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Gardner–Salinas braille codes

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Title: Gardner–Salinas braille codes  
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Subject: Braille, Korean Braille, Greek Braille, Braille pattern dots-14, Braille music
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Gardner–Salinas braille codes

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]


Symbol 0 1 2 3 4 5 6 7 8 9
Braille ⠬ (braille pattern dots-346) ⠡ (braille pattern dots-16) ⠣ (braille pattern dots-126) ⠩ (braille pattern dots-146) ⠹ (braille pattern dots-1456) ⠱ (braille pattern dots-156) ⠫ (braille pattern dots-1246) ⠻ (braille pattern dots-12456) ⠳ (braille pattern dots-1256) ⠪ (braille pattern dots-246)

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 ⡁ (braille pattern dots-17) ⡃ (braille pattern dots-127) ⡉ (braille pattern dots-147) ⡙ (braille pattern dots-1457) ⡑ (braille pattern dots-157) ⡋ (braille pattern dots-1247) ⡛ (braille pattern dots-12457) ⡓ (braille pattern dots-1257) ⡊ (braille pattern dots-247) ⡚ (braille pattern dots-2457) ⡅ (braille pattern dots-137) ⡇ (braille pattern dots-1237) ⡍ (braille pattern dots-1347)
Symbol N O P Q R S T U V W X Y Z
Braille ⡝ (braille pattern dots-13457) ⡕ (braille pattern dots-1357) ⡏ (braille pattern dots-12347) ⡟ (braille pattern dots-123457) ⡗ (braille pattern dots-12357) ⡎ (braille pattern dots-2347) ⡞ (braille pattern dots-23457) ⡥ (braille pattern dots-1367) ⡧ (braille pattern dots-12367) ⡺ (braille pattern dots-24567) ⡭ (braille pattern dots-13467) ⡽ (braille pattern dots-134567) ⡵ (braille pattern dots-13567)

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 ⢁ (braille pattern dots-18) ⢃ (braille pattern dots-128) ⢛ (braille pattern dots-12458) ⢙ (braille pattern dots-1458) ⢑ (braille pattern dots-158) ⢵ (braille pattern dots-13568) ⢱ (braille pattern dots-1568) ⢹ (braille pattern dots-14568) ⢊ (braille pattern dots-248) ⢅ (braille pattern dots-138) ⢇ (braille pattern dots-1238) ⢍ (braille pattern dots-1348)
Symbol ν ξ ο π ρ σ τ υ φ χ ψ ω
Braille ⢝ (braille pattern dots-13458) ⢭ (braille pattern dots-13468) ⢕ (braille pattern dots-1358) ⢏ (braille pattern dots-12348) ⢗ (braille pattern dots-12358) ⢎ (braille pattern dots-2348) ⢞ (braille pattern dots-23458) ⢥ (braille pattern dots-1368) ⢋ (braille pattern dots-1248) ⢯ (braille pattern dots-123468) ⢽ (braille pattern dots-134568) ⢺ (braille pattern dots-24568)
Symbol Γ Δ Θ Λ Ξ Π Σ Υ Φ Ψ Ω
Braille ⣛ (braille pattern dots-124578) ⣙ (braille pattern dots-14578) ⣹ (braille pattern dots-145678) ⣇ (braille pattern dots-12378) ⣭ (braille pattern dots-134678) ⣏ (braille pattern dots-123478) ⣎ (braille pattern dots-23478) ⣥ (braille pattern dots-13678) ⣋ (braille pattern dots-12478) ⣽ (braille pattern dots-1345678) ⣺ (braille pattern dots-245678)

Characters differing from English Braille

Symbol Parentheses Brackets single quote  
open close open close open close ?
Braille ⢆ (braille pattern dots-238) ⡘ (braille pattern dots-457) ⣦ (braille pattern dots-23678) ⣴ (braille pattern dots-35678) ⣄ (braille pattern dots-378) ⠄ (braille pattern dots-3) ⠶ (braille pattern dots-2356)

ASCII symbols and mathematical operators

Symbol " $ & @ \ ^ _ ` { } ~
Braille ⣒ (braille pattern dots-2578) ⡼ (braille pattern dots-34567) ⠯ (braille pattern dots-12346) ⢌ (braille pattern dots-348) ⣡ (braille pattern dots-1678) ⡐ (braille pattern dots-57) ⢂ (braille pattern dots-28) ⣄ (braille pattern dots-378) ⣷ (braille pattern dots-1235678) ⣾ (braille pattern dots-2345678) ⣠ (braille pattern dots-678)
Symbol # % * + / < = > × · ÷
Braille ⠼ (braille pattern dots-3456) ⠞ (braille pattern dots-2345) ⢜ (braille pattern dots-3458) ⡒ (braille pattern dots-257) ⣌ (braille pattern dots-3478) ⢔ (braille pattern dots-358) ⣶ (braille pattern dots-235678) ⡢ (braille pattern dots-267) ⣂ (braille pattern dots-278) ⢒ (braille pattern dots-258) ⣐ (braille pattern dots-578)

