How is braille used in mathematics?

Answer 1

There are several Braille signs used in mathematics, commonly known as Nemeth Braille, proposed by Dr. Abraham Nemeth in 1952. Blind from birth, but Professor Emeritus of Mathematics at the University of Detroit, US, he proposed a system which has gained universal acceptance in the world since its creation.

The following answer uses the numbers 1 to 6 to make transcription easier. The numbers 1, 2, and 3 represent the dots top left, middle left, and bottom left respectively, while the numbers 4, 5, and 6 represent the dots top right, middle right, and bottom right respectively.

Numbers:

The digits 0 - 9 are prefixed with a digit indicator, 3,4,5,6 - but are otherwise represented in the same way as the letter J (zero is represented with the same symbol as the letter J, prefixed by a number indicator), and the letters A to I (once again prefixed by a number indicator).

The digits are as follows:
0 - 2,4,5
1 - 1
2 - 1,2
3 - 1,4
4 - 1,4,5
5 - 1,5
6 - 1,2,4
7 - 1,2,4,5
8 - 1,2,5
9 - 2,4

For the numbers from 10 to 99, two symbols follow the number indicator, simply representative of which digits compose the numbers.

Similarly for three-digit numbers, four-digit numbers, for any number of digits you care to name.

Operator signs:

The five basic operator signs are represented by the following:
Plus - 3,4,6
Minus - 3,6
Multiplication - 4 1,6 (two different symbols)
Dot multiplier (•) - 1,6
Divide - 4,6 3,4 (two different symbols)
Equals - 4,6 1,3 (two different symbols)

Decimal point - 4,6
Square root sign - 3,4,5
Index of radical (that is, representing n for the nth root of x): 1,2,6. (This is then succeeded by the braille digit representing the nth root, rather than preceding it, like in conventional notation).

Inner radical indicator: 4,6
Second inner radical indicator: 4,6 4,6 (two different symbols)
End of first radical indicator: 4,6 1,2,4,5,6 (two different symbols)
End of second radical indicator: 4,6 4,6 1,2,4,5,6 (three different symbols)
Not: 3,4

Therefore: Is not equal to will be represented by the "NOT" symbol followed by the "EQUALS symbol", as above.

Long division: 1,3,5
Factorial: 1,2,3,4,6

Brackets

Opening round bracket: 1,2,3 5,6
Closing round bracket: 2,3,4,5,6
Opening square bracket: 4 1,2,3,5,6 (two symbols)
Closing square bracket: 4 2,3,4,5,6 (two symbols)
Opening brace bracket { : 4,6 1,2,3,5,6 (two symbols)
Closing brace bracket } : 4,6 2,3,4,5,6 (two symbols)

Therefore sign: 6, 1,6 (two symbols)
Ratio symbol (colon): 5 2 (two symbols)
Infinity: 6, 1,2,3,4,5,6 (two symbols)
Degree (angles): 4,6 1,6 (two symbols)
Percentage sign: 4, 3,5,6 (two symbols)

Superscript indicator: 4,5 (appears before indices and so on)
Subscript indicator: 5,6 (used for position in a vector/set)

Signs of comparison:

Greater than: 4,6 2 (two different symbols)
Less than: 2 1,3 (two different symbols)
Greater than or equal to: 4,6 2 1,5,6 (three different symbols)
Less than or equal to: 5 1,3 1,5,6 (three different symbols)
Is not equal to: 3,4 4,6 1,3 (three different symbols)
Is approximately equal to: 4 1,5,6 4 1,5,6 (four different symbols)
Plus or minus: 3,4,6 3,6 (two different symbols)
Minus or plus: 3,6 3,4,6 (two different symbols)

This is a list of the most commonly used symbols. If there are any others that you wish to know, please say so on the talk page, which I am keeping an eye on.