2/11/2015 Arabic numerals - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Arabic_numerals 2/10 The numerals used in the Bakhshali manuscript, dated between the 2nd century BC and the 2nd century AD. Brahmi numerals (lower row) in India in the 1st century AD History Origins By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC), the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges. [7] The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them. The decimal Hindu-Arabic numeral system was invented in India around AD 500. [8][9] The system was revolutionary by including a zero and positional notation. It is considered an important milestone in the development of mathematics. One may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which vary regionally. The glyphs most commonly used in conjunction with the Latin script since early modern times are 0 1 2 3 4 5 6 7 8 9. The first universally accepted inscription containing the use of the 0 glyph is first recorded in the 9th century, in an inscription at Gwalior in Central India dated to 870. By this time, the use of the glyph had already reached Persia, and was mentioned in Al-Khwarizmi's descriptions of Indian numerals. Numerous Indian documents on copper plates exist, with the same symbol for zero in them, dated back as far as the 6th century AD. [10] The numeral system came to be known to both the Persian mathematician Al- Khwarizmi, whose book On the Calculation with Hindu Numerals written about 825 in Arabic, and the Arab mathematician Al- Kindi, who wrote four volumes, "On the Use of the Indian Numerals" (Ketab fi Isti'mal al- 'Adad al-Hindi) about 830. Their work was principally responsible for the diffusion of the Indian system of numeration in the Middle East and the West. [11] In the 10th century, Middle-Eastern mathematicians extended the decimal numeral system to include fractions, as recorded in a treatise by Syrian mathematician Abu'l-Hasan al-Uqlidisi in 952–953. The decimal point notation was introduced by Sind ibn Ali, he also wrote the earliest treatise on Arabic numerals. A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in the Maghreb and Al-Andalus, called ghubar ("sand-table" or "dust-table") numerals, which are the direct ancestor of the modern Western Arabic numerals used throughout the world. Ghubar numerals themselves are probably of Roman origin. [12]
4
Embed
Arabic numerals - Wikipedia, the free encyclopedia · PDF file2/11/2015 Arabic numerals - Wikipedia, the free encyclopedia 2/10 The numerals used in the Bakhshali manuscript, dated
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
2/11/2015 Arabic numerals - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Arabic_numerals 2/10
The numerals used in the Bakhshali manuscript, datedbetween the 2nd century BC and the 2nd century AD.
Brahmi numerals (lower row) in India in the 1st centuryAD
HistoryOrigins
By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimalpositional numeral system. The lack of a positional value (or zero) was indicated by a space betweensexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as aplaceholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC),the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.[7]
The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at theend of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked thesame because the larger numbers lacked a final sexagesimal placeholder. Only context coulddifferentiate them.
The decimal Hindu-Arabic numeral system was invented in India around AD 500.[8][9] The system wasrevolutionary by including a zero and positional notation. It is considered an important milestone in thedevelopment of mathematics. One may distinguish between this positional system, which is identicalthroughout the family, and the precise glyphs used to write the numerals, which vary regionally. Theglyphs most commonly used in conjunction with the Latin script since early modern times are 0 1 2 3 45 6 7 8 9. The first universally accepted inscription containing the use of the 0 glyph is first recorded inthe 9th century, in an inscription at Gwalior in Central India dated to 870. By this time, the use of theglyph had already reached Persia, and was mentioned in Al-Khwarizmi's descriptions of Indiannumerals. Numerous Indian documents on copper plates exist, with the same symbol for zero in them,dated back as far as the 6th century AD.[10]
The numeral system came to be known toboth the Persian mathematician Al-Khwarizmi, whose book On the Calculationwith Hindu Numerals written about 825 inArabic, and the Arab mathematician Al-Kindi, who wrote four volumes, "On the Useof the Indian Numerals" (Ketab fi Isti'mal al-
'Adad al-Hindi) about 830. Their work wasprincipally responsible for the diffusion of theIndian system of numeration in the MiddleEast and the West.[11] In the 10th century,Middle-Eastern mathematicians extended thedecimal numeral system to include fractions,as recorded in a treatise by Syrianmathematician Abu'l-Hasan al-Uqlidisi in
952–953. The decimal point notation was introduced by Sind ibn Ali, he also wrote the earliest treatiseon Arabic numerals.
