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The HINDU–ARABIC NUMERAL SYSTEM (also called the ARABIC NUMERAL SYSTEM or HINDU NUMERAL SYSTEM) is a positional decimal numeral system that is the most common system for the symbolic representation of numbers in the world. It was an ancient Indian numeral system which was re-introduced in the book On the Calculation with Hindu
Hindu
Numerals written by the medieval-era Iranian mathematician and engineer Khwarazmi , whose name was latinized as Algoritmi. The system later spread to medieval Europe
Europe
by the High Middle Ages .

The system is based upon ten (originally nine) different glyphs . The symbols (glyphs) used to represent the system are in principle independent of the system itself. The glyphs in actual use are descended from Brahmi numerals and have split into various typographical variants since the Middle Ages .

These symbol sets can be divided into three main families: Arabic numerals used in the Greater Maghreb and in Europe
Europe
, Eastern Arabic numerals (also called "Indic numerals") used in the Middle East
Middle East
, and the Indian numerals
Indian numerals
used in the Indian subcontinent
Indian subcontinent
.

CONTENTS

* 1 Etymology * 2 Positional notation

* 3 Symbols

* 3.1 Glyph comparison

* 4 History

* 4.1 Predecessors * 4.2 Development * 4.3 Adoption in Europe
Europe
* 4.4 Adoption in East Asia * 4.5 Spread of the Western Arabic
Arabic
variant

* 5 See also * 6 Notes * 7 References * 8 Bibliography

ETYMOLOGY

The Hindu- Arabic
Arabic
or Indo-Persian numerals originated from India. Following its re-introduction in the book On the Calculation with Hindu
Hindu
Numerals written by the medieval-era Iranian mathematician and engineer Khwarazmi , whose name was latinized as Algoritmi, , it began to be referred to by the Persian and Arabic
Arabic
mathematicians as the " Hindu
Hindu
numerals" (where " Hindu
Hindu
" meant Indian). After its subsequent introduction to Europe, the Europeans referred to it as the "Arabic Numerals" based on a common misconception of associating the origin of oriental science with Arabic
Arabic
peoples .

POSITIONAL NOTATION

Main articles: Positional notation and 0 (number)

The Hindu– Arabic
Arabic
system is designed for positional notation in a decimal system. In a more developed form, positional notation also uses a decimal marker (at first a mark over the ones digit but now more usually a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recur ad infinitum ". In modern usage, this latter symbol is usually a vinculum (a horizontal line placed over the repeating digits). In this more developed form, the numeral system can symbolize any rational number using only 13 symbols (the ten digits, decimal marker, vinculum, and a prepended dash to indicate a negative number ).

Although generally found in text written with the Arabic
Arabic
abjad ("alphabet"), numbers written with these numerals also place the most-significant digit to the left, so they read from left to right. The requisite changes in reading direction are found in text that mixes left-to-right writing systems with right-to-left systems.

SYMBOLS

Various symbol sets are used to represent numbers in the Hindu– Arabic
Arabic
numeral system, most of which developed from the Brahmi numerals .

The symbols used to represent the system have split into various typographical variants since the Middle Ages , arranged in three main groups:

* The widespread Western " Arabic numerals
Arabic numerals
" used with the Latin , Cyrillic , and Greek alphabets in the table, descended from the "West Arabic
Arabic
numerals" which were developed in al-Andalus and the Maghreb (there are two typographic styles for rendering western Arabic numerals, known as lining figures and text figures ). * The "Arabic–Indic" or "Eastern Arabic numerals
Arabic numerals
" used with Arabic
Arabic
script, developed primarily in what is now Iraq
Iraq
. A variant of the Eastern Arabic numerals
Arabic numerals
is used in Persian and Urdu. * The Indian numerals
Indian numerals
in use with scripts of the Brahmic family in India and Southeast Asia. Each of the roughly dozen major scripts of India has its own numeral glyphs (as one will note when perusing Unicode character charts).

