Nemeth Braille

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The Nemeth Braille Code for Mathematics is a Braille code for encoding mathematical and scientific notation linearly using standard six-dot Braille cells for tactile reading by the visually impaired. The code was developed by Abraham Nemeth. The Nemeth Code was first written up in 1952. It was revised in 1956, 1965, and 1972,[1] and beginning in 1992 was integrated into Unified English Braille. It is an example of a compact human-readable markup language.

Nemeth Braille is just one code used to write mathematics in braille. There are many systems in use around the world.[2]

Principles of the Nemeth Code[edit]

The Nemeth Code Book (1972) opens with the following words:

This Braille Code for Mathematics and Science Notation has been prepared to provide a system of symbols which will allow technical literature to be presented and read in braille. The Code is intended to convey as accurate an impression as is possible to the braille reader of the corresponding printed text, and this is one of its principal features. When the braille reader has a clear conception of the corresponding printed text, the area of communication between himself and his teacher, his colleagues, his associates, and the world at large is greatly broadened. A test of the accuracy with which the Code conveys information from the print to the braille text is to effect a transcription in the reverse direction. The amount of agreement between the original printed text and one transcribed from the braille is a measure of the Code's accuracy.

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One consequence is that the braille transcriber does not need to know the underlying mathematics. The braille transcriber needs to identify the inkprint symbols, and to know how to render them in Nemeth Code braille. For example, if the same math symbol might have two different meanings, this would not matter. Both instances would be brailled the same. This is in contrast to the International Braille Music Code, where the braille depends on the meaning of the inkprint music. Thus a knowledge of music is required to produce braille music, but a knowledge of mathematics is not required to produce mathematical braille in the Nemeth code.

Table of Nemeth braille codes[edit]

General Signs[edit]

Symbol * ,
Braille ⠈ (braille pattern dots-4) ⠼ (braille pattern dots-3456) ⠠ (braille pattern dots-6) ⠄ (braille pattern dots-3) ⠄ (braille pattern dots-3) ⠄ (braille pattern dots-3)

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Number Signs[edit]

Symbol Number prefix . / , (decimal) , / . (separator) 0 1 2 3 4 5 6 7 8 9
Braille ⠼ (braille pattern dots-3456) ⠨ (braille pattern dots-46) ⠠ (braille pattern dots-6) ⠴ (braille pattern dots-356) ⠂ (braille pattern dots-2) ⠆ (braille pattern dots-23) ⠒ (braille pattern dots-25) ⠲ (braille pattern dots-256) ⠢ (braille pattern dots-26) ⠖ (braille pattern dots-235) ⠶ (braille pattern dots-2356) ⠦ (braille pattern dots-236) ⠔ (braille pattern dots-35)

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Operators[edit]

Symbol + - × · ÷ = . (decimal) i√ (radical index)
Braille ⠬ (braille pattern dots-346) ⠤ (braille pattern dots-36) ⠈ (braille pattern dots-4) ⠡ (braille pattern dots-16) ⠡ (braille pattern dots-16) ⠨ (braille pattern dots-46) ⠌ (braille pattern dots-34) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠨ (braille pattern dots-46) ⠜ (braille pattern dots-345) ⠣ (braille pattern dots-126)
Symbol inner √ (1st) inner √ (2nd) end 1st √ end 2nd √ long division /  !
Braille ⠨ (braille pattern dots-46) ⠨ (braille pattern dots-46) ⠨ (braille pattern dots-46) ⠨ (braille pattern dots-46) ⠻ (braille pattern dots-12456) ⠨ (braille pattern dots-46) ⠨ (braille pattern dots-46) ⠻ (braille pattern dots-12456) ⠕ (braille pattern dots-135) ⠌ (braille pattern dots-34) ⠯ (braille pattern dots-12346)

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Parentheses and Brackets[edit]

