Nemeth Braille
Nemeth Braille  

Type  Alphabet Braille code for encoding mathematical and scientific notation linearly

Languages  Several 
Creator  Abraham Nemeth 
Time period 
1952 to the present 
The Nemeth Braille Code for Mathematics is a Braille code for encoding mathematical and scientific notation linearly using standard sixdot 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,^{[1]} and beginning in 1992 was integrated into Unified English Braille. It is an example of a compact humanreadable markup language.
Nemeth Braille is just one code used to write mathematics in braille. There are many systems in use around the world.^{[2]}
Principles of the Nemeth Code
The Nemeth Code Book (1972) opens with the following words:
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.
— ^{[3]}
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
Symbol  *  ,  … 

Braille 
^{[4]}
Number Signs
Symbol  Number prefix  . / , (decimal)  , / . (separator)  0  1  2  3  4  5  6  7  8  9 

Braille 
^{[3]}
Operators
Symbol  +    ×  ·  ÷  . (decimal)  √  i√ (radical index) 

Braille  
Symbol  inner √ (1st)  inner √ (2nd)  end 1st √  end 2nd √  long division  /  !  
Braille 
^{[4]}
Parentheses and Brackets
Symbol  (  )  [  ]  {  } 

Braille 
^{[4]}
Fractions
Symbol  simple  complex  hypercomplex  fraction in mixed number  

open  line  close  open  line  close  open  line  close  open  line  close  
Braille 
^{[4]}
Other modifiers
Symbol  ∵  ∴  ∶  ∷  ′  ″ 

Braille 
^{[4]}
Symbol  ∞  ∝  °  %  ✓ 

Braille 
^{[4]}
Braille indicators
Symbol  Punctuation  Superscript  Subscript  Baseline  Omission  Cancel (close)  Cancel (open)  Run Over  Directly Over  Directly Under  Beginning  Termination 

Braille 
^{[4]}
Comparison Signs
Symbol  >  <  ≥  ≤  ≧  ≦ 

Braille 
^{[4]}
Symbol  ⋝  ⋜  ⪚  ⪙ 

Braille 
^{[4]}
Symbol  ><  <>  >=<  <=> 

Braille 
^{[4]}
Symbol  =  ≠  ≱  ≰  ∼  ≈  ≅  ±  ∓ 

Braille 
^{[4]}
Geometry
Symbol  Parallel  Perpendicular  Angle  Right angle 

Braille 
^{[4]}
Symbol  Arc down  Arc up  Trapezoid  Square  Rectangle  Parallelogram 

Braille 
^{[4]}
Symbol  Rhombus  Isosceles trapezoid  Triangle  Right triangle  Circle  Ellipse 

Braille 
^{[4]}
Arrows
Symbol  ⟶  ⟵  ⟷ 

Braille 
^{[4]}
Symbol  →  ⇌  ⇒ 

Braille 
^{[4]}
Trig functions
Function  Sine  Cosine  Tangent 

Braille 
^{[4]}
Function  Secant  Cosecant  Cotangent  Logarithm 

Braille 
^{[4]}
Set Theory
Symbol  ∈  ∋  ∪  ∩  ∅  {  } 

Braille 
^{[4]}
Symbol  ⊂  ⊃  ⊆  ⊇ 

Braille 
^{[4]}
Misc. signs
Symbol  ⊕  ⊗  ⊡ 

Braille 
^{[4]}
Symbol  Intersecting lines  @  Ditto  Tally mark  +  + 

Braille 
^{[4]}
Symbol    ≃  ≡  ―    (modulus)  . dot 

Braille 
^{[4]}
Polygons
Symbol  Pentagon  Hexagon  Heptagon  Octagon  Nonagon  agon 

Braille 
+ (Nemeth Braille of )

^{[4]}
Triangles
Symbol  Acute  Right  Isosceles  Obtuse  Scalene 

Braille 
^{[4]}
Other signs
Symbol  Acute angle  Right angle  Obtuse angle  Hexagon star  ¶  §  

Braille 
^{[4]}
Symbol  ref. indicator  <i>  <b>  letter sign  composite function  det matrix  ∫  ∂ 

Braille 
^{[4]}
Greek letters and Latin letters
Greek and Latin letters are based on the assignments of International Greek Braille.
Symbol  small Latin letters  capital Latin letters  small Greek letters  capital Greek letters 

Braille  (Braile of the letter)  + (Braile of the letter)  + (Braile of the letter)  + (Braile of the letter) 
^{[4]}
See also
 Gardner Salinas braille
 WIMATS, application software to transcript mathematical and scientific text input into braille script.
References
 ^ "The History of Nemeth Code". Retrieved 20120426.
 ^ "Braille Mathematical Notations". 20080722. Retrieved 20120426.
 ^ ^{a} ^{b} "The Nemeth Braille Code for Mathematics and Science Notation 1972 Revision" (PDF). Retrieved 20120426.
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} ^{h} ^{i} ^{j} ^{k} ^{l} ^{m} ^{n} ^{o} ^{p} ^{q} ^{r} ^{s} ^{t} ^{u} ^{v} ^{w} ^{x} ^{y} ^{z} ^{aa} ^{ab} "Nemeth Braille (Mathematics Braille)". Archived from the original on 20120421. Retrieved 20120425.
External links
 An Introduction to the Nemeth Braille Code for Mathematics
 PDF of the 1972 Nemeth Braille Code for Mathematics
 latex2nemeth, application software that transcribes LaTeX to Nemeth Braille.
 Braille files for the Nemeth Braille Code for Mathematics; and other resources about braille transcribing
 The History of Nemeth Code
 Braille Mathematical Notations: Different Braille Mathematical Codes from Around the World