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Nemeth Braille

For other uses, see Nemeth (disambiguation).

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,[1] and beginning in 1992 was integrated into Unified English Braille. It is an example of a compact human-readable 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 to 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, but a knowledge of mathematics is not required to produce mathematical braille in the Nemeth code.

Table of Nemeth braille codes

General Signs

Symbol * ,
Braille 40px40px 40px 40px40px40px
[4]

Number Signs

Symbol Number prefix . / , (decimal) , / . (separator) 0 1 2 3 4 5 6 7 8 9
Braille 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px
[3]

Operators

Symbol + - × · ÷ = . (decimal) i√ (radical index)
Braille 40px 40px 40px40px 40px 40px40px 40px40px 40px 40px 40px
Symbol inner √ (1st) inner √ (2nd) end 1st √ end 2nd √ long division /  !
Braille 40px 40px40px 40px40px 40px40px40px 40px 40px 40px
[4]

Parentheses and Brackets

Symbol ( ) [ ] { }
Braille 40px 40px 40px40px 40px40px 40px40px 40px40px
[4]

Fractions

Symbol simple complex hypercomplex fraction in mixed number
open close open close open close open close
Braille 40px 40px 40px40px 40px40px 40px40px40px 40px40px40px 40px40px 40px40px
[4]
Symbol / complex / complex ― hypercomplex ―
Braille 40px40px 40px 40px40px40px 40px40px 40px40px40px
[4]

Other modifiers

Symbol
Braille 40px40px 40px40px 40px40px 40px40px 40px 40px40px
[4]
Symbol °  %
Braille 40px40px 40px40px 40px40px 40px40px 40px40px
[4]

Braille indicators

Symbol Punctuation Superscript Subscript Baseline Omission Cancel (close) Cancel (open) Run Over Directly Over Directly Under Beginning Termination
Braille 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px 40px
[4]

Comparison Signs

Symbol > <
Braille 40px40px 40px40px 40px40px40px 40px40px40px 40px40px40px40px 40px40px40px40px
[4]
Symbol
Braille 40px40px40px 40px40px40px 40px40px40px40px 40px40px40px40px
[4]
Symbol >< <> >=< <=>
Braille 30px30px30px30px30px 30px30px30px30px30px 30px30px30px30px30px30px30px30px 30px30px30px30px30px30px30px30px
[4]
Symbol ±
Braille 40px40px40px 40px40px40px 40px40px40px 40px40px 40px40px40px40px 40px40px40px40px 40px40px 40px40px
[4]

Geometry

Symbol <math>\perp</math>
Braille 40px40px 40px40px 40px40px 40px40px40px40px40px
[4]
Symbol 10px
Braille 40px40px 40px40px 40px40px 40px40px 40px40px 40px40px
[4]
Symbol 20px x14px
Braille 40px40px 40px40px 40px40px 40px40px40px40px40px 40px40px 40px40px
[4]

Arrows

Symbol
Braille 40px40px40px40px 40px40px40px40px 40px40px40px40px40px
[4]
Symbol
Braille 40px40px 40px40px40px40px40px40px40px40px 40px40px40px40px
[4]

Trig functions

Function Sine Cosine Tangent
Braille 40px40px40px 40px40px40px 40px40px40px
[4]
Function Secant Cosecant Cotangent Logarithm
Braille 40px40px40px 40px40px40px 40px40px40px 40px40px40px
[4]

Set Theory

Symbol {}
Braille 40px40px 40px40px 40px40px 40px40px 40px40px 40px40px40px40px
[4]
Symbol
Braille 40px40px40px 40px40px40px 40px40px40px40px 40px40px40px40px
[4]

Misc. signs

Symbol
Braille 40px40px40px40px40px40px 40px40px40px40px40px40px 40px40px40px40px40px40px
[4]
Symbol Intersecting lines @ Ditto Tally mark +- -+
Braille 40px40px 40px40px 40px40px 40px 40px40px40px 40px40px40px
[4]
Symbol | | | (modulus) . dot
Braille 40px 40px40px40px 40px40px 40px 40px40px 40px
[4]

Polygons

Symbol Regular Irregular  
Pentagon Hexagon Pentagon Hexagon Heptagon Octagon Nonagon
Braille 40px40px 40px40px 40px40px40px 40px40px40px 40px40px 40px40px 40px40px
[4]

Triangles

Symbol Acute Isosceles Obtuse Scalene
Braille 40px40px40px40px40px Template:Braille cell Template:Braille cell Template:Braille cell
[4]

Other signs

Symbol Acute angle Obtuse angle Hexagon star §
Braille Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell
[4]
Symbol ref. indicator <i> <b> letter sign composite function |det| matrix
Braille Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell
[4]

Greek letters

Greek letters are based on the assignments of International Greek Braille.

Symbol α β γ δ θ μ ν π ρ
Braille Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell
[4]
Symbol σ ω Σ Δ ϵ λ υ φ
Braille Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell Template:Braille cell
[4]

See also

References

Template:Reflist

External links

Template:Braille