GLYPH COMPARISON

# # # # # # # # # # Script See

0 1 2 3 4 5 6 7 8 9 Latin script Arabic numerals
Arabic numerals

〇/零 一 二 三 四 五 六 七 八 九 East Asia Chinese numerals , Japanese numerals , Korean numerals
Korean numerals

ο/ō Αʹ Βʹ Γʹ Δʹ Εʹ Ϛʹ Ζʹ Ηʹ Θʹ Modern Greek Greek numerals

א ב ג ד ה ו ז ח ט Hebrew
Hebrew
Hebrew numerals

० १ २ ३ ४ ५ ६ ७ ८ ९ Devanagari Indian numerals
Indian numerals

૦ ૧ ૨ ૩ ૪ ૫ ૬ ૭ ૮ ૯ Gujarati

੦ ੧ ੨ ੩ ੪ ੫ ੬ ੭ ੮ ੯ Gurmukhi

༠ ༡ ༢ ༣ ༤ ༥ ༦ ༧ ༨ ༩ Tibetan

০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ৯ Assamese / Bengali / Sylheti Bengali-Assamese numerals
Bengali-Assamese numerals

೦ ೧ ೨ ೩ ೪ ೫ ೬ ೭ ೮ ೯ Kannada

୦ ୧ ୨ ୩ ୪ ୫ ୬ ୭ ୮ ୯ Odia

൦ ൧ ൨ ൩ ൪ ൫ ൬ ൭ ൮ ൯ Malayalam
Malayalam

௦ ௧ ௨ ௩ ௪ ௫ ௬ ௭ ௮ ௯ Tamil Tamil numerals
Tamil numerals

0 ౧ ౨ ౩ ౪ ౫ ౬ ౭ ౮ ౯ Telugu

០ ១ ២ ៣ ៤ ៥ ៦ ៧ ៨ ៩ Khmer Khmer numerals

๐ ๑ ๒ ๓ ๔ ๕ ๖ ๗ ๘ ๙ Thai Thai numerals
Thai numerals

໐ ໑ ໒ ໓ ໔ ໕ ໖ ໗ ໘ ໙ Lao

၀ ၁ ၂ ၃ ၄ ၅ ၆ ၇ ၈ ၉ Burmese

٠ ١ ٢ ٣ ٤ ٥ ٦ ٧ ٨ ٩ Arabic
Arabic
Eastern Arabic numerals
Arabic numerals

۰ ۱ ۲ ۳ ۴ ۵ ۶ ۷ ۸ ۹ Persian (Farsi) / Dari / Pashto
Pashto

Urdu / Shahmukhi

As in many numbering systems, the numbers 1, 2, and 3 represent simple tally marks ; 1 being a single line, 2 being two lines (now connected by a diagonal) and 3 being three lines (now connected by two vertical lines). After three, numbers tend to become more complex symbols (examples are the Chinese numerals and Roman numerals ). Theorists believe that this is because it becomes difficult to instantaneously count objects past three .

HISTORY

Main article: History of the Hindu– Arabic
Arabic
numeral system

PREDECESSORS

The Brahmi numerals at the basis of the system predate the Common Era . They replaced the earlier Kharosthi numerals
Kharosthi numerals
used since the 4th century BC. Brahmi and Kharosthi numerals
Kharosthi numerals
were used alongside one another in the Maurya Empire period, both appearing on the 3rd century BC edicts of Ashoka .

Buddhist
Buddhist
inscriptions from around 300 BC use the symbols that became 1, 4 and 6. One century later, their use of the symbols that became 2, 4, 6, 7 and 9 was recorded. These Brahmi numerals are the ancestors of the Hindu– Arabic
Arabic
glyphs 1 to 9, but they were not used as a positional system with a zero , and there were rather separate numerals for each of the tens (10, 20, 30, etc.).

The actual numeral system, including positional notation and use of zero, is in principle independent of the glyphs used, and significantly younger than the Brahmi numerals.

DEVELOPMENT

The "Galley " method of division.

The place-value system is used in the Bakhshali Manuscript
Bakhshali Manuscript
. Although date of the composition of the manuscript is uncertain, the language used in the manuscript indicates that it could not have been composed any later than 400. The development of the positional decimal system takes its origins in Hindu
Hindu
mathematics during the Gupta period . Around 500, the astronomer Aryabhata uses the word kha ("emptiness") to mark "zero" in tabular arrangements of digits. The 7th century Brahmasphuta Siddhanta contains a comparatively advanced understanding of the mathematical role of zero . The Sanskrit translation of the lost 5th century Prakrit Jaina cosmological text Lokavibhaga
Lokavibhaga
may preserve an early instance of positional use of zero.

These Indian developments were taken up in Islamic mathematics in the 8th century, as recorded in al-Qifti 's Chronology of the scholars (early 13th century).

