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Mathematics
 Advances in mathematics in Muslim lands have long been
recognized. The high degree of skill in mathematics led to
advancements in many other fields, such as astronomy,
cartography, surveying and engineering, commerce, art, and
architecture. The best-known contribution by early Muslim
mathematicians was the transfer of Indian numerals, the
concept of zero, and its notation.
This
transfer was a direct result of the openness of Muslims to
new ideas, and the burst of exploration and travel,
collection of books and scholarly work from every
civilization Muslims encountered. As in other fields of
scholarship, the translation and collection of mathematical
knowledge from Greek, Persian, Indian and other sources
resulted in preserving the highest state of the eastern
hemisphere’s mathematics up to that time.
 Persian
mathematician and astronomer Muhammad Ibn Musa al-Khwarizmi
(780-850 CE), was appointed court astronomer at Baghdad by
the Abbasid Caliph Al-Ma’mun. He is known in Latin as
Algoritimi (from which the math and computer term
algorithm is
derived). He is also known as “the father of algebra,” from
the title of his work,
Hisab Al-Jabr wal Muqabalah,
The Book of Calculations, Restoration and Reduction.
He gave the name to that branch of mathematics.
In
fact, his algebra was a book of arithmetic featuring Hindi
numerals -- a huge improvement over Roman numerals and other
systems of dots, pictographs, and finger reckoning. His
introduction of the Indian concept of zero, along with the
other nine digits, meant that mathematicians could express
any number. Algebra was a method for moving terms from one
side of an equation to the other to find the value of an
unknown. He also described how to find the square root of a
number, and was the first to demonstrate the concept of
exponents for unknown variables. He demonstrated the use of
equations, algebraic multiplication and division, and
measuring area.
Damascus mathematician Abu al-Hasan Ahmad ibn Ibrahim al-Uqlidisi
("the Euclidian," fl. ca. 953 CE) further advanced the
Indian mode of calculation. The Indian
system had used a dustboard to perform and erase a series of
calculations.
 Al-Uqlidisi
adapted the Indian system for pen and paper. Mathematicians
could now “show their work,” sharing problems, equations,
and methods for solving them across time and space.
Mathematics advanced rapidly as a result of recording and
publication.
Al-Battani (850-929 CE) contributed significant work
developing trigonometry, computing the first table of
cotangents. Al-Biruni (973-1050 CE) also advanced
trigonometry, and used it to calculate the coordinates of
cities to determine the
qibla (direction of Makkah) from any location.
Omar Khayyam (b. 1048 CE) classified and solved cubic
equations.
By the
10th century, Muslim mathematicians had developed and
applied the theory of trigonometric functions -- sine,
cosine, and tangent -- as well as spherical trigonometry.
They used symbols to describe the binomial theorem, and used
decimals to express fractions that aided accurate solution
of complex problems.
 Major
Arabic mathematical works were brought to Al-Andalus by the
9th century, along with important Greek translations and
commentaries. Together with a translation of Euclid’s
Elements, they became the two foundations of
subsequent mathematical developments in Al-Andalus. It is
clear from their own achievements that scholars in Al-Andalus
followed advancements in other Muslim lands, and contributed
their own.
Today,
al-Khwarizmi’s work exists only as a Latin translation made
in Toledo, Spain, by Gerard of Cremona (d. 1187 CE).
Europeans did not gain access to the mathematical knowledge
found in Spain and North Africa until the 12th
and 13th centuries CE. It entered Europe both
through scholarly and commercial means. Fibonacci (d. 1250
CE), an Italian mathematician who traveled between Europe
and North Africa, transmitted mathematical knowledge from
Muslim lands to Europe and made his own discoveries.
Mathematicians in Al-Andalus also did original work. Maslama
al-Majriti (d. 1007 CE) was a mathematician and astronomer
who translated Ptolemy’s
Almagest,
and corrected and added to al-Khwarizmi’s astronomical
tables. Al-Majriti also used advanced techniques of
surveying using triangulation.
