Braille Formats
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  • Rule 5

    Mathematical and Nonalphabetical Signs
    Print Shapes, Numbers, and Numeration Systems

    1. General Provisions. In recent years the use of mathematical and other non-alphabetical signs has increased in textbooks for all grade levels. The special signs and other characters once found only in highly technical texts now appear in notations used for subjects other than mathematics and science. Therefore, the directives given below must be followed in determining the correct method of transcription for a particular textbook.

      1. Technical materials. Transcriptions of the following materials should be undertaken only by braillists who are trained in the use of the appropriate braille code(s).

          (1) Computer notation. Whether it consists of entire programs, arrays of computer commands, or simple e-mail addresses the transcription of all computer notation that is shown in any textbook must be in accordance with the provisions of the Computer Braille Code.

          (2) Mathematics and science texts. In transcribing technical works, such as textbooks for logic, mathematics, statistics, and physics, the symbols and usage rules of The Nemeth Braille Code for Mathematics and Science Notation must be used throughout.

          (3) Music notation. The transcription of all music notation that is shown in any textbook must be in accordance with the provisions of the Manual of Braille Music Notation, American Edition, with its International Supplement.

      2. Partially technical works. Science books written for laymen or text-books in fields that use occasional mathematical or scientific terminology and notation require careful and thorough examination before beginning the transcription. Refer to the section labeled Signs and Symbols found at the back of any standard collegiate dictionary for help in identifying any unfamiliar print signs or consult the classroom teacher.

          (1) When a particular mathematical or nonalphabetical sign that is being discussed in the text is identified by name and followed by the print sign, it is not necessary to include the braille symbol for that sign or to give its identifying dot numbers in the braille edition.

          (2) As a general rule, if a mathematical or nonalphabetical sign is simply shown as an incidental example to illustrate some technical information in the text, it is not necessary to use the braille symbol for that print sign. Interrupt the text at the appropriate point and insert a transcriber's note to provide identification or a brief description of the print sign.

          (3) When access to the braille symbols representing mathematical and nonalphabetical signs used in technical notation in the text is required by the reader to perform computations, express technical facts and quantities, or for a full understanding and use of the text, such notation must be transcribed by a braillist trained in the use of the appropriate technical code.

            (a) In texts containing material that requires Nemeth Code or other technical notation frequently throughout the transcription, notice of this usage must be given on the Transcriber's Notes page(s) according to Rule 2, Section 6.

            (b) When Nemeth Code or other technical notation is required infrequently in the braille edition, insert a transcriber's note of explanation before the affected text in accordance with Rule 1, Sections 7a(2)(a) and (b).

    2. Mathematical and nonalphabetical signs in general textbooks. The braille symbols provided in this Code must never be used for the transcription of any form of mathematics or scientific notation. These symbols are intended for use in the notations shown in certain formats found in general textbooks. Observe the specific directives that are provided as follows.

      Glossaries and dictionaries, Rule 19
      Pronunciation systems, Rule 18
      Reference marks, Rule 12
      Spellers, grammars, sentence diagramming, Rule 15

      Depending upon the frequency of their use in a text, these symbols must be identified and/or explained in transcriber's's notes according to Rule 1, Section 7, or included in a special symbols list according to Rule 2, Section 5.
      The meaning or function of a symbol's print equivalent must be given as it is explained in the text. Names and identifications that are shown with the symbols listed in this Code section are to be used only when the text does not provide identifications or explanations of the equivalent print signs.

      1. Arrows and arrowheads. Braille symbols for the arrows and arrowheads below must be separated by a blank cell from material that precedes or follows them.

          (1) Arrows. For the arrows shown in sentence diagrams see Rule 15, Section 3b(1).

          dots 1-2-4-6dots 2-4-6dots 2-5dots 2-5 left arrow
          dots 1-2-4-6dots 2-5dots 2-5dots 1-3-5 right arrow
          dots 1-2-4-6dots 2-4-6dots 2-5dots 2-5dots 1-3-5 left and right arrow
          dots 1-2-4-6dots 1-2-6dots 2-5dots 2-5dots 1-3-5 up arrow
          dots 1-2-4-6dots 1-4-6dots 2-5dots 2-5dots 1-3-5 down arrow
          dots 1-2-4-6dots 1-2-6dots 2-4-6dots 2-5dots 2-5dots 1-3-5 up and down arrow
          dots 1-2-4-6dots 4-5dots 2-5dots 2-5dots 1-3-5 northeast arrow
          dots 1-2-4-6dots 5-6dots 2-5dots 2-5dots 1-3-5 southeast arrow
          (2) Arrowheads. The arrowheads listed below indicate either direction or derivation. They must not be confused with similar print signs that are often used to show comparison between items, i.e., the mathematical signs meaning greater than and less than that a provided in Section 2c below.

