed by the Arabs. Several
of his books were translated into Latin in the early 12th century. According to
Parshall[3], “AI-Khwarizmi systematically presented the algebraic solutions, known
since Babylonian times, of particular cases of these equations and then provided
geometric justification for his algebraic rules." The English word "algorithm" derives
from the Latin form of al-Khwarizmi's name[1].
Ya'qub ibn Ishaq al-Kindi (801-873 AC), a Philosopher and
Mathematician, who wrote many works on arithmetic, including: the numbers, relative
quantities, measuring proportion and time, and numerical procedures, He also wrote
on space and time.
Ahmed ibn Yusuf al-Misri (835-912 AC), his works on ratio
and proportion, and geometry' of circles were translated into Latin.
AI-Fadl ibn Hatim al-Nayrizi (865-922 AC) employed principles
of trigonometry to calculate geographical directions.
Banu Musa brothers (Ja'far Muhammad, Ahmad and al-Hasan (sons
of) Musa ibn Shakir) (9th century AC): Ja'far Muhammad worked on geometry and
astronomy while al-Hasan worked mainly on geometry and wrote "The elongated circular
figure" which is a work on the "ellipse." Ahmad worked mainly on mechanics and wrote
on pneumatic devices. The most studied work written by the Banu Musa is "The Book
of the Measurement of Plane and Spherical Figures." This work became well known
through the translation into Latin.
Ibrahim ibn Sinan ibn Thabit ibn Qurra (908-946
AC) who introduced
a method of integration in studying the quadrature of the parabola. His work was
a continuation of his grandfather's (Thabit ibn Qurra) research work. He also studied
the motions of the Sun.
Abu Mansur ibn Tahir al-Baghdadi (980-1037 AC) gave an Interesting
discussion of "abundant numbers," "deficient numbers," "perfect numbers" and "equivalent
numbers."
References:
[1] Gillispie, Charles C. ed. The Dictionary of Scientific
Biography, 16 vols. 2 supps. New York: Charles Scribner's Sons, 1970-1990. S.v.
"AI-Khwarizmi, Abu Ja'far Muhammad ibn Musa" by Gerald Toomer; S.v. "Banu Musa"
by J. al-Dabbagh.
[2] Articles by: O'Connor, J. J. and Robertson, E. F.; (HTML
encoded version):
http://www-history.mcs.st-andrews.ac.uk/history/
[3] Parshall, Karen Hunger; "The Art of Algebra from AL-Khwarizmi
to Viete: A Study in the Natural Selection of Ideas"; (HTML encoded version): This
document previously appeared as an article in the June 1988 issue of History of
Science, Vol. 26, No.72, pp.129-164.
[4] Sarton, George. Introduction to the History of Science,
3 vols. Baltimore: Carngie Institution of Washington, 1927-1948. 1:545-46.
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