A distinctive West Arabic variant of the symbols begins to emerge around the 10th century in theMaghreb and Al-Andalus, called ghubar ("sand-table" or "dust-table") numerals, which are the directancestor of the modern Western Arabic numerals used throughout the world. Ghubar numeralsthemselves are probably of Roman origin.[12]
2/11/2015 Arabic numerals - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Arabic_numerals 3/10
Modern-day Arab telephone keypad
with two forms of Arabic numerals:
Western Arabic/European numerals
on the left and Eastern Arabic
numerals on the rightWoodcut showing the 16th century astronomical
clock of Uppsala Cathedral, with two clockfaces,
one with Arabic and one with Roman numerals.
A German manuscript page teaching
use of Arabic numerals (Talhoffer
Thott, 1459). At this time, knowledge
of the numerals was still widely seen
as esoteric, and Talhoffer presents
them with the Hebrew alphabet and
astrology.
Folk etymologies
Some folk etymologies have argued that the original forms of
these symbols indicated their value through the number of angles
they contained, but no evidence exists of any such origin.[13]
Adoption in Europe
In 825 Al-
Khwārizmī
wrote a
treatise in
Arabic, OntheCalculationwith HinduNumerals,
[14]
which
survives only
as the 12th-
century Latin
translation, Algoritmi de numero Indorum.[15][16]
Algoritmi, the
translator's rendition of the author's name, gave rise to the word
- ٨۸ - ٩۹ ) used in the Middle East, or any of the numerals currently
used in Indian languages (e.g. Devanagari:
०.१.२.३.४.५.६.७.८.९).[8]
The European acceptance of the numerals was accelerated by the
invention of the printing press, and they became widely known
during the 15th century. Early evidence of their use in Britain
includes: an equal hour horary quadrant from 1396,[21]
in England, a 1445 inscription on the tower of
Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a
1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription
on the tomb of the first Earl of Huntly in Elgin Cathedral. (See G.F. Hill, The Development of ArabicNumerals in Europe for more examples.) In central Europe, the King of Hungary Ladislaus the
Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of
1456.[22]
By the mid-16th century, they were in common use in most of Europe.[23]
Roman numerals
remained in use mostly for the notation of Anno Domini years, and for numbers on clockfaces.
Sometimes, Roman numerals are still used for enumeration of lists (as an alternative to alphabetical
enumeration), for sequential volumes, to differentiate monarchs or family members with the same first
names, and (in lower case) to number pages in prefatory material in books.
Adoption in Russia
Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East
Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great
replaced it with Arabic numerals.
Adoption in China
Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui
people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and
Portuguese Jesuits.[24][25][26]
Evolution of symbols
2/11/2015 Arabic numerals - Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Arabic_numerals 5/10
Iron plate with an order 6 magic
square in Persian/ Arabic numbers
from China, dating to the Yuan
Dynasty (1271–1368).
The numeral system employed, known as algorism, is positional decimal notation. Various symbol sets
are used to represent numbers in the Hindu-Arabic numeral system, which may have evolved from the
Brahmi numerals, or developed independently from it. The symbols used to represent the system have
split into various typographical variants since the Middle Ages:
The widespread Western Arabic numerals used with the Latin script, in the table below labelled
European, descended from the West Arabic numerals developed in al-Andalus (Andalucía, Spain)
and the Maghreb. Spanish scholars because of the
geographic proximity, trade and constant warfare with the
Muslim kingdoms of Southern Spain saw a potential in the
simplicity of Arabic numbers, and decided to adopt those
symbols, later other Europeans followed and incorporated
them too. (There are two typographic styles for rendering
European numerals, known as lining figures and text
figures).
The Arabic–Indic or Eastern Arabic numerals, used with
the Arabic script, developed primarily in what is now Iraq.
A variant of the Eastern Arabic numerals used in the
Persian and Urdu languages is shown as East Arabic-Indic.
There is substantial variation in usage of glyphs for the
Eastern Arabic-Indic digits, especially for the digits four, five, six, and seven.[27]
The Devanagari numerals used with Devanagari and related variants are grouped as Indian
numerals.
The evolution of the numerals in early Europe is shown on a table created by the French scholar J.E.
Montucla in his Histoire de la Mathematique, which was published in 1757: