Gardner–Salinas braille codes

From HandWiki
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.[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. However, 15 years later Nemeth code was still the standard, with no further change as of 2024.[2]


See also: Braille and 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.[1]

Digits

Symbol 0? 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 Template:Braille Cell

Apart from 0, this is the same as the Antoine notation used in 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.

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

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

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 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 ⠔ (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-2357) ⢲ (braille pattern dots-2568)

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

The difference between the two underline markers is not explained.

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

  1. ↑ 1.0 1.1 "Index of Topics in Braille Section". Oregon State University Science Access Project Braille topics.. http://dots.physics.orst.edu/gs_index.html. 
  2. ↑ [1]



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