The numeral system came to be known to both the Perso-Arabic mathematician Khwarizmi
Khwarizmi
, who wrote a book, On the Calculation with Hindu
Hindu
Numerals in about 825, and the Arab mathematician Al-Kindi , who wrote four volumes, On the Use of the Hindu
Hindu
Numerals (كتاب في استعمال العداد الهندي ) around 830. These earlier texts did not use the Hindu
Hindu
numerals. Kushyar ibn Labban who wrote Kitab fi usul hisab al-hind (Principles of Hindu
Hindu
Reckoning ) is one of the oldest surviving manuscripts using the Hindu
Hindu
numerals. These books are principally responsible for the diffusion of the Hindu system of numeration throughout the Islamic world and ultimately also to Europe.

The first dated and undisputed inscription showing the use of a symbol for zero appears on a stone inscription found at the Chaturbhuja Temple at Gwalior
Gwalior
in India, dated 876.

In 10th century Islamic mathematics , the system was extended to include fractions , as recorded in a treatise by Syrian mathematician Abu\'l-Hasan al-Uqlidisi in 952–953.

ADOPTION IN EUROPE

The bottom row shows the numeral glyphs as they appear in type in German incunabula (Nicolaus Kesler, Basel
Basel
, 1486) Main article: Arabic numerals
Arabic numerals

In Christian Europe, the first mention and representation of Hindu- Arabic numerals
Arabic numerals
(from one to nine, without zero), is in the Codex Vigilanus , an illuminated compilation of various historical documents from the Visigothic period in Spain , written in the year 976 by three monks of the Riojan monastery of San Martín de Albelda . Between 967 and 969, Gerbert of Aurillac discovered and studied Arab science in the Catalan abbeys. Later he obtained from these places the book De multiplicatione et divisione (On multiplication and division). After becoming Pope Sylvester II in the year 999, he introduced a new model of abacus , the so-called Abacus of Gerbert , by adopting tokens representing Hindu-Arab numerals, from one to nine.

Leonardo Fibonacci
Fibonacci
brought this system to Europe. His book Liber Abaci introduced Arabic
Arabic
numerals, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century to replace Roman numerals .

The familiar shape of the Western Arabic
Arabic
glyphs as now used with the Latin alphabet (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they enter early typesetting . Muslim scientists used the Babylonian numeral system , and merchants used the Abjad numerals
Abjad numerals
, a system similar to the Greek numeral system and the Hebrew
Hebrew
numeral system . Similarly, Fibonacci's introduction of the system to Europe
Europe
was restricted to learned circles. The credit for first establishing widespread understanding and usage of the decimal positional notation among the general population goes to Adam Ries , an author of the German Renaissance , whose 1522 Rechenung auff der linihen und federn was targeted at the apprentices of businessmen and craftsmen.

*

Gregor Reisch
Gregor Reisch
, Madame Arithmatica, 1508 *

A calculation table (de), used for arithmetic using Roman numerals *

Adam Ries , Rechenung auff der linihen und federn, 1522 *

Two arithmetic books published in 1514—Köbel (left) using a calculation table and Böschenteyn using numerals *

Adam Ries , Rechenung auff der linihen und federn (2nd Ed.), 1525 *

Robert Recorde , The ground of artes, 1543 *

Peter Apian , Kaufmanns Rechnung, 1527 *

Adam Ries , Rechenung auff der linihen und federn (2nd Ed.), 1525

ADOPTION IN EAST ASIA

In AD 690 , Empress Wu promulgated Zetian characters , one of which was "〇". The word is now used as a synonym for the number zero.

In China
China
, Gautama Siddha introduced Hindu
Hindu
numerals with zero in 718, but Chinese mathematicians did not find them useful, as they had already had the decimal positional counting rods .

In Chinese numerals, a circle (〇) is used to write zero in Suzhou numerals . Many historians think it was imported from Indian numerals by Gautama Siddha in 718, but some Chinese scholars think it was created from the Chinese text space filler "□".

Chinese and Japanese finally adopted the Hindu– Arabic numerals
Arabic numerals
in the 19th century, abandoning counting rods.

SPREAD OF THE WESTERN ARABIC VARIANT

An Arab telephone keypad with both the Western " Arabic
Arabic
numerals" and the Arabic
Arabic
"Arabic–Indic numerals" variants.

The "Western Arabic" numerals as they were in common use in Europe since the Baroque period have secondarily found worldwide use together with the Latin alphabet , and even significantly beyond the contemporary spread of the Latin alphabet , intruding into the writing systems in regions where other variants of the Hindu– Arabic
Arabic
numerals had been in use, but also in conjunction with Chinese and Japanese writing (see Chinese numerals , Japanese numerals ).