Symbol ( ) [ ] { }
Braille ⠷ (braille pattern dots-12356) ⠾ (braille pattern dots-23456) ⠈ (braille pattern dots-4) ⠷ (braille pattern dots-12356) ⠈ (braille pattern dots-4) ⠾ (braille pattern dots-23456) ⠨ (braille pattern dots-46) ⠷ (braille pattern dots-12356) ⠨ (braille pattern dots-46) ⠾ (braille pattern dots-23456)

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Fractions[edit]

Symbol simple complex hypercomplex fraction in mixed number
open close open close open close open close
Braille ⠹ (braille pattern dots-1456) ⠼ (braille pattern dots-3456) ⠠ (braille pattern dots-6) ⠹ (braille pattern dots-1456) ⠠ (braille pattern dots-6) ⠼ (braille pattern dots-3456) ⠠ (braille pattern dots-6) ⠠ (braille pattern dots-6) ⠹ (braille pattern dots-1456) ⠠ (braille pattern dots-6) ⠠ (braille pattern dots-6) ⠼ (braille pattern dots-3456) ⠸ (braille pattern dots-456) ⠹ (braille pattern dots-1456) ⠸ (braille pattern dots-456) ⠼ (braille pattern dots-3456)

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Symbol / complex / complex ― hypercomplex ―
Braille ⠸ (braille pattern dots-456) ⠌ (braille pattern dots-34) ⠌ (braille pattern dots-34) ⠠ (braille pattern dots-6) ⠸ (braille pattern dots-456) ⠌ (braille pattern dots-34) ⠠ (braille pattern dots-6) ⠌ (braille pattern dots-34) ⠠ (braille pattern dots-6) ⠠ (braille pattern dots-6) ⠌ (braille pattern dots-34)

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Other modifiers[edit]

Symbol
Braille ⠈ (braille pattern dots-4) ⠌ (braille pattern dots-34) ⠠ (braille pattern dots-6) ⠡ (braille pattern dots-16) ⠐ (braille pattern dots-5) ⠂ (braille pattern dots-2) ⠰ (braille pattern dots-56) ⠆ (braille pattern dots-23) ⠄ (braille pattern dots-3) ⠄ (braille pattern dots-3) ⠄ (braille pattern dots-3)

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Symbol °  %
Braille ⠠ (braille pattern dots-6) ⠿ (braille pattern dots-123456) ⠸ (braille pattern dots-456) ⠿ (braille pattern dots-123456) ⠨ (braille pattern dots-46) ⠡ (braille pattern dots-16) ⠈ (braille pattern dots-4) ⠴ (braille pattern dots-356) ⠈ (braille pattern dots-4) ⠜ (braille pattern dots-345)

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Braille indicators[edit]

Symbol Punctuation Superscript Subscript Baseline Omission Cancel (close) Cancel (open) Run Over Directly Over Directly Under Beginning Termination
Braille ⠸ (braille pattern dots-456) ⠘ (braille pattern dots-45) ⠰ (braille pattern dots-56) ⠐ (braille pattern dots-5) ⠿ (braille pattern dots-123456) ⠻ (braille pattern dots-12456) ⠪ (braille pattern dots-246) ⠐ (braille pattern dots-5) ⠣ (braille pattern dots-126) ⠩ (braille pattern dots-146) ⠐ (braille pattern dots-5) ⠻ (braille pattern dots-12456)

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Comparison Signs[edit]

Symbol > <
Braille ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠨ (braille pattern dots-46) ⠐ (braille pattern dots-5) ⠱ (braille pattern dots-156) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠱ (braille pattern dots-156) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13)

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Symbol
Braille ⠱ (braille pattern dots-156) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠱ (braille pattern dots-156) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13)

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Symbol >< <> >=< <=>
Braille ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠐ (braille pattern dots-5) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠐ (braille pattern dots-5) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠐ (braille pattern dots-5) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2)

