Nemeth Braille
Template:Short description Template:Redirect Template:Infobox writing system 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.<ref name=interview>Template:Cite web</ref> 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.<ref name=world>Template:Cite web</ref>
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 | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Number signs
| Symbol | Number prefix |
Decimal point |
Thousands separator |
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Operators
| Symbol | + | - | × | · | ÷ | . (decimal) | √ | i√ (radical index) |
|---|---|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
| Symbol | inner √ (1st) | inner √ (2nd) | end 1st √ | end 2nd √ | long division | / | ! | |
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Parentheses and brackets
| Symbol | ( | ) | [ | ] | { | } |
|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Fractions
| Symbol | simple | complex | hypercomplex | fraction in mixed number | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| open | line | close | open | line | close | open | line | close | open | line | close | |
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Other modifiers
| Symbol | ∵ | ∴ | : | ∷ | Template:Prime | ″ |
|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | ∞ | ∝ | ° | % | ✓ |
|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Braille indicators
| Symbol | Punctuation | Superscript | Subscript | Baseline | Omission | Cancel (close) | Cancel (open) | Run Over | Directly Over | Directly Under | Beginning | Termination |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Comparison signs
| Symbol | > | < | ≥ | ≤ | ≧ | ≦ |
|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | ⋝ | ⋜ | ⪚ | ⪙ |
|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | >< | <> | >=< | <=> |
|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Geometry
| Symbol | Parallel | Perpendicular | Angle | Right angle |
|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Arrows
| Symbol | ⟶ | ⟵ | ⟷ |
|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | → | ⇌ | ⇒ |
|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Trig functions
| Function | Sine | Cosine | Tangent |
|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Function | Secant | Cosecant | Cotangent | Logarithm |
|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Set theory
| Symbol | ∈ | ∋ | ∪ | ∩ | ∅ | { | } |
|---|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | ⊂ | ⊃ | ⊆ | ⊇ |
|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Misc. signs
| Symbol | ⊕ | ⊗ | ⊡ |
|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | Intersecting lines | @ | Ditto | Tally mark | +- | -+ |
|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Polygons
| Symbol | Pentagon | Hexagon | Heptagon | Octagon | Nonagon | <math>n</math>-agon |
|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell + (Nemeth Braille of <math>n</math>)
|
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Triangles
| Symbol | Acute | Right | Isosceles | Obtuse | Scalene |
|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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Other signs
| Symbol | Acute angle | Right angle | Obtuse angle | Hexagon star | ¶ | § |
|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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| Symbol | ref. indicator | <i> | <b> | letter sign | composite function | Template:PipedetTemplate:Pipe matrix | ∫ | ∂ |
|---|---|---|---|---|---|---|---|---|
| Braille | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell | Template:Braille cell |
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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) | Template:Braille cell + (Braille of the letter) | Template:Braille cell + (Braille of the letter) | Template:Braille cell + (Braille of the letter) |
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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 Template:Webarchive
- 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