SEE ALSO

* Arabic numerals
Arabic numerals
* Decimal * Positional notation * Numeral system * History of mathematics * 0 (number)

NOTES

* ^ Hindu
Hindu
was the Persian name for "Indian" in the 10th century, when the Arabs adopted the number system. The connotation of " Hindu
Hindu
" as a religion was a later development. * ^ Other Latin transliterations include Algaurizin.

REFERENCES

* Flegg, Graham (2002). Numbers: Their History and Meaning. Courier Dover Publications. ISBN 0-486-42165-1 . * The Arabic
Arabic
numeral system – MacTutor History of Mathematics

* ^ David Eugene Smith and Louis Charles Karpinski , The Hindu– Arabic
Arabic
Numerals, 1911 * ^ William Darrach Halsey, Emanuel Friedman (1983). Collier\'s Encyclopedia, with bibliography and index. * ^ A B Brezina, Corona (2006), Al-Khwarizmi: The Inventor of Algebra, The Rosen Publishing Group, pp. 39–40, ISBN 978-1-4042-0513-0 , c.825) * ^ Rowlett, Russ (2004-07-04), Roman and "Arabic" Numerals, University of North Carolina at Chapel Hill , retrieved 2009-06-22 * ^ Language may shape human thought, New Scientist, news service, Celeste Biever, 19:00 19 August 2004. * ^ Flegg (2002), p. 6ff. * ^ Pearce, Ian (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Retrieved 2007-07-24. * ^ Ifrah, G. The Universal History of Numbers: From prehistory to the invention of the computer. John Wiley and Sons Inc., 2000. Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk * ^ al-Qifti 's Chronology of the scholars (early 13th century): ... a person from India presented himself before the Caliph al-Mansur in the year 776 who was well versed in the siddhanta method of calculation related to the movement of the heavenly bodies, and having ways of calculating equations based on the half-chord calculated in half-degrees ... Al-Mansur ordered this book to be translated into Arabic, and a work to be written, based on the translation, to give the Arabs a solid base for calculating the movements of the planets ... * ^ Martin Levey and Marvin Petruck, Principles of Hindu
Hindu
Reckoning, translation of Kushyar ibn Labban Kitab fi usul hisab al-hind, p3, University of Wisconsin Press, 1965 * ^ Bill Casselman (February 2007). "All for Nought". Feature Column. AMS. * ^ Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 518. ISBN 978-0-691-11485-9 . * ^ " Fibonacci
Fibonacci
Numbers". www.halexandria.org. * ^ Leonardo Pisano – page 3: "Contributions to number theory". Encyclopædia Britannica
Encyclopædia Britannica
Online, 2006. Retrieved 18 September 2006. * ^ A B Qian, Baocong (1964), Zhongguo Shuxue Shi (The history of Chinese mathematics), Beijing: Kexue Chubanshe * ^ Wáng, Qīngxiáng (1999), Sangi o koeta otoko (The man who exceeded counting rods), Tokyo: Tōyō Shoten, ISBN 4-88595-226-3

BIBLIOGRAPHY

* Menninger, Karl W. (1969). Number Words and Number Symbols: A Cultural History of Numbers. MIT Press. ISBN 0-262-13040-8 . * On the genealogy of modern numerals by Edward Clive Bayley

* v * t * e

Types of writing systems

OVERVIEW

* History of writing * Grapheme

LISTS

* Writing systems

* undeciphered * inventors * constructed

* Languages by writing system / by first written accounts

TYPES

ABJADS

* Numerals

* Aramaic

* Hatran

* Arabic
Arabic
* Pitman shorthand

* Hebrew
Hebrew

* Ashuri * Cursive * Rashi * Solitreo

* Tifinagh * Manichaean * Nabataean * Old North Arabian * Pahlavi * Pegon

* Phoenician

* Paleo- Hebrew
Hebrew

* Proto-Sinaitic * Psalter * Punic * Samaritan

* South Arabian

* Zabur * Musnad

* Sogdian

* Syriac

* ʾEsṭrangēlā * Serṭā * Maḏnḥāyā

* Teeline Shorthand
Teeline Shorthand
* Ugaritic

ABUGIDAS

BRAHMIC

NORTHERN

* Asamiya (Ôxômiya) * Bānglā * Bhaikshuki * Bhujinmol * Brāhmī * Devanāgarī * Dogri * Gujarati * Gupta * Gurmukhī * Kaithi * Kalinga * Khojki * Khotanese * Khudawadi * Laṇḍā * Lepcha * Limbu * Mahajani * Meitei Mayek * Modi * Multani * Nāgarī * Nandinagari * Odia * \'Phags-pa * Newar * Ranjana * Sharada * Saurashtra * Siddhaṃ * Soyombo * Sylheti Nagari * Takri