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Symbol ±
Braille ⠌ (braille pattern dots-34) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠌ (braille pattern dots-34) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠌ (braille pattern dots-34) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠈ (braille pattern dots-4) ⠱ (braille pattern dots-156) ⠈ (braille pattern dots-4) ⠱ (braille pattern dots-156) ⠈ (braille pattern dots-4) ⠱ (braille pattern dots-156) ⠈ (braille pattern dots-4) ⠱ (braille pattern dots-156) ⠨ (braille pattern dots-46) ⠅ (braille pattern dots-13) ⠬ (braille pattern dots-346) ⠤ (braille pattern dots-36) ⠤ (braille pattern dots-36) ⠬ (braille pattern dots-346)

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Geometry[edit]

Symbol \perp
Braille ⠫ (braille pattern dots-1246) ⠇ (braille pattern dots-123) ⠫ (braille pattern dots-1246) ⠏ (braille pattern dots-1234) ⠫ (braille pattern dots-1246) ⠪ (braille pattern dots-246) ⠫ (braille pattern dots-1246) ⠪ (braille pattern dots-246) ⠨ (braille pattern dots-46) ⠗ (braille pattern dots-1235) ⠻ (braille pattern dots-12456)

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Symbol Trapezoid small icon.png
Braille ⠫ (braille pattern dots-1246) ⠁ (braille pattern dots-1) ⠫ (braille pattern dots-1246) ⠄ (braille pattern dots-3) ⠫ (braille pattern dots-1246) ⠟ (braille pattern dots-12345) ⠫ (braille pattern dots-1246) ⠲ (braille pattern dots-256) ⠫ (braille pattern dots-1246) ⠗ (braille pattern dots-1235) ⠫ (braille pattern dots-1246) ⠛ (braille pattern dots-1245)

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Symbol Isosceles trapezoid.jpg Ellipse black.svg
Braille ⠫ (braille pattern dots-1246) ⠓ (braille pattern dots-125) ⠫ (braille pattern dots-1246) ⠵ (braille pattern dots-1356) ⠫ (braille pattern dots-1246) ⠞ (braille pattern dots-2345) ⠫ (braille pattern dots-1246) ⠞ (braille pattern dots-2345) ⠨ (braille pattern dots-46) ⠗ (braille pattern dots-1235) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠉ (braille pattern dots-14) ⠫ (braille pattern dots-1246) ⠑ (braille pattern dots-15)

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Arrows[edit]

Symbol
Braille ⠫ (braille pattern dots-1246) ⠒ (braille pattern dots-25) ⠒ (braille pattern dots-25) ⠕ (braille pattern dots-135) ⠫ (braille pattern dots-1246) ⠪ (braille pattern dots-246) ⠒ (braille pattern dots-25) ⠒ (braille pattern dots-25) ⠫ (braille pattern dots-1246) ⠪ (braille pattern dots-246) ⠒ (braille pattern dots-25) ⠒ (braille pattern dots-25) ⠕ (braille pattern dots-135)

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Symbol
Braille ⠫ (braille pattern dots-1246) ⠕ (braille pattern dots-135) ⠫ (braille pattern dots-1246) ⠒ (braille pattern dots-25) ⠒ (braille pattern dots-25) ⠈ (braille pattern dots-4) ⠕ (braille pattern dots-135) ⠫ (braille pattern dots-1246) ⠠ (braille pattern dots-6) ⠪ (braille pattern dots-246) ⠫ (braille pattern dots-1246) ⠶ (braille pattern dots-2356) ⠶ (braille pattern dots-2356) ⠕ (braille pattern dots-135)

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Trig functions[edit]

Function Sine Cosine Tangent
Braille ⠎ (braille pattern dots-234) ⠊ (braille pattern dots-24) ⠝ (braille pattern dots-1345) ⠉ (braille pattern dots-14) ⠕ (braille pattern dots-135) ⠎ (braille pattern dots-234) ⠞ (braille pattern dots-2345) ⠁ (braille pattern dots-1) ⠝ (braille pattern dots-1345)

