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Nemeth Braille

## Summary

The Nemeth Braille Code for Mathematics and Science Notation 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] It is an example of a compact human-readable markup language.

Nemeth Braille
Script type Braille code for encoding mathematical and scientific notation linearly
CreatorAbraham Nemeth
Time period
1952 to the present
LanguagesSeveral
This article contains phonetic transcriptions in the International Phonetic Alphabet (IPA). For an introductory guide on IPA symbols, see Help:IPA. For the distinction between [ ], / / and ⟨ ⟩, see IPA § Brackets and transcription delimiters.

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

Symbol * , ...
Braille

### Number signs

Symbol Number
prefix
Decimal
point
Thousands
separator
0 1 2 3 4 5 6 7 8 9
Braille

### Operators

Symbol + - × · ÷ . (decimal) i√ (radical index)
Braille
Symbol inner √ (1st) inner √ (2nd) end 1st √ end 2nd √ long division / !
Braille

### Parentheses and brackets

Symbol ( ) [ ] { }
Braille

### Fractions

Symbol simple complex hypercomplex fraction in mixed number
open line close open line close open line close open line close
Braille

### Other modifiers

Symbol :
Braille
Symbol ° %
Braille

### Braille indicators

Symbol Punctuation Superscript Subscript Baseline Omission Cancel (close) Cancel (open) Run Over Directly Over Directly Under Beginning Termination
Braille

### Comparison signs

Symbol > <
Braille
Symbol
Braille
Symbol >< <> >=< <=>
Braille
Symbol = ~ ±
Braille

### Geometry

Symbol Parallel Perpendicular Angle Right angle
Braille
Symbol Arc down Arc up Trapezoid Square Rectangle Parallelogram
Braille

### Arrows

Symbol
Braille
Symbol
Braille

### Trig functions

Function Sine Cosine Tangent
Braille
Function Secant Cosecant Cotangent Logarithm
Braille

### Set theory

Symbol { }
Braille
Symbol
Braille

### Misc. signs

Symbol
Braille
Symbol Intersecting lines @ Ditto Tally mark +- -+
Braille
Symbol | | | (modulus) . dot
Braille

### Polygons

Symbol Pentagon Hexagon Heptagon Octagon Nonagon ${\displaystyle n}$ -agon
Braille                  + (Nemeth Braille of ${\displaystyle n}$ )

### Triangles

Symbol Acute Right Isosceles Obtuse Scalene
Braille

### Other signs

Symbol Acute angle Right angle Obtuse angle Hexagon star §
Braille
Symbol ref. indicator <i> <b> letter sign composite function |det| matrix
Braille

### 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 (Braille of the letter)   + (Braille of the letter)   + (Braille of the letter)    + (Braille of the letter)