          dots1-2-4-6dots 2-4-6 < left arrowhead, derived from
          dots 1-2-4-6dots 1-3-5 > right arrowhead, whence is derived
          dots 1-2-4-6dots 2-4-6dots spacedots 4dots 2-3-6 left arrowhead and question mark, source unknown

      2. Currency, domestic, and foreign monetary signs

        dots 4dots 1-4 ¢ cent sign
        dots 2-5-6 $ dollar sign*
        dots 1-2-3 pound sterling sign*
        dots 4dots 1-3-4-5-6 ¥ yen sign
        NOTE: When the signs marked with an asterisk are shown standing alone in the text or in conjunction with a word or an abbreviation, the braille symbol must be preceded by dot 4.

      3. Mathematical signs. Use the braille symbols listed below, preceded and followed by a blank cell, to represent these common mathematical signs in accordance with Section 2 above. EXCEPTION: Follow the print copy for placement of the percent and empty set signs, as well as when the plus, minus, or the plus or minus sign is shown unspaced before or after a number.

        dots 4dots 3-4-6 + plus sign
        dots 4dots 3-6 - minus sign
        dots 4dots 3-4-6dots 3-6 ± plus or minus sign
        dots 4dots 1-6 × multiplication, times sign
        dots 4-6dots 3-4 division sign
        dots 4-6dots 1-3 = equal sign
        dots 3-4dots 4-6dots 1-3 negated equal sign
        dots 4-6dots 2 > greater than sign
        dot 5dots 1-3 < less than sign
        dots 5dots 2 : ratio sign
        dots 5-6dots 2-3 : : proportion sign
        dots 4dots 3-4 because
        dots 6dots 1-6 therefore
        dots 4dots 2-5dots 1-2-3-4 % percent sign
        dots 4-5-6dots 3-5-6 slashed zero, null or empty set

          (1) Dimensions. Substitute the word by for the print sign x or X that is printed between numbers to indicate dimensions, e.g., 9 x 12 ft.

          (2) Degree of magnification. When the x sign is used to show degree of magnification, substitute the letter x preceded by the letter indicator and unspaced from the number, e.g., a 10x lens.

      4. Signs and abbreviations for units of measure

          (1) Signs for units of measure. Print signs for units of measure must be represented by the braille symbols listed below, spaced as shown in print.

          NOTE: If any of these signs except the inch sign is printed unspaced after a number, it must be preceded by the letter indicator.

          dots1-4-5dots1-2-4-5 ° degree sign
          dots1-2-4dots 2345 ' foot sign
          dots 4dots 3-5 " inch sign
          dots 1-3-4dots 3-5 ' minute of arc sign
          dots 1-2-3dots 1-2 # pound of weight sign
          dots 2-3-4dots 1-5dots 1-4 " second of arc sign

          (2) Abbreviations for units of measure. Follow the print copy for punctuation, placement and spacing of all abbreviations for area, length, mass, volume, and other units. When an abbreviation is printed unspaced following a number, it must be preceded by the letter indicator.

      5. Nonalphabetical signs. Placement and spacing of the braille symbols listed below should follow the print copy.

        dots 4dots 1-2-3-4-6 & ampersand
        dots 3-5dots 3-5 * asterisk
        dots 4dots 1dots 2-3-4-5 @ at sign
        dots 4dots 3-4-5 check mark
        dots 4-6dots 2-5 : boldface or symbolic colon
        dots 3-4dots 1-6 combined stress signs
        dots 4dots 3-4-5-6 # crosshatch, number sign
        dots 2-6dots 2-6 dagger
        dots 3-5dots 2-6 double dagger
        dots 3-6dots 3-6 - lightface dash
        dots 4-6dots 3-6dots 3-6 ~ lightface swung dash
        dots 4-5-6dots 4-6dots 3-6dots 3-6 ~ boldface swung dash
        dots 5dots 2 " ditto sign
        dots 1-2-3-4dots 3-4-5 paragraph sign
        dots 1-2-5-6dots 1-2-5-6 parallels
        dots 4dots 2-3-6 ? question mark
        dots 2-3-4dots 3 § section sign
        dots 4dots 1-2-5-6 vertical bar

          (1) Nonalphabetical signs as footnote and reference marks. When used as footnote and reference marks, the print signs below must be transcribed according to Rule 12, section 1b.

