View source for Gardner–Salinas braille codes

{{Short description|Tactile system for encoding mathematical and scientific notation}}
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''.<ref name=OSU>{{cite web |title=Index of Topics in Braille Section |url=http://dots.physics.orst.edu/gs_index.html |work=Oregon State University Science Access Project Braille topics. |access-date=2012-04-29 |url-status=dead |archive-url=https://web.archive.org/web/20120420124208/http://dots.physics.orst.edu/gs_index.html |archive-date=2012-04-20 }}</ref>

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 {{as of|lc=y|2024}}.<ref>[https://www.brailleauthority.org/formats/2011manual-web/index.html]</ref>

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|date=September 2014}}

{{See also|Braille|Braille music}}

==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]].<ref name=OSU/>

=== Digits ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! 0? !! 0? !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
|-
! [[Braille]]
| {{Braille Cell|type=8|136}} || {{Braille Cell|type=8|346}} || {{Braille Cell|type=8|16}} || {{Braille Cell|type=8|126}} || {{Braille Cell|type=8|146}} || {{Braille Cell|type=8|1456}} || {{Braille Cell|type=8|156}} || {{Braille Cell|type=8|1246}} || {{Braille Cell|type=8|12456}} || {{Braille Cell|type=8|1256}} || {{Braille Cell|type=8|246}} 
|}

Apart from 0, this is the same as the [[Antoine notation]] used in [[French Braille|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.

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! A !! B !! C !! D !! E !! F !! G !! H !! I !! J !! K !! L !! M
|-
! [[Braille]]
| {{Braille Cell|type=8|17}} || {{Braille Cell|type=8|127}} || {{Braille Cell|type=8|147}} || {{Braille Cell|type=8|1457}} || {{Braille Cell|type=8|157}} || {{Braille Cell|type=8|1247}} || {{Braille Cell|type=8|12457}} || {{Braille Cell|type=8|1257}} || {{Braille Cell|type=8|247}} || {{Braille Cell|type=8|2457}} || {{Braille Cell|type=8|137}} || {{Braille Cell|type=8|1237}} || {{Braille Cell|type=8|1347}} 
|- 
! Symbol !! N !! O !! P !! Q !! R !! S !! T !! U !! V !! W !! X !! Y !! Z
|-
! [[Braille]]
| {{Braille Cell|type=8|13457}} || {{Braille Cell|type=8|1357}} || {{Braille Cell|type=8|12347}} || {{Braille Cell|type=8|123457}} || {{Braille Cell|type=8|12357}} || {{Braille Cell|type=8|2347}} || {{Braille Cell|type=8|23457}} || {{Braille Cell|type=8|1367}} || {{Braille Cell|type=8|12367}} || {{Braille Cell|type=8|24567}} || {{Braille Cell|type=8|13467}} || {{Braille Cell|type=8|134567}} || {{Braille Cell|type=8|13567}} 
|}

Compare [[Luxembourgish Braille]].

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

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! α !! β !! γ !! δ !! ε !! ζ !! η !! θ !! ι !! κ !! λ !! μ 
|-
! [[Braille]]
| {{Braille Cell|type=8|18}} || {{Braille Cell|type=8|128}} || {{Braille Cell|type=8|12458}} || {{Braille Cell|type=8|1458}} || {{Braille Cell|type=8|158}} || {{Braille Cell|type=8|13568}} || {{Braille Cell|type=8|1568}} || {{Braille Cell|type=8|14568}} || {{Braille Cell|type=8|248}} || {{Braille Cell|type=8|138}} || {{Braille Cell|type=8|1238}} || {{Braille Cell|type=8|1348}} 
|- 
! Symbol !! ν !! ξ !! ο !! π !! ρ !! σ !! τ !! υ !! φ !! χ !! ψ !! ω
|-
! [[Braille]]
| {{Braille Cell|type=8|13458}} || {{Braille Cell|type=8|13468}} || {{Braille Cell|type=8|1358}} || {{Braille Cell|type=8|12348}} || {{Braille Cell|type=8|12358}} || {{Braille Cell|type=8|2348}} || {{Braille Cell|type=8|23458}} || {{Braille Cell|type=8|1368}} || {{Braille Cell|type=8|1248}} || {{Braille Cell|type=8|123468}} || {{Braille Cell|type=8|134568}} || {{Braille Cell|type=8|24568}} 
|- 
! Symbol !! Γ !! Δ !! Θ !! Λ !! Ξ !! Π !! Σ !! Υ !! Φ !! Ψ !! Ω 
|-
! [[Braille]]
| {{Braille Cell|type=8|124578}} || {{Braille Cell|type=8|14578}} || {{Braille Cell|type=8|145678}} || {{Braille Cell|type=8|12378}} || {{Braille Cell|type=8|134678}} || {{Braille Cell|type=8|123478}} || {{Braille Cell|type=8|23478}} || {{Braille Cell|type=8|13678}} || {{Braille Cell|type=8|12478}} || {{Braille Cell|type=8|1345678}} || {{Braille Cell|type=8|245678}} 
|}

