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.
Principles of the Nemeth Code The Nemeth Code Book (1972) 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 Symbol Numberprefix Decimalpoint Thousandsseparator 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
Symbol Rhombus Isosceles trapezoid Triangle Right triangle Circle Ellipse 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 -agon Braille + (Nemeth Braille of )
Triangles
Symbol Acute Right Isosceles Obtuse Scalene Braille
Other signs
+ Symbol Acute angle Right angle Obtuse angle Hexagon star ¶ § Braille
+ Symbol ref. indicator italics bold 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)
See also Gardner-Salinas braille WIMATS, application software to transcript mathematical and scientific text input into braille script.
References
External links An Introduction to the Nemeth Braille Code for Mathematics PDF of the 1972 Nemeth Braille Code for Mathematics latex2nemeth, application software that transcribes LaTeX to Nemeth Braille. Braille files for the Nemeth Braille Code for Mathematics; and other resources about braille transcribing The History of Nemeth Code Braille Mathematical Notations: Different Braille Mathematical Codes from Around the World