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Nemeth Braille

Braille code for mathematics and science

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. It is an example of a compact human-readable markup language.

Nemeth Braille is one code used to write mathematics in braille. There are many systems in use around the world.

01Principles 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.

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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.

02Table of Nemeth braille codes

General signs

Symbol*,...
Braille

Number signs

SymbolNumber
prefix
Decimal
point
Thousands
separator
0123456789
Braille

Operators

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

Parentheses and brackets

Symbol()[]{}
Braille

Fractions

Symbol simplecomplexhypercomplexfraction in mixed number
openlinecloseopenlinecloseopenlinecloseopenlineclose
Braille

Other modifiers

Symbol:
Braille
Symbol°%
Braille

Braille indicators

SymbolPunctuationSuperscriptSubscriptBaselineOmissionCancel (close)Cancel (open)Run OverDirectly OverDirectly UnderBeginningTermination
Braille

Comparison signs

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

Geometry

Arrows

Symbol
Braille
Symbol
Braille

Trig functions

FunctionSineCosineTangent
Braille
FunctionSecantCosecantCotangentLogarithm
Braille

Set theory

Symbol{}
Braille
Symbol
Braille

Misc. signs

Symbol
Braille
SymbolIntersecting lines@DittoTally mark+--+
Braille
Symbol|, | | (modulus). dot
Braille

Polygons

SymbolPentagonHexagonHeptagonOctagonNonagonn-agon
Braille + (Nemeth Braille of n)

Triangles

SymbolAcuteRightIsoscelesObtuseScalene
Braille

Other signs

SymbolAcute angleRight angleObtuse angleHexagon star§
Braille
Symbolref. indicatoritalicsboldletter signcomposite function|det| matrix
Braille

Greek letters and Latin letters

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

Symbolsmall Latin letterscapital Latin letterssmall Greek letterscapital Greek letters
Braille (Braille of the letter) + (Braille of the letter) + (Braille of the letter) + (Braille of the letter)
Watch videos about Nemeth BrailleExplainers and documentaries on YouTube (opens in a new tab)

Sources and credits

This article is adapted from the Wikipedia article Nemeth Braille, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.

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