* Tibetan

* Uchen * Umê

* Tirhuta
Tirhuta
* Tocharian * Zanabazar Square

* Zhang-Zhung

* Drusha * Marchen * Marchung * Pungs-chen * Pungs-chung

SOUTHERN

* Ahom * Balinese * Batak * Baybayin * Bhattiprolu * Buhid * Burmese * Chakma * Cham * Grantha * Goykanadi * Hanunó\'o * Javanese * Kadamba * Kannada * Kawi * Khmer * Kulitan * Lanna * Lao * Leke * Lontara * Malayalam
Malayalam

* Maldivian

* Dhives Akuru * Eveyla Akuru * Thaana

* Mon * Old Makassarese * Old Sundanese * Pallava * Pyu * Rejang * Rencong * Sinhala * Sundanese * Tagbanwa * Tai Le * Tai Tham * Tai Viet * Tamil * Telugu * Thai * Tigalari

* Vatteluttu

* Kolezhuthu * Malayanma

* Visayan

OTHERS

* Boyd\'s syllabic shorthand

* Canadian syllabics

* Blackfoot * Déné syllabics

* Fox I * Ge\'ez * Gunjala Gondi * Japanese Braille * Jenticha * Kayah Li * Kharosthi * Mandombe * Masaram Gondi * Meroitic * Miao * Mwangwego * Sorang Sompeng * Pahawh Hmong * Thomas Natural Shorthand
Thomas Natural Shorthand

ALPHABETS

LINEAR

* Abkhaz * Adlam * Armenian * Avestan * Avoiuli
Avoiuli
* Bassa Vah * Borama * Carian * Caucasian Albanian * Coorgi–Cox alphabet * Coptic * Cyrillic * Deseret

* Duployan shorthand
Duployan shorthand

* Chinook writing

* Early Cyrillic * Eclectic shorthand
Eclectic shorthand
* Elbasan * Etruscan * Evenki * Fox II * Fraser * Gabelsberger shorthand * Garay

* Georgian

* Asomtavruli
Asomtavruli
* Nuskhuri
Nuskhuri
* Mkhedruli
Mkhedruli

* Glagolitic * Gothic * Gregg shorthand * Greek * Greco-Iberian alphabet * Hangul * Hanifi * IPA * Kaddare

* Latin

* Beneventan * Blackletter
Blackletter
* Carolingian minuscule * Fraktur
Fraktur
* Gaelic * Insular * Kurrent * Merovingian * Sigla * Sütterlin * Tironian notes * Visigothic

* Luo * Lycian * Lydian * Manchu * Mandaic * Medefaidrin * Molodtsov * Mongolian * Mru * Neo- Tifinagh * New Tai Lue * N\'Ko * Ogham
Ogham
* Oirat * Ol Chiki * Old Hungarian * Old Italic * Old Permic * Orkhon * Old Uyghur * Osage * Osmanya * Pau Cin Hau

* Runic

* Anglo-Saxon * Cipher * Dalecarlian * Elder Futhark * Younger Futhark * Gothic * Marcomannic * Medieval * Staveless

* Sidetic * Shavian * Somali * Tifinagh * Vagindra * Visible Speech
Visible Speech
* Vithkuqi * Wancho * Zaghawa

NON-LINEAR

* Braille * Maritime flags * Morse code * New York Point * Semaphore line * Flag semaphore * Moon type

IDEOGRAMS /PICTOGRAMS

* Adinkra * Aztec * Blissymbol * Dongba * Ersu Shaba * Emoji * IConji * Isotype * Kaidā * Míkmaq * Mixtec * New Epoch Notation Painting * Nsibidi
Nsibidi
* Ojibwe Hieroglyphs * Siglas poveiras * Testerian * Yerkish * Zapotec

