Nemeth Braille  

Script type  Braille code for encoding mathematical and scientific notation linearly 
Creator  Abraham Nemeth 
Time period  1952 to the present 
Languages  Several 
The Nemeth Braille Code for Mathematics and Science Notation 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]} 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]}
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.
Symbol  *  ,  ... 

Braille 
^{[4]}
Symbol  Number prefix 
Decimal point 
Thousands separator 
0  1  2  3  4  5  6  7  8  9 

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

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

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

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

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

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

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

Braille 
^{[4]}
Symbol  ⋝  ⋜  ⪚  ⪙ 

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

Braille 
^{[4]}
Symbol  =  ≠  ≯  ≮  ~  ≈  ≅  ±  ∓ 

Braille 
^{[4]}
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]}
Symbol  ⟶  ⟵  ⟷ 

Braille 
^{[4]}
Symbol  →  ⇌  ⇒ 

Braille 
^{[4]}
Function  Sine  Cosine  Tangent 

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

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

Braille 
^{[4]}
Symbol  ⊂  ⊃  ⊆  ⊇ 

Braille 
^{[4]}
Symbol  ⊕  ⊗  ⊡ 

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

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

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

Braille  + (Nemeth Braille of )

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

Braille 
^{[4]}
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 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  (Braille of the letter)  + (Braille of the letter)  + (Braille of the letter)  + (Braille of the letter) 
^{[4]}