          * asterisk
          double dagger
          ° hollow dot
          paragraph sign
          § section sign
          (2) Nonalphabetical signs with no braille equivalents. Substitute the names for print signs that do not have braille equivalents, such as copyright for © and trademark for TM.

    3. Print shapes and other characters. If print shapes are used in a text solely for visual interest, they must be omitted in braille. Print signs that are quite different from footnote or reference marks are often found in readers, grammars, spellers, and similar texts. They may be used to indicate a relationship between terms, as where print circles identify one part of speech and print squares another. Some may give constant reference to similar materials throughout the text, as where small characters representing pencils or pens are printed before all composition exercises. The function or meaning of these print characters may be given in a footnote the first time they appear or they may be included in a list and explained elsewhere in the text.

      Such print shapes should be represented by the indicators given below. Additional indicators may be devised by using dots 1246 unspaced before the appropriate letter(s).

      dots 1-2-4-6dots 1-4 circle dots 1-2-4-6dots 1-4-5 diamond
      dots 1-2-4-6dots 1-2-3-4dots 2-6 pen dots 1-2-4-6dots 1-2dots 1-4-5 black diamond
      dots 1-2-4-6dots 1-2-3-4 pencil dots 1-2-4-6dots 1-2-4dots 1-3-4-5 fist note
      dots 1-2-4-6dots 2-3-4 square dots 1-2-4-6dots 3-4dots 3-4-5 star
      dots 1-2-4-6dots 2-3-4-5 triangle dots 1-2-4-6dots 1-2dots 2-3-4 black star

      1. A shape indicator, preceded and followed by a blank cell, must be placed as shown in the print text. However, if any of these shapes is printed in either the superscript or subscript position, this placement must be ignored in braille.

      2. The shape indicators must be identified in transcriber's notes according to Rule 1, Section 7 or included in the special symbols list in accordance with Rule 2, Section 5.

    4. Numbers and number combinations

      1. Dates

          (1) Follow print copy for the order in which month, day, and year are shown. Use the punctuation shown in print except that the braille decimal point (46) and not the period must be used to represent a print dot shown separating the component numerals of a date. The number indicator must be repeated following a slash or dash.

          (2) When a date is shown as a sequence of words and numerals, it may be divided between braille lines after a comma. Do not divide a date that is shown as a sequence of unspaced numerals separated by punctuation.

          (3) Abbreviated dates. If an apostrophe indicates omission of digits in the date of a year follow the print copy and insert a number indicator preceding the apostrophe.

          (4) Plurals of dates. For the plurals of decades or centuries shown in numerals, follow the print cop. Do not insert an apostrophe that is not shown in print. The letter indicator is required before a letter s that is printed unspaced after the numerals of the date.

          (5) Incomplete or indefinite dates

            (a) When the numbers of a date are shown preceded or followed by a hyphen or a dash to indicate an incomplete period of time, follow the print copy. However, if a date is printed in parentheses with a space preceding or following a hyphen or a dash, no space must be left in braille between the parenthesis and the hyphen or dash.

            (b) If the text shows an indefinite date by means of a question mark, follow the print copy.

      2. Hyphenated mixed numbers. When two mixed numbers or a mixed number and a whole number are joined by a hyphen or a dash, for clarity the number indicator must be repeated before the second numerical expression.

      3. Ordinal numbers. Do not insert the letter indicator before the st and th contractions when brailling ordinal numbers. When the second and third ordinal numbers are shown followed by only the letter d, do not insert the letters n or r . The letter indicator must be used before the letter d when it is printed unspaced after a numeral.

      4. Plurals of numbers. The letter indicator is required before an s that is printed unspaced after a number to indicate its plural form. Do not insert an apostrophe that is not shown in print.

