Session 7: Function Names and their Abbreviations, Continued

Enclosed Lists With Abbreviated or Unabbreviated Function Names: Although the numeric indicator must be used at the beginning of an item in an enclosed list, it must be used before a numeral or decimal point and a numeral in regular type following a function name or its abbreviation.

(2sin 30', 3cos 60')
(cos .8000, 2cos .8000)

Punctuation With Function Names: An abbreviated function name is a mathematical expression and must be punctuated accordingly. An unabbreviated function name must be punctuated in the mathematical or literary mode according to its content.

Some trigonometric functions are sin, cos, and tan.
"Arcsin" is the "inverse sine."
What is the meaning of logsine?
Some trigonometric functions are sine, cosine and tangent.
Arc ACB is a major arc.

DIVISION OF MATHEMATICAL EXPRESSIONS BETWEEN BRAILLE LINES

General Principles: Unless absolutely unavoidable, a mathematical expression must not be divided between braille lines or braille pages. Inorder to avoid a divsion, if there is insufficient space on the remainder of a line to accommodate the expression, the space must be left blank, and the entire expression must be brought down to the next line.

However when a mathematical expression is too long to be contained within the margins in effect, a division is unavoidable, and the expression may be divided between braille lines. Such expressions may begin in the remaining space on the line, provided the division in made in accordance with the principles defined below. The placement of all runovers must conform to the margin requirements for itemized, instructional, explanatory, labeled, subdivided, and displayed material.

Division of Long Numerals: A long numeral which cannot be contained on one braille line within the marginin effect must be divided aftera comma if a comma is present, and a hyphen must be inserted. If the numeral does not contained a comma, the hyphen may be inserted after any digit.

When a numeral is divided between braille lines, the numeric indicator must be used before the first digit of the numeral on the next line.

100,000,000,000,000,000,000,000
100000000000000000000000
A decillion is 1,000,000,000,000,000,000,000,000,000,000,000

Division of Long Mathematical Expressions:

a. Mathematical expressions, such as enclosed list, formulas, equations, etc., which cannot fit on one braille line within the boundaries of the margins used may be divided between lines in the following order of preference:

i. A division may be made after a comma between items in an enclosed list. When the items in an list must be divided between braille lines, neither the numeric indicator nor the English letter indicator must be used before a runover on the new line.

{11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
Does {. . ., -4, -3, -2, -1, 0, 1, 2, 3, 4, . . .} represent a set of integers?
(. . . ,.10, .09, .08, .07, .06, .05, .04, . . .)

ii. A division may be made before a sign of comparison on the baseline of writing, provided it is not part of an item enclosed in grouping symbols, fractions indicators, radical signs, or by the symbols of a modified expression. A transition to a new braille line made before a sign of comparison terminates the effect of any level indicator used on the line above.

1778 + 1294 + 865 + 905 + 1574 + 485 = 7901
2 x 423 = (2x400)+(2x20)+(2x3)

iii. A division may be made before a sign of operstion on the baseline of writing. If the transition to a new line is made before a minus sign, the numeric indicator must be used after the minus sign when followed by a numeral or decimal point and a numeral.

14x³-15y³+5x²-4y²+16x-10y+31
(3x10⁴)+(4x10³)+ (7x10²)+(5x10)+(4x1) = N

iv. A division may be made before a fraction line belonging to a fraction on the baseline of writing.

v. A division may be made before the baseline indicator. Thus, if a baseline indicator is required to show a return to the baseline of writing after a superscript or subscript, it must be the first symbol on the new braille line. However, if transition to a new line is made after a numeric subcript not requiring the subscript indicator, the baseline indicator is not required before the runover on the new line.

(49x⁷y⁶-63x⁶y⁴+56x ⁵y⁵+64x⁴y²)/7x²3y²2
(16x⁴ + 8x³y + 4x²y²+2xy³+ y⁴) (2x-y) = 32x⁵-y⁵
144 ft²+122 ft²+
145 ft²-131 ft²=N
((((((Z₂)₃)₅)₇) ₁₁)₁₅)₁₇
a₁b₂c₃+ a₃b₁c₂+ a₂b₃c₁- a₃b₂c₁- a₁b₃c₂- a₂b₁c₃

vi.A division may be made before a superscript or subscript change-of-level indicator, or before a sign of comparison, a sign of operation, or a fraction line within a superscript or subscript.

When an expression is divided before a superscript or subscript change-of-level indicator, the indicator must be placed before the continuation of the expression on the new braille line.

If transition to a new braille line is made within a superscript or subscript, the level in effect is not changed when the division is made before a sign of operation or a fraction line. However, if the transition is made before a sign of comparison, the level in effect is terminated, and the level must be restated before the sign of comparison on the new braille line.

vii. A division may be made between factors enclosed in signs of grouping.

(3x²y)(3x²y)(3x²y)(3x²y)= 81x³y⁴

viii.A division may be made after the termination indicator of a modified expression or a radical. The five componetsof a modified expression must not be separated from each other by transition to a new braille line unless the modified expression as a whole is so long that it cannot fit inside the margins in effect. In such cases, a division should be made in the order of preference listed above.

Nondivision of Symbols and Expressions:

a. The componets of the following signs must not be divided between braille lines:

i.Plus or minus

ii.Minus or plus

iii.Plus followed by minus

iv.Minus followed by Plus

v.Signs of comparison compounded vertically or horizontally

vi.Superposed signs

vii.Tally marks belonging to the same group

viii.Sings of the shape with structural or interior modification

b. The following expressions must not be divided between braille lines:

i.A hyphenated expressions containing one or more mathematical componets

ii.An abbreviation and its related preceding or following numeral or letter

iii.A sign of shape and its identifying numeral, letter, or sequence of letters

iv.A function name or its abbreviation and the sign following it

Developed by

The Shodor Education Foundation, Inc.
in cooperation with the
North Carolina Central University
and the Governor Morehead School for the Blind