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, 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.

Principles of the Nemeth Code

The Nemeth Code Book opens with the following words:
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

General Signs

Symbol*,…
Braille

Number Signs

Operators

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

Parentheses and Brackets

Symbol
Braille

Fractions

Other modifiers

Symbol∵∴∶∷′″
Braille

Symbol∞∝°%✓
Braille

Braille indicators

SymbolPunctuationSuperscriptSubscriptBaselineOmissionCancel Cancel Run OverDirectly OverDirectly UnderBeginningTermination
Braille

Comparison Signs

Symbol><≥≤≧≦
Braille

Symbol⋝⋜⪚⪙
Braille

Symbol><<>>=<<=>
Braille

Symbol=≠≱≰∼≈≅±∓
Braille

Geometry

SymbolParallelPerpendicularAngleRight angle
Braille

SymbolArc downArc upTrapezoidSquareRectangleParallelogram
Braille

SymbolRhombusIsosceles trapezoidTriangleRight triangleCircleEllipse
Braille

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|≃≡―| | . dot
Braille

Polygons

SymbolPentagonHexagonHeptagonOctagonNonagon-agon
Braille +

Triangles

SymbolAcuteRightIsoscelesObtuseScalene
Braille

Other signs

SymbolAcute angleRight angleObtuse angleHexagon star§
Braille-

Symbolref. indicatorletter 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 + + +