Gardner–Salinas braille codes

Short description: Tactile system for encoding mathematical and scientific notation

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.

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.

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	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

Apart from 0, this is the same as the Antoine notation used in French and Luxembourgish 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	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
Symbol	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
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

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	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
Symbol	ν	ξ	ο	π	ρ	σ	τ	υ	φ	χ	ψ	ω
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
Symbol	Γ	Δ	Θ	Λ	Ξ	Π	Σ	Υ	Φ	Ψ	Ω
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

Characters differing from English Braille

Symbol	Parentheses		Brackets		single quote
	open	close	open	close	open	close	?
Braille	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell

ASCII symbols and mathematical operators

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

Text symbols

Symbol	•	©	†	‡	£
Braille	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell

Math and science symbols

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

Symbol	〈	〉	∇	∂	...	→	←	○	ℵ	∈	⇌
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

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	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell

Shape symbols

Symbol	⊥	∥	∠	Open Square	⊿
Braille	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell

Set theory

Symbol	∪	∩	⊂	⊃
Braille	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell	Template:Braille Cell

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