Text symbols

Symbol © £
Braille ⢷ (braille pattern dots-123568) ⢉ (braille pattern dots-148) ⢻ (braille pattern dots-124568) ⢿ (braille pattern dots-1234568) ⢼ (braille pattern dots-34568)

Math/Science symbols

Symbol |x| (abs. value) line ∫ closed ∫
Braille ⡶ (braille pattern dots-23567) ⢶ (braille pattern dots-23568) ⣿ (braille pattern dots-12345678) ⣤ (braille pattern dots-3678) ⢳ (braille pattern dots-12568) ⢓ (braille pattern dots-1258) ⣮ (braille pattern dots-234678) ⡮ (braille pattern dots-23467) ⢮ (braille pattern dots-23468)
Braille ⣪ (braille pattern dots-24678) ⣕ (braille pattern dots-13578) ⣩ (braille pattern dots-14678) ⢩ (braille pattern dots-1468) ⢤ (braille pattern dots-368) ⡦ (braille pattern dots-2367) ⢴ (braille pattern dots-3568) ⢚ (braille pattern dots-2458) ⣱ (braille pattern dots-15678) ⣑ (braille pattern dots-1578) ⡾ (braille pattern dots-234567)


Symbol Superscript Subscript Left-superscript Left-subscript Begin fraction Denominator End fraction Over *
Braille ⠔ (braille pattern dots-35) ⠢ (braille pattern dots-26) ⣔ (braille pattern dots-3578) ⣢ (braille pattern dots-2678) ⠷ (braille pattern dots-12356) ⠌ (braille pattern dots-34) ⠾ (braille pattern dots-23456) ⠜ (braille pattern dots-345)

* 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 ⢪ (braille pattern dots-2468) ⣆ (braille pattern dots-2378) ⣰ (braille pattern dots-5678) ⣧ (braille pattern dots-123678) ⣼ (braille pattern dots-345678) ⣖ (braille pattern dots-23578) ⣲ (braille pattern dots-25678) ⣖ (braille pattern dots-23578) ⣲ (braille pattern dots-25678)

* 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 ⢄ (braille pattern dots-38) ⡠ (braille pattern dots-67) ⡂ (braille pattern dots-27) ⡆ (braille pattern dots-237) ⡬ (braille pattern dots-3467) ⣬ (braille pattern dots-34678) ⢬ (braille pattern dots-3468)
Symbol Misc. Symbol *     Modifiers
Begin End Quantity Markup indicator Inverted Stroke/Not Variant Large
Braille ⡄ (braille pattern dots-37) ⡀ (braille pattern dots-7) ⠿ (braille pattern dots-123456) ⡤ (braille pattern dots-367) ⣀ (braille pattern dots-78) ⡌ (braille pattern dots-347) ⢡ (braille pattern dots-168) ⡿ (braille pattern dots-1234567)

Typeface indicators

Symbol Script Bold Italic Underline Definable font 1 Fractur Roman Underline
Braille ⢈ (braille pattern dots-48) ⢘ (braille pattern dots-458) ⢨ (braille pattern dots-468) ⢸ (braille pattern dots-4568) ⣈ (braille pattern dots-478) ⣘ (braille pattern dots-4578) ⣨ (braille pattern dots-4678) ⣸ (braille pattern dots-45678)

Shape symbols

Symbol Open Square
Braille ⢀ (braille pattern dots-8) ⣆ (braille pattern dots-2378) ⢰ (braille pattern dots-568) ⡆ (braille pattern dots-237) ⢀ (braille pattern dots-8) ⣔ (braille pattern dots-3578) ⢰ (braille pattern dots-568) ⣲ (braille pattern dots-25678) ⢰ (braille pattern dots-568) ⣄ (braille pattern dots-378)

Set theory

Braille ⢰ (braille pattern dots-568) ⣰ (braille pattern dots-5678) ⢰ (braille pattern dots-568) ⢲ (braille pattern dots-2568) ⢰ (braille pattern dots-568) ⣒ (braille pattern dots-2578) ⢐ (braille pattern dots-58) ⣲ (braille pattern dots-25678)


  1. ^ 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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