# 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

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

### General Signs

Symbol | * | , | … |
---|---|---|---|

Braille |

^{[4]}

### Number Signs

Symbol | Number prefix | . / , (decimal) | , / . (separator) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Braille |

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### Operators

Symbol | + | - | × | · | ÷ | = | . (decimal) | √ | i√ (radical index) | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Braille | |||||||||||||

Symbol | inner √ (1st) | inner √ (2nd) | end 1st √ | end 2nd √ | long division | / | ! | ||||||

Braille | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B |

^{[4]}

### Parentheses and Brackets

Symbol | ( | ) | [ | ] | { | } |
---|---|---|---|---|---|---|

Braille |

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### Fractions

Symbol | simple | complex | hypercomplex | fraction in mixed number | ||||
---|---|---|---|---|---|---|---|---|

open | close | open | close | open | close | open | close | |

Braille |

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Symbol | / | ― | complex / | complex ― | hypercomplex ― |
---|---|---|---|---|---|

Braille |

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### Other modifiers

Symbol | ∵ | ∴ | ∶ | ∷ | ′ | ″ |
---|---|---|---|---|---|---|

Braille |

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Symbol | ∞ | ∝ | ° | % | ✓ |
---|---|---|---|---|---|

Braille |

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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 | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B |

^{[4]}

### Comparison Signs

Symbol | > | < | ≥ | ≤ | ≧ | ≦ |
---|---|---|---|---|---|---|

Braille |

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Symbol | ⋝ | ⋜ | ⪚ | ⪙ |
---|---|---|---|---|

Braille |

^{[4]}

Symbol | >< | <> | >=< | <=> |
---|---|---|---|---|

Braille |

^{[4]}

Symbol | ≠ | ≱ | ≰ | ∼ | ≈ | ≅ | ± | ∓ |
---|---|---|---|---|---|---|---|---|

Braille |

^{[4]}

### Geometry

Symbol | ∥ | ∠ | ∟ | |
---|---|---|---|---|

Braille | ⠻ (braille pattern dots-12456) U+283B |

^{[4]}

Symbol | ◡ | ◠ | □ | ▭ | ▱ | |
---|---|---|---|---|---|---|

Braille |

^{[4]}

Symbol | ◇ | △ | ⊿ | ◯ | ||
---|---|---|---|---|---|---|

Braille | ⠻ (braille pattern dots-12456) U+283B |

^{[4]}

### Arrows

Symbol | ⟶ | ⟵ | ⟷ |
---|---|---|---|

Braille |

^{[4]}

Symbol | → | ⇌ | ⇒ |
---|---|---|---|

Braille |

^{[4]}

### Trig functions

Function | Sine | Cosine | Tangent |
---|---|---|---|

Braille |

^{[4]}

Function | Secant | Cosecant | Cotangent | Logarithm |
---|---|---|---|---|

Braille |

^{[4]}

### Set Theory

Symbol | ∈ | ∋ | ∪ | ∩ | ∅ | {} |
---|---|---|---|---|---|---|

Braille |

^{[4]}

Symbol | ⊂ | ⊃ | ⊆ | ⊇ |
---|---|---|---|---|

Braille |

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### Misc. signs

Symbol | ⊕ | ⊗ | ⊡ |
---|---|---|---|

Braille | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B |

^{[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 | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B | ⠻ (braille pattern dots-12456) U+283B |

^{[4]}

### Other signs

Symbol | Acute angle | Obtuse angle | Hexagon star | ¶ | § |
---|---|---|---|---|---|

Braille | ⠻ (braille pattern dots-12456) U+283B |

^{[4]}

Symbol | ref. indicator | <i> | <b> | letter sign | composite function | |det| matrix | ∫ | ∂ |
---|---|---|---|---|---|---|---|---|

Braille | ⠻ (braille pattern dots-12456) U+283B |

^{[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 |

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Symbol | σ | ω | Σ | Δ | ϵ | λ | υ | φ |
---|---|---|---|---|---|---|---|---|

Braille |

^{[4]}

## See also

## References

- ↑ "The History of Nemeth Code". Retrieved 2012-04-26.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
- ↑ "Braille Mathematical Notations". Retrieved 2012-04-26.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
- ↑
^{3.0}^{3.1}"The Nemeth Braille Code for Mathematics and Science Notation 1972 Revision" (PDF). Retrieved 2012-04-26.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles> - ↑
^{4.00}^{4.01}^{4.02}^{4.03}^{4.04}^{4.05}^{4.06}^{4.07}^{4.08}^{4.09}^{4.10}^{4.11}^{4.12}^{4.13}^{4.14}^{4.15}^{4.16}^{4.17}^{4.18}^{4.19}^{4.20}^{4.21}^{4.22}^{4.23}^{4.24}^{4.25}^{4.26}^{4.27}^{4.28}^{4.29}"Nemeth Braille (Mathematics Braille)". Retrieved 2012-04-25.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>

## External links

- Nemeth Code Made Easy by Christopher Weaver
- An Introduction to the Nemeth Braille Code for Mathematics
- PDF of the 1972 Nemeth Braille Code for Mathematics
- 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