      5. Postal codes. Follow the print copy as to the spacing shown between groups of letters and numbers. Components of postal codes must not be divided between lines except where hyphens are shown in print. The number indicator must be repeated at the beginning of the second braille line in a divided postal code. The letter indicator is required before any letter that immediately follows a number or is joined by a hyphen to a number.

      6. Scores, results of votes. Do not divide sports scores and results of votes between braille lines. Follow print as to the use of a hyphen or dash shown between the numbers. The number indicator must be repeated following a dash.

      7. Segmented numbers. When numbers in a print text are shown segmented by the use of blank spaces, the appropriate braille symbol, e.g., a comma, decimal point, hyphen, etc., must be substituted for the print space. This usage must be explained in a transcriber's note.
        NOTE: The transcription of segmented numbers in technical works and in foreign language texts must be in accordance with the applicable braille code or supplement.

      8. Telephone numbers. Follow print copy for the spacing and punctuation of telephone numbers. These numbers may be divided between lines at any hyphen shown in print. When divided the number indicator must be repeated at the beginning of the second braille line. Uncontracted braille must be used in transcribing telephone numbers that consist of letters and numbers.

    5. Superior letters, words, or numbers, superscripts, and subscripts

      1. Letters words or numbers above or below lines of text. If the text shows abbreviations, words, or numbers printed above or below the words in sentences or other lines of text, these items must be placed in enclosure symbols not otherwise used in surrounding test and inserted after the affected text. A blank cell must precede and follow the insertion, and this usage must be explained in a transcriber's note.

      2. Superior letters in foreign expressions

          (1) Foreign abbreviations. When parts of foreign abbreviations are printed in a superscript position this placement must be ignored in braille. A period must be inserted after the abbreviation whether or not one is shown in print. A period that is printed beneath a superscript letter must be brailled after the entire abbreviation.

          (2) Foreign ordinal endings. In transcribing any number shown with a foreign ordinal ending, no contractions may be used and the letter(s) representing the ending must be preceded by the letter indicator. Ignore print placement when foreign ordinal endings are shown in superscript position.

      3. Superior letters or numbers in exercise materials. For superior letters or numbers in exercise materials, see Rule 13, Section 8e.

      4. Superior letters or numbers as footnote and reference marks. For the transcription of superior letters or numbers as footnote and reference marks, see Rule 12, Section 1a.

      5. Superior numbers in dictionaries, glossaries, and vocabularies

          (1) Superior numbers before or after entry works must be brailled according to Rule 19, Section 4a(3).

          (2) Superior numbers following words or syllables in an etymology must be brailled according to Rule 19, Section 7d(3)

      6. Superscript or subscript numbers before or after words. If small superscript or subscript numbers are printed before or after words, they must be enclosed in parentheses and placed, unspaced, before or after the affected words according to the print placement. A transcriber's note must be inserted to explain this usage.

      7. Superscripts in pronunciation. Directives for transcribing superscripts shown in pronunciation are given in other Code rules, as follows.

        Superscripts shown in diacritic notation, Rule 18, Section 3f(12)
        Superscripts shown in phonetic notation, Rule 18 Section 4f(3)(c)

    6. Numeration systems

      1. Consecutive numeration. Follow print copy when the numbering of text sections, headings, illustrations, and/or tables is consecutive from the beginning to the end of the book.

          (1) Numbered paragraphs must be transcribed according to Rule 1, Section 2a(8).

          (2) If a print heading consists of a section name and number, see Rule 4, Sections 1b(6) and (7).

          (3) Sequentially labeled illustrations in technical materials must be transcribed in accordance with Rule 1, Section 1a(1)(d)

          (4) See Rule 8, Section 4b for the transcription of consecutively numbered tables.

          (5) Follow the provisions given in Rule 17, Section 1g if any consecutively numbered illustrations or tables are omitted in the braille edition.

      2. Double numeration. When the numbering of text sections, illustrations, and tables is done chapter by chapter using two numbers separated by a dot, hyphen, dash, colon, or slash, follow the print copy except that the braille decimal point (46) and not the period must be used to represent the print dot. The number indicator must be repeated after a dash or a slash, but not after a hyphen or a decimal point.

        NOTE: If text pages are numbered with number/number combinations, see Rule 1, Section 13e.

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