

      basic braille mathematics notation
  full details and additional notation are given
in the braille mathematics notation 1987
(rnib).
                 layout
  set out formulae or equations begin in cell 5
with runovers in cell 7.
  dot 5 is used as a hyphen to break an
equation at the end of a line.
  dot 6 is used to separate a formula or
expression from following punctuation.
         numeral and letter fount signs
  numeral sign: # (dots 3-4-5-6).
  fractions are coded as an upper number
followed by a lower number, after the numeral sign.
    ex. 1; (one half)
    23. (two and three quarters)
  the decimal point is coded as dot 2.
    ex. 2,3
  letter signs: [in the following table these are
preceded by the full cell to indicate the position
of the dots.]

       basic braille mathematics notation
                   small capital
       latin ...... for for
       greek ...'' for. for
       bold latin for@ for^
       bold greek for@. for^
  these precede the letter to which they apply. a letter within
a mathematical expression without a letter sign is
assumed to be small latin; the dots 5-6 letter
sign must, however, be asserted when the letter stands
alone or starts a mathematical expression within
ordinary text, or is an a-just immediately
following a number.
  double letter signs have force over subsequent letters
until the sequence is interrupted by a space or
any other mathematical sign except a lower
number, dash or star.
    ex. 2.pr Xally ABC
  special letter fount rules are adopted for
chemical formulae: the force of the dot 6
capital sign carries over all letters in an
unspaced chemical formula until another letter
fount sign or numeral sign intervenes; and dot
5 is used to indicate a two letter element
symbol, letters following that symbol being assumed

       basic braille mathematics notation
to be capital unless shown otherwise.
    ex. nameaoh H.cl
  for further details see the section on
chemistry notation.
                indices
  subscript sign: child (dots 1-6).
  superscript sign: + (dots 3-4-6).
  these indicate that the expression which follows is
a subscript or superscript to the preceding
expression. indices which are whole numbers are
brailled as lower numbers without the numeral sign, and
if subscripts the subscript sign child is
omitted. indices other than whole numbers
written in the lower part of the cell are ended with the
index termination sign er (dots 1-2-4-5-6)
unless a space or a bracket containing the
whole term follows.
    ex. xing; ding-, xingyerCan xchaering;
    teaingn Hbbo Hbbso.
  superscript or subscript ! and -
signs are brailled without the + or child signs.
    ex. H! (have superscript ff[
    O-- pffer.p-
  left-hand indices are shown by preceding the main

       basic braille mathematics notation
symbol by the index group.
    ex. +eaffch8O (superscript 16,
    subscript 8 O[
    ingnerIt (superscript n X[
               brackets
  the following mathematical brackets are
used:
    gh ... ar round brackets
    of ... with square brackets
    ow ... o curly or brace brackets
    of ... with angle brackets
          operation and relation signs
  the following signs are spaced on the left, but
not on the right:
  ! plus
  - minus
  !- plus or minus
  ? multiplied by
  . divided by
  ) equals
  .) is not equal to
  -- equivalent to
  ) approximately equal to
  o) greater than or equal to

       basic braille mathematics notation
  ow) less than or equal to
  :) proportional to
  .- swung dash or tilde (dots
       53-6)
  out! union
  out? intersection
  ouow contained in
  ouow) contained in or equal to
  ouo contains
  ouo) contains or equal to
  ouin is an element of
    ex. 2 ff3 (5
    A ou8But ouowCan
  the following signs are unspaced:
  still fraction line (dots 3-4)
  ' multiplication dot (dots 5-F3)
    ex. astb
  the following signs are spaced on both
sides:
  ow less than (dots 2-4-6)
  o greater than (dots 1-3-5)
    ex. not ow 6

       basic braille mathematics notation
                 arrows
  in mathematics and physics equations arrows are
spaced on the left but not on the right. in chemistry
equations arrows should be spaced on both sides,
except for the up-arrow and down-arrow referring to the
preceding terms, which are unspaced from those terms and
placed in brackets.
  cono right arrow
  ow: left arrow
  owcco leftstright arrow
  ^cco right arrow with vertical bar on shaft
  oucco double shaft right arrow
  ouowcco double shaft leftstright arrow
  coni up arrow
  conen down arrow
  encce right half or full arrow with left
          half or full arrow beneath
  iccin left half or full arrow with right
          half or full arrow beneath
  enencce short right half or full arrow with long
          left half or full arrow beneath
  enccee long right half or full arrow with short
          left half or full arrow beneath
  other arrows may be constructed analogously.

       basic braille mathematics notation
           special functions
  special functions are introduced by the ed
sign (dots 1-2-4-6), and may be followed
by any mathematical sign; an immediately following
small latin letter thus requiring its letter sign.
trigonometric, hyperbolic, logarithmic and
vector analysis functions have special braille
abbreviations; otherwise, the function is written
as in print (without contractions).
    ex. edsx (sin x[
    edc.th (cos th[
    edhcz (cosh z[
    edlx (log x[
    edlchea"x (log to the base 10 x[
    edlnx edexpA edlimxchildren
             additional signs
  : (dots 62-5) colon; ex. xCony
  inch (dots 43-5) dash, prime;
      ex. xinch x@* (x double prime)
  `en (dots 42-6) star; ex. y`en
      y`enen (y double star)
  which bar; ex. zwh
  @wh hat; ex. x@wh
  whose tilde (above letter); ex. p^wh

       basic braille mathematics notation
  @. (dots 42-5-6) dagger; ex. A@.
  edd triangle; ex. eddABC
  edq square; ex. edqABCD
  { angle; ex. {XOY
  shall (dots 1-4-6) square root;
      ex. sh2
  (dots 4-5-6) vertical line;
      ex. ofab.with
        (a letter following and unspaced from the
      vertical line sign must have a letter fount
      sign.)
  the integral; ex. thefdx
            unit abbreviations
  unit abbreviations are placed before or after the
number as in print. those placed after the number are
spaced, apart from monetary unit abbreviations
carrying an initial letter sign (such as p for
pence), and the signs for degrees was (dots
3-5-6), minutes . (dots 4-6) and
seconds (dots 4-5-6). dot 6 is
generally used to indicate capital letters, though this
indication is not made for conventional informal
abbreviations (e.g. m.p.h.). the dots 5-6
letter sign is used before lower case single letter

       basic braille mathematics notation
abbreviations standing alone or with just an index or
punctuation following, but is not used before units
composed of two or more letters (e.g. cm for
centimetre). the percent sign is coded as
conp, the pound sterling sign as l, the dollar
sign as $. unit abbreviations are
transcribed as in print.
    ex. 6 m (6 metres)
    10 cm (10 centimetres)
    5 Not (5 newtons)
    4 Hz (4 hertz)
    3 mA (3 milliamperes)
    l10 (10 pounds sterling)
    30p (30 pence)
    90 conp (90 percent)
    30"50.20 (30 degrees 50
      minutes 20 seconds)
    20"Can (20 degrees celsius)
  indices are indicated using the + sign by the
usual mathematics code method described
above, and the oblique stroke coded as still (dots
3-4).
  in combined units, a dot 3 is used
to separate the individual unit symbols unless

       basic braille mathematics notation
a stroke or index is present at that point.
    ex. 5 Nstming; (5 newtons per
      metreingbb[
    10 N'm (10 newton metres)
    25 more'sing-be (25 metre
      seconding-be[
  the dot 6 separator is not required after
unit abbreviations before following punctuation unless
they end with an index, or are one of the angle
units for degrees, minutes or seconds.
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