View source for Nemeth Braille

{{Short description|Braille code for mathematics and science}}
{{Infobox writing system
| name = Nemeth Braille
| altname = 
| type = [[Social:Alphabet|Alphabet]]
| typedesc = Braille code for encoding mathematical and scientific notation linearly
| time = 1952 to the present
| languages = Several
| fam1 = 
| fam2 = 
| sisters = 
| children = 
| creator = Abraham Nemeth
| sample = 
| imagesize = 3
| unicode = 
| note = 
}}
The '''Nemeth Braille Code for Mathematics''' is a Braille code for encoding mathematical and scientific notation linearly using standard six-dot Braille cells for tactile reading by the visually impaired. The code was developed by Abraham Nemeth. The Nemeth Code was first written up in 1952. It was revised in 1956, 1965, and 1972.<ref name=interview>{{cite web|title=The History of Nemeth Code|url=http://nfb.org/images/nfb/publications/fr/fr28/fr280110.htm|access-date=2012-04-26}}</ref> It is an example of a compact human-readable [[Markup language|markup language]].

Nemeth Braille is just one code used to write mathematics in braille. There are many systems in use around the world.<ref name=world>{{cite web|title=Braille Mathematical Notations|url=http://chezdom.net/blog/?page_id=51|access-date=2012-04-26|date = 2008-07-22}}</ref>

== Principles of the Nemeth Code ==
The Nemeth Code Book (1972) opens with the following words:

{{quote|text=This Braille Code for Mathematics and Science Notation has been prepared to provide a system of symbols which will allow technical literature to be presented and read in braille. The Code is intended to convey as accurate an impression as is possible to the braille reader of the corresponding printed text, and this is one of its principal features. When the braille reader has a clear conception of the corresponding printed text, the area of communication between himself and his teacher, his colleagues, his associates, and the world at large is greatly broadened. ''A test of the accuracy with which the Code conveys information from the print to the braille text is to effect a transcription in the reverse direction. The amount of agreement between the original printed text and one transcribed from the braille is a measure of the Code's accuracy''.|source=<ref name="codebook">{{cite web|title=The Nemeth Braille Code for Mathematics and Science Notation 1972 Revision |url=http://www.brailleauthority.org/mathscience/nemeth1972.pdf |access-date=2012-04-26}}</ref>}}

One consequence is that the braille transcriber does not need to know the underlying mathematics. The braille transcriber needs to identify the inkprint symbols and know how to render them in Nemeth Code braille. For example, if the same math symbol might have two different meanings, this would not matter; both instances would be brailled the same. This is in contrast to the International Braille Music Code, where the braille depends on the meaning of the inkprint music. Thus a knowledge of music is required to produce braille music.

== Table of Nemeth braille codes ==

=== General signs ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! * !! , !! ...
|-
! [[Braille]]
| {{Braille cell|type=image|4|4536}} || {{Braille cell|type=image|6}} || {{Braille cell|type=image|3|3|3}} 
|}<ref name=Acharya>{{cite web|title=Nemeth Braille (Mathematics Braille)|url=http://acharya.iitm.ac.in/disabilities/nemeth_brl.php|access-date=2012-04-25|url-status=dead|archive-url=https://web.archive.org/web/20120421113105/http://acharya.iitm.ac.in/disabilities/nemeth_brl.php|archive-date=2012-04-21}}</ref>

===Number signs===
{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Number<br>prefix !! Decimal<br>point !! Thousands<br>separator !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
|-
! [[Braille]]
| {{Braille cell|type=image|4536}} || {{Braille cell|type=image|46}} || {{Braille cell|type=image|6}} || {{Braille cell|type=image|536}} || {{Braille cell|type=image|2}} || {{Braille cell|type=image|23}} || {{Braille cell|type=image|25}} || {{Braille cell|type=image|256}} || {{Braille cell|type=image|26}} || {{Braille cell|type=image|253}} || {{Braille cell|type=image|2536}} || {{Braille cell|type=image|236}} || {{Braille cell|type=image|53}} 
|}<ref name=codebook />

=== Operators ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! + !! - !! × !! · !! ÷ !! . (decimal) !! √ !! i√ (radical index)
|-
! [[Braille]]
| {{Braille cell|type=image|436}} || {{Braille cell|type=image|36}} || {{Braille cell|type=image|4|16}} || {{Braille cell|type=image|16}} || {{Braille cell|type=image|46|43}} || {{Braille cell|type=image|46}} || {{Braille cell|type=image|453}} || {{Braille cell|type=image|126}} 
|-
! Symbol !! inner √ (1st) !! inner √ (2nd) !! end 1st √ !! end 2nd √ !! long division !! / !! !
|-
! [[Braille]]
| {{Braille cell|type=image|46}} || {{Braille cell|type=image|46|46}} || {{Braille cell|type=image|46|14256}} || {{Braille cell|type=image|46|46|14256}} || {{Braille cell|type=image|153}} || {{Braille cell|type=image|43}} || {{Braille cell|type=image|14236}} 
|}<ref name=Acharya />