LOGOGRAMS

CHINESE FAMILY OF SCRIPTS

CHINESE CHARACTERS

* Simplified * Traditional * Oracle bone script * Bronze Script

* Seal Script

* large * small * bird-worm

* Hanja
Hanja
* Idu * Kanji * Chữ nôm * Zhuang

CHINESE-INFLUENCED

* Jurchen * Khitan large script * Sui * Tangut

CUNEIFORM

* Akkadian * Assyrian * Elamite * Hittite * Luwian * Sumerian

OTHER LOGO-SYLLABIC

* Anatolian * Bagam * Cretan * Isthmian * Maya * Proto-Elamite * Yi (Classical)

LOGO-CONSONANTAL

* Demotic * Hieratic * Hieroglyphs

NUMERALS

* Hindu-Arabic * Abjad * Attic (Greek) * Muisca * Roman

SEMI-SYLLABARIES

FULL

* Celtiberian * Northeastern Iberian * Southeastern Iberian * Khom

REDUNDANT

* Espanca * Pahawh Hmong * Khitan small script * Southwest Paleohispanic * Zhuyin fuhao

SOMACHEIROGRAMS

* ASLwrite * SignWriting * si5s * Stokoe Notation

SYLLABARIES

* Afaka * Bamum * Bété * Byblos * Cherokee * Cypriot * Cypro-Minoan * Ditema tsa Dinoko * Eskayan * Geba * Great Lakes Algonquian syllabics * Iban

* Japanese

* Hiragana * Katakana * Man\'yōgana * Hentaigana * Sogana * Jindai moji

* Kikakui * Kpelle * Linear B * Linear Elamite * Lisu * Loma * Nüshu * Nwagu Aneke script * Old Persian Cuneiform * Vai * Woleai * Yi (Modern) * Yugtun

* v * t * e

Braille ⠃⠗⠁⠊⠇⠇⠑

BRAILLE CELL

* 1829 braille * International uniformity * ASCII braille * Unicode braille patterns

BRAILLE SCRIPTS

French-ordered scripts (see for more)

* Albanian * Amharic * Arabic
Arabic
* Armenian * Azerbaijani * Belarusian

* Bharati

* Devanagari (Hindi / Marathi / Nepali) * Bengali * Punjabi * Sinhalese * Tamil * Urdu * etc.

* Bulgarian * Burmese * Cambodian * Cantonese * Catalan * Chinese (Mandarin, mainland) * Czech * Dutch * Dzongkha (Bhutanese) * English (Unified English ) * Esperanto * Estonian * Faroese * French * Georgian * German * Ghanaian * Greek * Guarani * Hawaiian * Hebrew
Hebrew
* Hungarian * Icelandic * Inuktitut (reassigned vowels) * Iñupiaq * IPA * Irish * Italian * Kazakh * Kyrgyz * Latvian * Lithuanian * Maltese * Mongolian * Māori * Nigerian * Northern Sami * Persian * Philippine * Polish * Portuguese * Romanian * Russian * Samoan * Scandinavian * Slovak * South African * Spanish * Tatar * Taiwanese Mandarin (largely reassigned) * Thai border-left-width:2px;border-left-style:solid;width:100%;padding:0px">

* Algerian Braille (obsolete)

FREQUENCY-BASED SCRIPTS

* American Braille (obsolete)

INDEPENDENT SCRIPTS

* Japanese * Korean * Two-Cell Chinese

EIGHT-DOT SCRIPTS

* Luxembourgish * Kanji * Gardner–Salinas braille codes (GS8)

SYMBOLS IN BRAILLE

* Braille music * Canadian currency marks * Computer Braille Code * Gardner–Salinas braille codes (GS8/GS6) * International Phonetic Alphabet (IPA) * Nemeth braille code

BRAILLE TECHNOLOGY

* Braille e-book * Braille embosser * Braille translator * Braille watch * Mountbatten Brailler * Optical braille recognition * Perforation * Perkins Brailler * Refreshable braille display * Slate and stylus * Braigo

PERSONS

* Louis Braille * Charles Barbier * Valentin Haüy * Thakur Vishva Narain Singh * Sabriye Tenberken * William Bell Wait

ORGANISATIONS

* Braille Institute of America * Braille Without Borders * Japan
Japan
Braille Library * National Braille Association * Blindness organizations * Schools for the blind * American Printing House for the Blind

OTHER TACTILE ALPHABETS

* Decapoint
Decapoint
* Moon type * New York Point * Night writing * Vibratese

RELATED TOPICS

* Accessible publishing * Braille literacy * Robo Braille

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