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Tactile system for encoding mathematical and scientific notation From Wikipedia, the free encyclopedia
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]
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]
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.
GS8 upper-case letters are indicated by the same cell as standard English braille (and GS8) lower-case letters, with dot #7 added.
Compare Luxembourgish Braille.
Dot 8 is added to the letter forms of International Greek Braille to derive Greek letters:
Symbol | Parentheses | Brackets | single quote | ||||
---|---|---|---|---|---|---|---|
open | close | open | close | open | close | ? | |
Braille | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Symbol | • | © | † | ‡ | £ |
---|---|---|---|---|---|
Braille | ![]() | ![]() | ![]() | ![]() | ![]() |
Symbol | ~ | ≈ | ≡ | ∝ | |x| (abs. value) | ∞ | ∫ | line ∫ | closed ∫ |
---|---|---|---|---|---|---|---|---|---|
Braille | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Symbol | 〈 | 〉 | ∇ | ∂ | ... | → | ← | ○ | ℵ | ∈ | ⇌ |
---|---|---|---|---|---|---|---|---|---|---|---|
Braille | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
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 | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Symbol | Script | Bold | Italic | Underline | Definable font 1 | Fractur | Roman | Underline |
---|---|---|---|---|---|---|---|---|
Braille | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Symbol | ⊥ | ∥ | ∠ | Open Square | ⊿ |
---|---|---|---|---|---|
Braille | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
Symbol | ∪ | ∩ | ⊂ | ⊃ |
---|---|---|---|---|
Braille | ![]() ![]() | ![]() ![]() | ![]() ![]() | ![]() ![]() |
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