=== Parentheses and brackets ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ( !! ) !! [ !! ] !! { !! }
|-
! [[Braille]]
| {{Braille cell|type=image|12536}} || {{Braille cell|type=image|42536}} || {{Braille cell|type=image|4|12536}} || {{Braille cell|type=image|4|42536}} || {{Braille cell|type=image|46|12536}} || {{Braille cell|type=image|46|42536}} 
|}<ref name=Acharya />

=== Fractions ===

{| class="wikitable" style="text-align:center"
|- 
!rowspan=2| Symbol 
!colspan=3|simple ||colspan=3|complex ||colspan=3|hypercomplex ||colspan=3|fraction in mixed number
|-
! open !! line !! close !! open !! line !! close !! open !! line !! close !! open !! line !! close
|-
! [[Braille]]
| {{Braille cell|type=image|1456}} || {{Braille cell|type=image|43}} || {{Braille cell|type=image|4536}} || {{Braille cell|type=image|6|1456}} || {{Braille cell|type=image|6|43}} || {{Braille cell|type=image|6|4536}} || {{Braille cell|type=image|6|6|1456}} || {{Braille cell|type=image|6|6|43}} || {{Braille cell|type=image|6|6|4536}} || {{Braille cell|type=image|456|1456}} || {{Braille cell|type=image|456|43}} || {{Braille cell|type=image|456|4536}}
|}<ref name=Acharya />

===Other modifiers===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ∵ !! ∴ !! : !! ∷ !! {{prime}} !! ″
|- 
! [[Braille]]
| {{Braille cell|type=image|4|43}} || {{Braille cell|type=image|6|16}} || {{Braille cell|type=image|46}} || {{Braille cell|type=image|46|46}} || {{Braille cell|type=image|3}} || {{Braille cell|type=image|3|3}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ∞ !! ∝ !! ° !! % !! ✓
|- 
! [[Braille]]
| {{Braille cell|type=image|6|142536}} || {{Braille cell|type=image|456|142536}} || {{Braille cell|type=image|46|16}} || {{Braille cell|type=image|4|536}} || {{Braille cell|type=image|4|453}} 
|}<ref name=Acharya />

=== Braille indicators ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Punctuation !! Superscript !! Subscript !! Baseline !! Omission !! Cancel (close) !! Cancel (open) !! Run Over !! Directly Over !! Directly Under !! Beginning !! Termination
|-
! [[Braille]]
| {{Braille cell|type=image|456}} || {{Braille cell|type=image|45}} || {{Braille cell|type=image|56}} || {{Braille cell|type=image|5}} || {{Braille cell|type=image|142536}} || {{Braille cell|type=image|14256}} || {{Braille cell|type=image|426}} || {{Braille cell|type=image|5}} || {{Braille cell|type=image|126}} || {{Braille cell|type=image|146}} || {{Braille cell|type=image|5}} || {{Braille cell|type=image|14256}}
|}<ref name=Acharya />

=== Comparison signs ===
{| class="wikitable" style="text-align:center;white-space: nowrap;"
|- 
! Symbol !! > !! < !! ≥ !! ≤ !! ≧ !! ≦
|-
! [[Braille]]
| {{Braille cell|type=image|46|2}} || {{Braille cell|type=image|5|13}} || {{Braille cell|type=image|46|2|156}} || {{Braille cell|type=image|5|13|156}} || {{Braille cell|type=image|46|2|46|13}} || {{Braille cell|type=image|5|13|46|13}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ⋝ !! ⋜ !! ⪚ !! ⪙
|-
! [[Braille]]
| {{Braille cell|type=image|156|46|2}} || {{Braille cell|type=image|156|5|13}} || {{Braille cell|type=image|46|13|46|2}} || {{Braille cell|type=image|46|13|5|13}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center; white-space: nowrap;"
|- 
! Symbol !! >< !! <> !! >=< !! <=>
|-
! [[Braille]]
| {{Braille cell|type=image|46|2|5|5|13}} || {{Braille cell|type=image|5|13|5|46|2}} || {{Braille cell|type=image|46|2|46|13|5|13}} || {{Braille cell|type=image|5|13|46|13|46|2}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center; white-space: nowrap;"
|- 
! Symbol !! = !! ≠ !! ≯ !! ≮ !! ~ !! ≈ !! ≅ !! ± !! ∓
|-
! [[Braille]]
| {{Braille cell|type=image|46|13}} || {{Braille cell|type=image|43|46|13}} || {{Braille cell|type=image|43|46|2}} || {{Braille cell|type=image|43|5|13}} || {{Braille cell|type=image|4|156}} || {{Braille cell|type=image|4|156|4|156}} || {{Braille cell|type=image|4|156|46|13}} || {{Braille cell|type=image|436|36}} || {{Braille cell|type=image|36|436}} 
|}<ref name=Acharya />

