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# Nemeth Braille

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 Title: Nemeth Braille Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Nemeth Braille

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]

## Contents

• Principles of the Nemeth Code 1
• Table of Nemeth braille codes 2
• General Signs 2.1
• Number Signs 2.2
• Operators 2.3
• Parentheses and Brackets 2.4
• Fractions 2.5
• Other modifiers 2.6
• Braille indicators 2.7
• Comparison Signs 2.8
• Geometry 2.9
• Arrows 2.10
• Trig functions 2.11
• Set Theory 2.12
• Misc. signs 2.13
• Polygons 2.14
• Triangles 2.15
• Other signs 2.16
• Greek letters 2.17
• References 4

## 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

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 close open close open close open close
Braille
[4]
Symbol / complex / complex ― hypercomplex ―
Braille
[4]

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]

Symbol \perp
Braille
[4]
Symbol
Braille
[4]
Symbol
Braille
[4]

Symbol
Braille
[4]
Symbol
Braille
[4]

### Trig functions

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

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 Regular Irregular
Pentagon Hexagon Pentagon Hexagon Heptagon Octagon Nonagon
Braille
[4]

### Triangles

Symbol Acute Isosceles Obtuse Scalene
Braille
[4]

### Other signs

Symbol Acute angle Obtuse angle Hexagon star §
Braille
[4]
Symbol ref. indicator letter sign composite function |det| matrix
Braille
[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
[4]
Symbol σ ω Σ Δ ϵ λ υ φ
Braille
[4]