=== Characters differing from English Braille ===

{| class="wikitable" style="text-align:center"
|- 
!rowspan=2| Symbol !!colspan=2| Parentheses !!colspan=2| Brackets !!colspan=2| single quote !! 
|-
! open !! close !! open !! close !! open !! close !! ?
|-
! [[Braille]]
| {{Braille Cell|type=8|238}} || {{Braille Cell|type=8|457}} <!--Seems like it should be 567. Needs to be confirmed.--> || {{Braille Cell|type=8|23678}} || {{Braille Cell|type=8|35678}} || {{Braille Cell|type=8|378}} || {{Braille Cell|type=8|3}} || {{Braille Cell|type=8|2356}} 
|}

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

=== ASCII symbols and mathematical operators ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! " !! $ !! & !! @ !! \ !! ^ !! _ !! ` !! { !! } !! ~
|-
! [[Braille]]
| {{Braille Cell|type=8|2578}} || {{Braille Cell|type=8|34567}} || {{Braille Cell|type=8|12346}} || {{Braille Cell|type=8|348}} || {{Braille Cell|type=8|1678}} || {{Braille Cell|type=8|57}} || {{Braille Cell|type=8|28}} || {{Braille Cell|type=8|378}} || {{Braille Cell|type=8|1235678}} || {{Braille Cell|type=8|2345678}} || {{Braille Cell|type=8|678}} 
|- 
! Symbol !! # !! % !! * !! + !! / !! < !! = !! > !! × !! · !! ÷
|-
! [[Braille]]
| {{Braille Cell|type=8|3456}} || {{Braille Cell|type=8|2346}} || {{Braille Cell|type=8|3458}} || {{Braille Cell|type=8|257}} || {{Braille Cell|type=8|3478}} || {{Braille Cell|type=8|358}} || {{Braille Cell|type=8|235678}} || {{Braille Cell|type=8|267}} || {{Braille Cell|type=8|278}} || {{Braille Cell|type=8|258}} || {{Braille Cell|type=8|578}} 
|}

=== Text symbols ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! • !! © !! † !! ‡ !! £
|-
! [[Braille]]
| {{Braille Cell|type=8|123568}} || {{Braille Cell|type=8|148}} || {{Braille Cell|type=8|124568}} || {{Braille Cell|type=8|1234568}} || {{Braille Cell|type=8|34568}} 
|}

=== Math and science symbols ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ≈ !! ≅ !! ≡ !! ∝ !! {{pipe}}x{{pipe}} (abs. value) !! ∞ !! ∫ !! line ∫ !! closed ∫
|-
! [[Braille]]
| {{Braille Cell|type=8|23567}} || {{Braille Cell|type=8|23568}} || {{Braille Cell|type=8|12345678}} || {{Braille Cell|type=8|3678}} || {{Braille Cell|type=8|12568}}...{{Braille Cell|type=8|12568}} || {{Braille Cell|type=8|1258}} || {{Braille Cell|type=8|234678}} || {{Braille Cell|type=8|23467}} || {{Braille Cell|type=8|23468}} 
|}

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! 〈 !! 〉 !! ∇ !! ∂ !! ... !! → !! ← !! ○ !! ℵ !! ∈ !! ⇌
|-
! [[Braille]]
| {{Braille Cell|type=8|24678}} || {{Braille Cell|type=8|13578}} || {{Braille Cell|type=8|14678}} || {{Braille Cell|type=8|1468}} || {{Braille Cell|type=8|368}} || {{Braille Cell|type=8|2367}} || {{Braille Cell|type=8|3568}} || {{Braille Cell|type=8|2458}} || {{Braille Cell|type=8|15678}} || {{Braille Cell|type=8|1578}} || {{Braille Cell|type=8|234567}} 
|}

=== Markup ===

{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Superscript !! Subscript !! Left-superscript !! Left-subscript !! Begin fraction !! Denominator !! End fraction !! Over *
|-
! [[Braille]]
| {{Braille cell|type=8|35}} || {{Braille cell|type=8|26}} || {{Braille cell|type=8|3578}} || {{Braille cell|type=8|2678}} || {{Braille cell|type=8|12356}} || {{Braille cell|type=8|34}} || {{Braille cell|type=8|23456}} || {{Braille cell|type=8|345}} 
|}