Al-Zarqali,
or Arzachel in Latin, was a mathematician and astronomer who
worked in Córdoba during the 11th century. He was skilled at
making instruments for the study of astronomy, and built a
famous water clock that could tell the hours of the day and
night, as well as the days of the lunar month. Al-Zarqali
contributed to the famous
Toledan Tables of astronomical data, and
published an almanac that correlated the days of the month
on different calendars such as the Coptic, Roman, lunar and
Persian, gave the positions of the planets, and predicted
solar and lunar eclipses. He created tables of latitude and
longitude to aid navigation and cartography.
Another
prominent Andalusian mathematician and astronomer in Seville
was al-Bitruji (d. 1204 CE), known in Europe as Alpetragius.
He developed a theory of the movement of stars described in
The Book of Form.
Ibn Bagunis of Toledo was a mathematician renowned for his
work in geometry. Abraham bar Hiyya was a Jewish
mathematician who assisted Plato of Tivoli with translation
of important mathematical and astronomical works, including
his own
Liber Embadorum,
in 1145 CE. Abu al-Hakam al-Kirmani was a prominent
12th century scholar of Al-Andalus, a scholar of
geometry and logic.
 No
branch of mathematics is more visible in Muslim culture than
geometry. Geometric design reached heights of skill and
beauty that was applied to nearly every art form, from
textiles to illustration to architectural decoration.
Tessellated, or complex, overall patterns were used in
Andalusian architecture to cover walls, ceilings, floors and
arches. Some scholars of Islamic arts believe that these
designs were much more than artisans’ work -- they
consciously expressed the mathematical knowledge of the
culture that produced them.
Recently, Paul J. Steinhardt of Princeton and Peter J. Lu of
Harvard University discovered Medieval Islamic tessellations
designed 500 years ago; they were unusually complex, with
polygons of multiple shapes, overlaid by zigzag lines. These
designs are known today as
quasicrystalline
because they have fivefold or tenfold rotational symmetry;
that means they can be rotated around a point to five or ten
positions and still look the same. Such designs can be
infinitely extended without repeating. In the 1970s, Oxford
mathematician Roger Penrose calculated the principles behind
quasicrystalline symmetry. Steinhardt and Lu discovered that
such patterns of stars and polygons have decorated mosques
and palaces since the 15th century CE.
Further Reading:
Ali
Abdullah Al-Daffa.
The
Muslim Contribution to Mathematics. Croom Helm
Ltd.: London, 1977.
Life
Science Library.
Mathematics. Time-Life International, 1963, 1965.
Florence A. Yeldham.
The
Story of Reckoning in the Middle Ages George C.
Harrop and Company, 1948.
B. Lynn
Bodner. “Constructing and Classifying Designs of Al-Andalus,”
Mathematics Department, Monmouth University, retrieved at
http://mathematics.monmouth.edu/coursenotes/bodner/papers/2003/ISAMA03.htm
Julie J. Rehmeyer. Ancient Islamic Penrose Tiles.
Science News Online,
171:8 (2/24/07), retrieved at
http://www.sciencenews.org/articles/20070224/mathtrek.asp.
Charles
Burnett. “Leonard of Pisa (Fibonacci) and Arabic
Arithmetic,” Warburg Institute, retrieved at
http://www.muslimheritage.com/topics/default.cfm?ArticleID=472
Images:
Tile
design from Al-Andalus, “Designs and Decoration” at Medieval
Islamic Cultures by Horace Mann, retrieved at
http://www.sfusd.k12.ca.us/schwww/sch618/Islam_New_Main.html
Russian
postage stamp honoring al-Khwarizmi, retrieved at
http://www.muslimheritage.com/topics/default.cfm?ArticleID=359
Image
of Hindi/Arabic numerals and decimals from Arabic manuscript
in Sayyed Hossein Nasr,
Islamic Science, An Illustrated History (World of
Islam Festival Publishing Company Ltd., 1976).
Pattern
Math Lesson, Pippa Drew and Dorothy Wallace, Dartmouth
College, retrieved at
http://www.dartmouth.edu/~matc/math5.pattern/lesson5math.html
.
Penrose
tiling (Wikimedia image) reproduced in “Ancient Islamic
Penrose Tiles,”
Science
News Online, 171:8, at
http://www.sciencenews.org/articles/20070224/mathtrek.asp.
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