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Function Secant Cosecant Cotangent Logarithm
Braille ⠎ (braille pattern dots-234) ⠑ (braille pattern dots-15) ⠉ (braille pattern dots-14) ⠉ (braille pattern dots-14) ⠎ (braille pattern dots-234) ⠉ (braille pattern dots-14) ⠉ (braille pattern dots-14) ⠕ (braille pattern dots-135) ⠞ (braille pattern dots-2345) ⠇ (braille pattern dots-123) ⠕ (braille pattern dots-135) ⠛ (braille pattern dots-1245)

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Set Theory[edit]

Symbol {}
Braille ⠈ (braille pattern dots-4) ⠑ (braille pattern dots-15) ⠈ (braille pattern dots-4) ⠢ (braille pattern dots-26) ⠨ (braille pattern dots-46) ⠬ (braille pattern dots-346) ⠨ (braille pattern dots-46) ⠩ (braille pattern dots-146) ⠸ (braille pattern dots-456) ⠦ (braille pattern dots-236) ⠨ (braille pattern dots-46) ⠷ (braille pattern dots-12356) ⠨ (braille pattern dots-46) ⠾ (braille pattern dots-23456)

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Symbol
Braille ⠸ (braille pattern dots-456) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠸ (braille pattern dots-456) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠸ (braille pattern dots-456) ⠐ (braille pattern dots-5) ⠅ (braille pattern dots-13) ⠱ (braille pattern dots-156) ⠸ (braille pattern dots-456) ⠨ (braille pattern dots-46) ⠂ (braille pattern dots-2) ⠱ (braille pattern dots-156)

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Misc. signs[edit]

Symbol
Braille ⠫ (braille pattern dots-1246) ⠉ (braille pattern dots-14) ⠸ (braille pattern dots-456) ⠫ (braille pattern dots-1246) ⠬ (braille pattern dots-346) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠉ (braille pattern dots-14) ⠸ (braille pattern dots-456) ⠫ (braille pattern dots-1246) ⠡ (braille pattern dots-16) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠲ (braille pattern dots-256) ⠸ (braille pattern dots-456) ⠫ (braille pattern dots-1246) ⠡ (braille pattern dots-16) ⠻ (braille pattern dots-12456)

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Symbol Intersecting lines @ Ditto Tally mark +- -+
Braille ⠫ (braille pattern dots-1246) ⠊ (braille pattern dots-24) ⠈ (braille pattern dots-4) ⠁ (braille pattern dots-1) ⠠ (braille pattern dots-6) ⠄ (braille pattern dots-3) ⠸ (braille pattern dots-456) ⠬ (braille pattern dots-346) ⠐ (braille pattern dots-5) ⠤ (braille pattern dots-36) ⠤ (braille pattern dots-36) ⠐ (braille pattern dots-5) ⠬ (braille pattern dots-346)

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Symbol | | | (modulus) . dot
Braille ⠳ (braille pattern dots-1256) ⠈ (braille pattern dots-4) ⠱ (braille pattern dots-156) ⠱ (braille pattern dots-156) ⠸ (braille pattern dots-456) ⠇ (braille pattern dots-123) ⠱ (braille pattern dots-156) ⠳ (braille pattern dots-1256) ⠳ (braille pattern dots-1256) ⠡ (braille pattern dots-16)

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Polygons[edit]

Symbol Regular Irregular  
Pentagon Hexagon Pentagon Hexagon Heptagon Octagon Nonagon
Braille ⠫ (braille pattern dots-1246) ⠢ (braille pattern dots-26) ⠫ (braille pattern dots-1246) ⠖ (braille pattern dots-235) ⠫ (braille pattern dots-1246) ⠏ (braille pattern dots-1234) ⠛ (braille pattern dots-1245) ⠫ (braille pattern dots-1246) ⠓ (braille pattern dots-125) ⠭ (braille pattern dots-1346) ⠫ (braille pattern dots-1246) ⠶ (braille pattern dots-2356) ⠫ (braille pattern dots-1246) ⠦ (braille pattern dots-236) ⠫ (braille pattern dots-1246) ⠔ (braille pattern dots-35)

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Triangles[edit]