=== Geometry ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! [[Parallel (geometry)|Parallel]] !! [[Perpendicular]] !! [[Angle]] !! [[Right angle]]
|-
! [[Braille]]
| {{Braille cell|type=image|1426|123}} || {{Braille cell|type=image|1426|1423}} || {{Braille cell|type=image|1426|426}} || {{Braille cell|type=image|1426|426|46|1253|14256}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! [[Arc (geometry)|Arc]] down !! Arc up !! [[Trapezoid]] !! [[Square]] !! [[Rectangle]] !! [[Parallelogram]]
|-
! [[Braille]]
| {{Braille cell|type=image|1426|1}} || {{Braille cell|type=image|1426|3}} || {{Braille cell|type=image|1426|14253}} || {{Braille cell|type=image|1426|256}} || {{Braille cell|type=image|1426|1253}} || {{Braille cell|type=image|1426|1425}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! [[Rhombus]] !! [[Isosceles trapezoid]] !! [[Triangle]] !! [[Right triangle]] !! [[Circle]] !! [[Ellipse]]
|-
! [[Braille]]
| {{Braille cell|type=image|1426|125}} || {{Braille cell|type=image|1426|1536}} || {{Braille cell|type=image|1426|4253}} || {{Braille cell|type=image|1426|4253|46|1253|14256}} || {{Braille cell|type=image|1426|14}} || {{Braille cell|type=image|1426|15}} 
|}<ref name=Acharya />

=== Arrows ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ⟶ !! ⟵ !! ⟷
|-
! [[Braille]]
| {{Braille cell|type=image|1426|25|25|153}} || {{Braille cell|type=image|1426|426|25|25}} || {{Braille cell|type=image|1426|426|25|25|153}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! → !! ⇌ !! ⇒
|-
! [[Braille]]
| {{Braille cell|type=image|1426|153}} || {{Braille cell|type=image|1426|25|25|4|153|1426|6|426}} || {{Braille cell|type=image|1426|2536|2536|153}} 
|}<ref name=Acharya />

=== Trig functions ===

{| class="wikitable" style="text-align:center"
|- 
! Function !! Sine !! Cosine !! Tangent
|-
! [[Braille]]
| {{Braille cell|type=image|423|42|1453}} || {{Braille cell|type=image|14|153|423}} || {{Braille cell|type=image|4253|1|1453}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Function !! Secant !! Cosecant !! Cotangent !! Logarithm
|-
! [[Braille]]
| {{Braille cell|type=image|423|15|14}} || {{Braille cell|type=image|14|423|14}} || {{Braille cell|type=image|14|153|4253}} || {{Braille cell|type=image|123|153|1425}} 
|}<ref name=Acharya />

=== Set theory ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ∈ !! ∋ !! ∪ !! ∩ !! ∅ !! { !! }
|-
! [[Braille]]
| {{Braille cell|type=image|4|15}} || {{Braille cell|type=image|4|26}} || {{Braille cell|type=image|46|436}} || {{Braille cell|type=image|46|146}} || {{Braille cell|type=image|456|236}} || {{Braille cell|type=image|46|12536}} || {{Braille cell|type=image|46|42536}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ⊂ !! ⊃ !! ⊆ !! ⊇
|-
! [[Braille]]
| {{Braille cell|type=image|456|5|13}} || {{Braille cell|type=image|456|46|2}} || {{Braille cell|type=image|456|5|13|156}} || {{Braille cell|type=image|456|46|2|156}} 
|}<ref name=Acharya />