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

{| class="wikitable" style="text-align:center"
! rowspan=2 scope="row" | Symbol
! rowspan=2 scope="col" | {{abbr|√|square root symbol}}
! colspan=2 scope="col" | complex radicand *
! colspan=2 scope="col" | displayed equation **
! colspan=2 scope="col" | math expressions **
! colspan=2 scope="col" | hyperlink **
|-
! scope="col" | Open
! scope="col" | Close
! scope="col" | Open
! scope="col" | Close
! scope="col" | Open
! scope="col" | Close
! scope="col" | Open
! scope="col" | Close
|-
! [[Braille]]
| {{Braille cell|type=8|2468}} || {{Braille cell|type=8|2378}} || {{Braille cell|type=8|5678}} || {{Braille cell|type=8|123678}} || {{Braille cell|type=8|345678}} || {{Braille cell|type=8|23578}} || {{Braille cell|type=8|25678}} || {{Braille cell|type=8|2357}} || {{Braille cell|type=8|2568}} 
|}

<nowiki>*</nowiki> Used for any > 1 digit radicand.

<nowiki>**</nowiki> Used for markup to represent inkprint text.

{| class="wikitable" style="text-align:center"
|- 
!rowspan=2| Symbol !!colspan=4| Array !!  !!  !! 
|-
! Begin !! End !! End element !! End line !! vert. stack !! horiz. combo !! superposition
|-
! [[Braille]]
| {{Braille cell|type=8|38}} || {{Braille cell|type=8|67}} || {{Braille cell|type=8|27}} || {{Braille cell|type=8|237}} || {{Braille cell|type=8|3467}} || {{Braille cell|type=8|34678}} || {{Braille cell|type=8|3468}} 
|}

{| class="wikitable" style="text-align:center"
|- 
!rowspan=2| Symbol !!colspan=2| Misc. Symbol * !!  !!  !!colspan=4| Modifiers
|-
! Begin !! End !! Quantity !! Markup indicator !! Inverted !! Stroke/Not !! Variant !! Large
|-
! [[Braille]]
| {{Braille cell|type=8|37}} || {{Braille cell|type=8|7}} || {{Braille cell|type=8|123456}} || {{Braille cell|type=8|367}} || {{Braille cell|type=8|78}} || {{Braille cell|type=8|347}} || {{Braille cell|type=8|168}} || {{Braille cell|type=8|1234567}} 
|}

=== Typeface indicators ===
{| class="wikitable" style="text-align:center"
|- 
! Symbol !! Script !! Bold !! Italic !! Underline !! Definable font 1 !! Fractur !! Roman !! Underline
|-
! [[Braille]]
| {{Braille Cell|type=8|48}} || {{Braille Cell|type=8|458}} || {{Braille Cell|type=8|468}} || {{Braille Cell|type=8|4568}} || {{Braille Cell|type=8|478}} || {{Braille Cell|type=8|4578}} || {{Braille Cell|type=8|4678}} || {{Braille Cell|type=8|45678}} 
|}

The difference between the two underline markers is not explained.

=== Shape symbols ===
{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ⊥ !! ∥ !! ∠ !! Open Square !! ⊿
|-
! [[Braille]]
| {{Braille Cell|type=8|8|2378}} || {{Braille Cell|type=8|568|237}} || {{Braille Cell|type=8|8|3578}} || {{Braille Cell|type=8|568|25678}} || {{Braille Cell|type=8|568|378}} 
|}

=== Set theory ===
{| class="wikitable" style="text-align:center"
|- 
! Symbol !! ∪ !! ∩ !! ⊂ !! ⊃
|-
! [[Braille]]
| {{Braille Cell|type=8|568|5678}} || {{Braille Cell|type=8|568|2568}} || {{Braille Cell|type=8|568|2578}} || {{Braille Cell|type=8|58|25678}} 
|}

== References ==

{{reflist}}
*[https://web.archive.org/web/20060615173923/http://www-cgi.cnn.com/TECH/9511/new_braille/index.html Blind physicist creates better Braille] — a [[Cable News Network|CNN]] news item, November 9, 1995
*[https://www.ams.org/notices/200210/comm-morin.pdf The world of blind mathematicians] — article in ''Notices of the [[American Mathematical Society|AMS]]'', November 2002

{{Braille}}

{{DEFAULTSORT:Gardner-Salinas Braille}}
[[Category:Braille symbols]]
[[Category:8-dot braille scripts]]
[[Category:Mathematical notation]]