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 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.[1]
Digits
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
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
ASCII symbols and mathematical operators
Symbol
|
"
|
$
|
&
|
@
|
\
|
^
|
_
|
`
|
{
|
}
|
~
|
Braille
|
|
|
|
|
|
|
|
|
|
|
|
Symbol
|
#
|
%
|
*
|
+
|
/
|
<
|
=
|
>
|
×
|
·
|
÷
|
Braille
|
|
|
|
|
|
|
|
|
|
|
|
Text symbols
Math/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
|
|
|
|
|
|
|
|
|
Shape symbols
Set theory
References
-
^ a b "Index of Topics in Braille Section". Oregon State University Science Access Project Braille topics. 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
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