Symbol Acute Isosceles Obtuse Scalene
Braille ⠫ (braille pattern dots-1246) ⠞ (braille pattern dots-2345) ⠨ (braille pattern dots-46) ⠁ (braille pattern dots-1) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠞ (braille pattern dots-2345) ⠨ (braille pattern dots-46) ⠊ (braille pattern dots-24) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠞ (braille pattern dots-2345) ⠨ (braille pattern dots-46) ⠕ (braille pattern dots-135) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠞ (braille pattern dots-2345) ⠨ (braille pattern dots-46) ⠎ (braille pattern dots-234) ⠻ (braille pattern dots-12456)

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Other signs[edit]

Symbol Acute angle Obtuse angle Hexagon star §
Braille ⠫ (braille pattern dots-1246) ⠪ (braille pattern dots-246) ⠫ (braille pattern dots-1246) ⠪ (braille pattern dots-246) ⠨ (braille pattern dots-46) ⠕ (braille pattern dots-135) ⠻ (braille pattern dots-12456) ⠫ (braille pattern dots-1246) ⠎ (braille pattern dots-234) ⠈ (braille pattern dots-4) ⠠ (braille pattern dots-6) ⠏ (braille pattern dots-1234) ⠈ (braille pattern dots-4) ⠠ (braille pattern dots-6) ⠎ (braille pattern dots-234)

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Symbol ref. indicator <i> <b> letter sign composite function |det| matrix
Braille ⠈ (braille pattern dots-4) ⠻ (braille pattern dots-12456) ⠨ (braille pattern dots-46) ⠸ (braille pattern dots-456) ⠰ (braille pattern dots-56) ⠨ (braille pattern dots-46) ⠡ (braille pattern dots-16) ⠠ (braille pattern dots-6) ⠳ (braille pattern dots-1256) ⠮ (braille pattern dots-2346) ⠈ (braille pattern dots-4) ⠙ (braille pattern dots-145)

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Greek letters[edit]

Greek letters are based on the assignments of International Greek Braille.

Symbol α β γ δ θ μ ν π ρ
Braille ⠨ (braille pattern dots-46) ⠁ (braille pattern dots-1) ⠨ (braille pattern dots-46) ⠃ (braille pattern dots-12) ⠨ (braille pattern dots-46) ⠛ (braille pattern dots-1245) ⠨ (braille pattern dots-46) ⠙ (braille pattern dots-145) ⠨ (braille pattern dots-46) ⠹ (braille pattern dots-1456) ⠨ (braille pattern dots-46) ⠍ (braille pattern dots-134) ⠨ (braille pattern dots-46) ⠝ (braille pattern dots-1345) ⠨ (braille pattern dots-46) ⠏ (braille pattern dots-1234) ⠨ (braille pattern dots-46) ⠗ (braille pattern dots-1235)

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Symbol σ ω Σ Δ ϵ λ υ φ
Braille ⠨ (braille pattern dots-46) ⠎ (braille pattern dots-234) ⠨ (braille pattern dots-46) ⠺ (braille pattern dots-2456) ⠨ (braille pattern dots-46) ⠠ (braille pattern dots-6) ⠎ (braille pattern dots-234) ⠨ (braille pattern dots-46) ⠠ (braille pattern dots-6) ⠙ (braille pattern dots-145) ⠨ (braille pattern dots-46) ⠑ (braille pattern dots-15) ⠨ (braille pattern dots-46) ⠇ (braille pattern dots-123) ⠨ (braille pattern dots-46) ⠥ (braille pattern dots-136) ⠨ (braille pattern dots-46) ⠋ (braille pattern dots-124)

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See also[edit]

References[edit]

  1. ^ "The History of Nemeth Code". Retrieved 2012-04-26. 
  2. ^ "Braille Mathematical Notations". Retrieved 2012-04-26. 
  3. ^ a b "The Nemeth Braille Code for Mathematics and Science Notation 1972 Revision". Retrieved 2012-04-26. 
  4. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad "Nemeth Braille (Mathematics Braille)". Retrieved 2012-04-25. 

External links[edit]