Reading Nemeth Code
Basic Issues
In Nemeth Code, numbers are written using lower signs. In some situations, they are not preceded by a number sign (dots 3-4-5-6).
Number sign #
There is ambiguity between punctuation and numbers. When in doubt, a numeric indicator is used to show that something is a number. Dots 4-5-6 is the punctuation indicator. It is used to show that punctuation is being used (when in a math context).
Punctuation indicator _
A plus sign is the "ing" sign, a minus sign is the braille hyphen. The equals sign is space, dots 4-6, dots 1-3, space.
Plus sign +
Minus sign -
Equals sign .k
Fractions are easy. The start of the fraction is marked with the "th" sign, the fraction line is the "st" sign, and the end of the fraction is marked with the number or "ble" sign.
Fraction ?number/number#
You can also have fractions of fractions (complex fractions). The larger fraction elements are marked with a dot 6. The smaller fraction elements are not.
Dot six ,
You can also have fractions of fraction of fractions. These are called hypercomplex fractions. The major elements are marked with a double dot 6. The rest are as above.
A Greek letter is marked with dots 4-6.
Greek letter indicator .
A square root starts with dot 3-4-5 (the "ar" sign), and ends with dots 1-2-4-5-6 (the "er" sign).
Square root >number}
Braille Cells in Transcriber Order
This index is arranged in "transcriber order". This order gives a number from 1 to 63 to all the braille cells. Here is the order:
· Cell 26 (the "and" sign)
· Cell 27 (the "for" sign) =
· Cell 28 (the "of" sign) (
· Cell 29 (the "the" sign) !
· Cell 30 (the "with" sign) )
· Cell 31 (the "ch" sign) *
· Cell 32 (the "gh" sign)
· Cell 33 (the "sh" sign) %
· Cell 34 (the "th" sign) ?
· Cell 35 (the "wh" sign) :
· Cell 36 (the "ed" sign) $
· Cell 37 (the "er" sign) ]
· Cell 38 (the "ou" sign) \
· Cell 39 (the "ow" sign) [
· Cell 40 (the letter w) w
· Cell 41 (dropped a) 1
· Cell 42 (dropped b) 2
· Cell 43 (dropped c) 3
· Cell 44 (dropped d) 4
· Cell 45 (dropped e) 5
· Cell 46 (dropped f) 6
· Cell 47 (dropped g) 7
· Cell 48 (dropped h) 8
· Cell 49 (dropped i) 9
· Cell 50 (dropped j) 0
· Cell 51 (the "st" sign) /
· Cell 52 (the "ing" sign) +
· Cell 53 (the "ble" sign) #
· Cell 54 (the "ar" sign)
· Cell 55 (dot 3) '
· Cell 56 (dots 3-6) -
· Cell 57 (dot 4) @
· Cell 58 (dots 4-5) ^
· Cell 59 (dots 4-5-6) _
· Cell 60 (dot 5) "
· Cell 61 (dots 4-6) .
· Cell 62 (dots 5-6) ;
· Cell 63 (dot 6) ,
Index to Braille Symbols in Nemeth Code
Cells 1-25 (letters)
The letters a-z (excluding w). The letter w is listed as cell 40.
Cell 26 (the "and" sign)
The "and" sign means factorial in a math context. In inkprint this is written as an exclamation mark. For example, 6! is written as #6& in Nemeth Code.
Six Factorial (6!) #6&
If preceded by a dots 4-6, the "and" sign means the Greek letter chi.
chi .
Cell 27 (the "for" sign)
The "for" sign means general omission sign. In arithmetic problems, the general omission symbol shows what the reader is expected to calculate. Often shown as a question mark in inkprint. For example, 2+3=? would be written as #2+3 .k = in Nemeth Code.
2+3=? #2+3 .k =
Cell 28 (the "of" sign)
The "of" sign means a left parenthesis in Nemeth Code. It is used in both a math and a literary context. The right parenthesis is a "with" sign. The dropped "g" parenthesis are not used in Nemeth Code at all.
parentheses () ()
Cell 29 (the "the" sign)
The "the" sign means integral in Nemeth Code. This basic symbol in calculus is shown as a tall stylized S. The integral of x dx is written as !x dx in Nemeth Code.
Integral !x dx
Cell 30 (the "with" sign)
The "with" sign means a right parenthesis in Nemeth Code. It is used in both a math and a literary context. The left parenthesis is an "of" sign. The dropped "g" parenthesis are not used in Nemeth Code at all.
parentheses () ()
Cell 31 (the "ch" sign)
The "ch" sign means times or centered dot in Nemeth Code. The centered dot is used to show multiplication in algebra (where the x used in arithmetic might be confused with the letter x). Five times x might be written as #5x or #5*x in Nemeth Code, depending on whether the inkprint shows a centered dot or not.
times dot *
Cell 32 (the "gh" sign)
The "gh" sign is a bit tricky. If there is a multipurpose indicator (a dot 5) starting off an expression, then the presence of the "gh" sign means that the next portion is placed above the first expression. Without a multipurpose indicator, then "gh" signals an index of radical (such as a cube root).
Here are the two structures: (gh) index (ar) root (er) for a radical with an index of radical; or (dot 5) base expression (gh) over expression (er). In both structures, the "er" sign terminates the expression. To write the cube root of 64, write <#3>#27] in Nemeth Code. To write an 8 above an x, write "x<#8] in Nemeth Code.
cube root of 64 #3>#27]
8/x "x<#8]
Cell 33 (the "sh" sign)
The "sh" sign means to place underneath the base expression. Its use is symmetrical with the "gh" (when the "gh" means above). To write a 6 below an x, write "x%#6] in Nemeth Code.
x/6 "x%#6]
Cell 34 (the "th" sign)
The "th" sign means start a simple fraction. A fraction starts with the "th" sign, uses the "st" sign for the fraction line, and the "ble" or number sign to close the fraction.
