# Gardner–Salinas braille codes

The **Gardner–Salinas** braille codes are a method of encoding mathematical and scientific notation linearly using braille cells for tactile reading by the visually impaired. The most common form of Gardner–Salinas braille is the 8-cell variety, commonly called *GS8*. There is also a corresponding 6-cell form called *GS6*.^{[1]}

The codes were developed as a replacement for Nemeth Braille by John A. Gardner, a physicist at Oregon State University, and Norberto Salinas, an Argentinian mathematician.

The Gardner–Salinas braille codes are an example of a compact human-readable markup language. The syntax is based on the LaTeX system for scientific typesetting.^{[citation needed]}

## Table of Gardner–Salinas 8-dot (GS8) braille[edit]

The set of lower-case letters, the period, comma, semicolon, colon, exclamation mark, apostrophe, and opening and closing double quotes are the same as in Grade-2 English Braille.^{[1]}

### Digits[edit]

Symbol | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|---|

Braille |

Apart from 0, this is the same as the Antoine notation used in French and Luxembourgish Braille.

### Upper-case letters[edit]

GS8 upper-case letters are indicated by the same cell as standard English braille (and GS8) lower-case letters, with dot #7 added.

Symbol | A | B | C | D | E | F | G | H | I | J | K | L | M |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

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

Symbol | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Braille |

Compare Luxembourgish Braille.

### Greek letters[edit]

Dot 8 is added to the letter forms of International Greek Braille to derive Greek letters:

Symbol | α | β | γ | δ | ε | ζ | η | θ | ι | κ | λ | μ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

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

Symbol | ν | ξ | ο | π | ρ | σ | τ | υ | φ | χ | ψ | ω |

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

Symbol | Γ | Δ | Θ | Λ | Ξ | Π | Σ | Υ | Φ | Ψ | Ω | |

Braille |

### Characters differing from English Braille[edit]

Symbol | Parentheses | Brackets | single quote | ||||
---|---|---|---|---|---|---|---|

open | close | open | close | open | close | ? | |

Braille |

### ASCII symbols and mathematical operators[edit]

Symbol | " | $ | & | @ | \ | ^ | _ | ` | { | } | ~ |
---|---|---|---|---|---|---|---|---|---|---|---|

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

Symbol | # | % | * | + | / | < | = | > | × | · | ÷ |

Braille |

### Text symbols[edit]

Symbol | • | © | † | ‡ | £ |
---|---|---|---|---|---|

Braille |

### Math/Science symbols[edit]

Symbol | ∼ | ≈ | ≡ | ∝ | |x| (abs. value) | ∞ | ∫ | line ∫ | closed ∫ |
---|---|---|---|---|---|---|---|---|---|

Braille |

Symbol | 〈 | 〉 | ∇ | ∂ | … | → | ← | ○ | ℵ | ∈ | ⇌ |
---|---|---|---|---|---|---|---|---|---|---|---|

Braille |

### Markup[edit]

Symbol | Superscript | Subscript | Left-superscript | Left-subscript | Begin fraction | Denominator | End fraction | Over * |
---|---|---|---|---|---|---|---|---|

Braille |

* Encodes the fraction-slash for the single adjacent digits/letters as numerator and denominator.

Symbol | √ | complex radicand * | displayed equation ** | math expressions ** | hyperlink ** | ||||
---|---|---|---|---|---|---|---|---|---|

Open | Close | Open | Close | Open | Close | Open | Close | ||

Braille |

* Used for any > 1 digit radicand.

** Used for markup to represent inkprint text.

Symbol | Array | ||||||
---|---|---|---|---|---|---|---|

Begin | End | End element | End line | vert. stack | horiz. combo | superposition | |

Braille |

Symbol | Misc. Symbol * | Modifiers | ||||||
---|---|---|---|---|---|---|---|---|

Begin | End | Quantity | Markup indicator | Inverted | Stroke/Not | Variant | Large | |

Braille |

### Typeface indicators[edit]

Symbol | Script | Bold | Italic | Underline | Definable font 1 | Fractur | Roman | Underline |
---|---|---|---|---|---|---|---|---|

Braille |

### Shape symbols[edit]

Symbol | ⊥ | ∥ | ∠ | Open Square | ⊿ |
---|---|---|---|---|---|

Braille |

### Set theory[edit]

Symbol | ∪ | ∩ | ⊂ | ⊃ |
---|---|---|---|---|

Braille |

## References[edit]

- ^
^{a}^{b}"Index of Topics in Braille Section".*Oregon State University Science Access Project Braille topics*. Archived from the original on 2012-04-20. Retrieved 2012-04-29.

- Blind physicist creates better Braille — a CNN news item, November 9, 1995
- The world of blind mathematicians — article in
*Notices of the AMS*, November 2002