=== Misc. signs  ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ⊕ !! ⊗ !! ⊡
|-
! [[Braille]]
| {{Braille cell|type=image|1426|14|456|1426|436|14256}} || {{Braille cell|type=image|1426|14|456|1426|16|14256}} || {{Braille cell|type=image|1426|256|456|1426|16|14256}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Intersecting lines !! @ !! Ditto !! Tally mark !! +- !! -+
|-
! [[Braille]]
| {{Braille cell|type=image|1426|42}} || {{Braille cell|type=image|4|1}} || {{Braille cell|type=image|6|3}} || {{Braille cell|type=image|456}} || {{Braille cell|type=image|436|5|36}} || {{Braille cell|type=image|36|5|436}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! {{pipe}} !! ≃ !! ≡ !! — !! {{pipe}}&nbsp;{{pipe}} (modulus) !! . dot
|-
! [[Braille]]
| {{Braille cell|type=image|1256}} || {{Braille cell|type=image|4|156|156}} || {{Braille cell|type=image|456|123}} || {{Braille cell|type=image|156}} || {{Braille cell|type=image|1256|1256}} || {{Braille cell|type=image|16}} 
|}<ref name=Acharya />

=== Polygons ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Pentagon !! Hexagon !! Heptagon !! Octagon !! Nonagon !! <math>n</math>-agon
|-
! [[Braille]]
| {{Braille cell|type=image|1426|26}} || {{Braille cell|type=image|1426|253}} || {{Braille cell|type=image|1426|2536}} || {{Braille cell|type=image|1426|236}} || {{Braille cell|type=image|1426|53}} || {{Braille cell|type=image|1426}} + (Nemeth Braille of <math>n</math>)


|}<ref name=Acharya />

=== Triangles ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Acute !! Right !! Isosceles !! Obtuse !! Scalene
|-
! [[Braille]]
| {{Braille cell|type=image|1426|4253|46|1|14256}} || {{Braille cell|type=image|1426|4253|46|1253|14256}} || {{Braille cell|type=image|1426|4253|46|42|14256}} || {{Braille cell|type=image|1426|4253|46|153|14256}} || {{Braille cell|type=image|1426|4253|46|423|14256}} 
|}<ref name=Acharya />

=== Other signs ===

{| class="wikitable sortable" style="text-align:center"
|+
|- 
! Symbol !! Acute angle !! Right angle !! Obtuse angle !! Hexagon star !! ¶ !! § 
|-
! [[Braille]]
| {{Braille cell|type=image|1426|426|46|1|14256}} || {{Braille cell|type=image|1426|426|46|1253|14256}} 
|| {{Braille cell|type=image|1426|426|46|153|14256}} || {{Braille cell|type=image|1426|423}} || {{Braille cell|type=image|4|6|1423}} || {{Braille cell|type=image|4|6|423}} 
|}<ref name=Acharya />

{| class="wikitable" style="text-align:center"
|+
|- 
! Symbol !! ref. indicator !! <nowiki><i></nowiki> !! <nowiki><b></nowiki> !! letter sign !! composite function !! {{pipe}}det{{pipe}} matrix !! ∫ !! ∂
|-
! [[Braille]]
| {{Braille cell|type=image|4|14256}} || {{Braille cell|type=image|46}} || {{Braille cell|type=image|456}} || {{Braille cell|type=image|56}} || {{Braille cell|type=image|46|16}} || {{Braille cell|type=image|6|1256}} || {{Braille cell|type=image|4236}} || {{Braille cell|type=image|4|145}} 
|}<ref name=Acharya />

===Greek letters and Latin letters ===
Greek and Latin letters are based on the assignments of International Greek Braille.

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! small Latin letters !! capital Latin letters !! small Greek letters !! capital Greek letters
|-
! [[Braille]]
| (Braile of the letter) || {{Braille cell|type=image|6}} + (Braile of the letter) || {{Braille cell|type=image|46}} + (Braile of the letter) || {{Braille cell|type=image|46|6}} + (Braile of the letter)
|}<ref name=Acharya />

==See also==
*Gardner-Salinas braille
*[[Software:WIMATS|WIMATS]], application software to transcript mathematical and scientific text input into braille script.

==References==
{{Reflist}}

== External links ==
* [http://www.dotlessbraille.org/NemethIntro.htm An Introduction to the Nemeth Braille Code for Mathematics]
* [http://www.brailleauthority.org/mathscience/nemeth1972.pdf PDF of the 1972 Nemeth Braille Code for Mathematics]
* [http://myria.math.aegean.gr/braille/index-en.html latex2nemeth], application software that transcribes LaTeX to Nemeth Braille.
* [http://www.duxburysystems.org/documentation/braille/index.htm Braille files for the Nemeth Braille Code for Mathematics; and other resources about braille transcribing]
* [https://nfb.org//images/nfb/publications/fr/fr28/fr280110.htm The History of Nemeth Code]
* [https://chezdom.net/mathematicalbraillecodes/ Braille Mathematical Notations: Different Braille Mathematical Codes from Around the World]


[[Category:Mathematical notation]]
[[Category:Mathematical markup languages]]

{{Sourceattribution|Nemeth Braille}}