When a dot 6 precedes the "th" sign, it means that you are looking at a complex fraction, or a fraction of a fraction. In that case dot 6 elements are the most significant. To write the complex fraction of the fraction x over 3 all over the fraction 4 over 5, write ,??x/3#,/?4/5#,# in Nemeth Code. Notice that the number sign is not used to show numbers inside the fraction.
fraction x over 3 all over the fraction 4 over 5 ,??x/3#,/?4/5#,#
If there are dot 6, dot 6, it means you have a hypercomplex fraction (a fraction of a fraction of a fraction).
Cell 35 (the "wh" sign)
The "wh" sign means a horizontal bar. To write x with an overbar, write x: in Nemeth Code. To write xyz with an overbar, write "xyz<:} in Nemeth Code.
x:
"xyz<:}
There are also a small number of obscure symbols starting with the "wh" sign, such as :"k (bar over less than sign) and :.1 (bar over greater than sign).
:"k
:.1
Cell 36 (the "ed" sign)
The "ed" sign is used to show special shapes in Nemeth Code. If you look at the index of the Nemeth Code, you will see a very long list of symbols that start with the "ed" sign. The most common are:
· $c circle $c
· $i intersecting lines $i
· $p is perpendicular to $p
· $s star $s
· $t triangle $t
Cell 37 (the "er" sign)
The "er" sign is the termination indicator. It ends a radical. It also ends above or below constructs.
cube root of 64 #3>#27]
Cell 38 (the "ou" sign)
The "ou" sign is a vertical bar. The vertical bar is used for many different things in inkprint, so this symbol is used in many different contexts. The most common is for absolute value. To write the absolute value of minus 4 is 4 in Nemeth Code, write \-4\ .k #4.
\-4\ .k #4
Cell 39 (the "ow" sign)
The "ow" sign is used for a comma located at the subscript or superscript level. In practice, it is usually used just at the subscript level. To write x sub i comma j, write x;i[j in Nemeth Code.
x;i[j
Cell 40 (the letter w)
Cell 40 is the letter w. It is out of order since Louis Braille was French, and the French despised the letter w.
Cell 41 (dropped a)
Cell 41 is the dropped a. In Nemeth Code, this is ambiguous. It is either the numeral 1 or the literary comma. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 42 (dropped b)
Cell 42 is the dropped b. In Nemeth Code, this is ambiguous. It is either the numeral 2 or the semicolon. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 43 (dropped c)
Cell 43 is the dropped c. In Nemeth Code, this is ambiguous. It is either the numeral 3 or the colon. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 44 (dropped d)
Cell 44 is the dropped d. In Nemeth Code, this is ambiguous. It is either the numeral 4 or the literary period. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 45 (dropped e)
Cell 41 is the dropped e. In Nemeth Code, this is the numeral 5.
Cell 46 (dropped f)
Cell 46 is the dropped f. In Nemeth Code, this is ambiguous. It is either the numeral 6 or the literary exclamation mark. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 47 (dropped g)
Cell 47 is the dropped g. In Nemeth Code, this is the numeral 7.
Cell 48 (dropped h)
Cell 48 is the dropped h. In Nemeth Code, this is ambiguous. It is either the numeral 8 or the literary quotation mark. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 49 (dropped i)
Cell 49 is the dropped i. In Nemeth Code, this is ambiguous. It is either the numeral 9 or the "in" sign.
Cell 50 (dropped j)
Cell 50 is the dropped j. In Nemeth Code, this is ambiguous. It is either the numeral 0 or the literary quotation mark. As a broad rule, if there was any ambiguity between digit or punctuation, then either the number sign ("ble" sign) or the punctuation indicator (dots 4-5-6) would be used to resolve the ambiguity.
Cell 51 (the "st" sign)
Cell 51 is the "st" sign. In Nemeth Code, it is the horizontal simple fraction line (the part of the fraction that separates the top part from the bottom part).
1/4 ?#1/4#
When a sign of comparison is negated by a superimposed slash or vertical bar, show it with the "st" sign. For example, the parallel sign is $l and the perpendicular sign is $p. The sign for not perpendicular is /$p and the sign for not parallel is /$l.
not perpendicular /$p
not parallel /$l
Cell 52 (the "ing" sign)
Cell 52 is the "ing" sign. In Nemeth Code it means plus.
2+3 #2+3
When followed by a minus (dots 3-6), it means "plus or minus".
plus or minus +-
If you need to write "a plus followed by a minus", separate them with a dot 5 as: +"-
a plus followed by a minus +"-
Cell 53 (the "ble" sign)
Cell 53 is the "ble" sign. It means closing fraction or the numeric indicator. To write 1 minus the fraction 1 over 3, write #1-?1/3# (the numeric indicator is not used inside the fraction. The first "ble" sign shows that you have the number 1. The second "ble" sign closes the fraction.
#1-?1/3#
Cell 54 (the "ar" sign)
Cell 54 is the "ar" sign. It starts off a radical or square root. To write the square root of x+3, write >x+3] in Nemeth Code. Notice how the "er" sign terminates the radical.
>x+3]
Cell 55 (dot 3)
Cell 55 is dot 3. In Nemeth Code it is the apostrophe or prime. To write x prime, write x' in Nemeth Code. Three dot 3's in a row are an ellipsis, just like in literary braille.