The Gardner–Salinas braille codes are a proposed 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.

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. However, 15 years later Nemeth code was still the standard, with no further change .

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.

Table of Gardner–Salinas 8-dot (GS8) braille

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.

Digits

Symbol 0? 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. Sources disagree on 0. Both claimed forms are presented above. The second is the ISO form. Note however that ISO is concerned only with a one-to-one assignment between 8-dot braille and ASCII, and so has no particular connection to Gardner–Salinas braille.

Upper-case letters

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 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

Symbol Parentheses Brackets single quote open close open close open close ? Braille

The single quotation marks are the ASCII back tick ` and apostrophe '.

ASCII symbols and mathematical operators

Symbol " $ & @ \ ^ _ ` { } ~ Braille Symbol # % * + / < = > × · ÷ Braille

Text symbols

Symbol • © † ‡ £ Braille

Math and science symbols

Symbol ≈ ≅ ≡ ∝ x (abs. value) ∞ ∫ line ∫ closed ∫ Braille ...

Symbol 〈 〉 ∇ ∂ ... → ← ○ ℵ ∈ ⇌ Braille

Markup

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 Symbol Script Bold Italic Underline Definable font 1 Fractur Roman Underline Braille

The difference between the two underline markers is not explained.

Shape symbols Symbol ⊥ ∥ ∠ Open Square ⊿ Braille

Set theory Symbol ∪ ∩ ⊂ ⊃ Braille

References

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