Math equations are reproduced as enlarged images of the equation as printed for a sighted person. The plus, minus, and equals signs, parentheses, brackets, the division line in fractions, and the multitude of exotic symbols used in advanced science and math are all printed as raised images. Some symbols may be enlarged more than others or their shapes may be emphasized for clarity, but all are instantly recognizable by sighted mathematicians. Braille is used only for alphabetic characters, numbers, and punctuation marks. The placement of symbols and characters is the same in dotsplus documents as it would be for a sighted person - subscripts are dropped below and superscripts are raised above the position of the main character; numerators of fractions are placed above the denominators; in advanced equations, symbol placement such as sum and integral limits, are preserved.
Text in a dotsplus document can be written in standard braille or dotsplus symbols. Dotsplus text may be preferable if the text contains many scientific symbols.
In order to avoid ambiguity and to incorporate most of the characters used in elementary math into single braille cells, dotsplus braille is based on the 8-dot cell and does not use any dropped symbols. Dotsplus braille cells have been chosen to be as intuitively-related as possible to literary braille. The lower case alphabet is standard braille. Capitalization is indicated by an additional dot on the lower left (usually called the dot-7 position). Greek characters, which are often used in algebra, are indicated by an additional dot in the lower right (usually called the dot-8 position). For example, a capital l is indicated by a dot 1,2,3,7 symbol. A lambda is indicated by a dot 1,2,3,8 symbol, and a capital lambda by a dot 1,2,3,7,8 symbol.
Dotsplus adopts the European computer braille standard to indicate numbers as single braille cells. In this standard, the digits 1-9 are given by the braille cells for the letters a-i with an added dot 6. For example, 1 is the cell dot 1,6. Seven is the cell dot 1,2,4,5,6. The digit 0 cannot be represented by a j with a dot 6, since this is the letter w. Instead 0 is represented by a dot 3,4,6 cell.
Dotsplus punctuation marks are a combination of graphics and braille. The usual literary 4-dot dropped cells are used with a graphics indicator directly above them. Several possibilities for the indicator symbol are still being tested. For example, a comma, usually represented by a dot 2 cell is represented in dotsplus by a square with a dot just below the left bottom corner of the square. For maximum international consistency, the original Louis Braille dropped cell punctuation definitions are used. Only the question mark is different from standard English language braille.
Not all mathematics can be represented with single braille cell characters. Bold, script, gothic, hebrew, etc. characters require two cells. These pose no particular difficulty but do increase the size of equations that contain large numbers of such symbols.
The single-cell dotsplus braille set is illustrated in Figure 1. The dotsplus image of a page from a high school algebra book is shown in Figure 2. The same image but overprinted with the ink print equivalent is shown in Figure 3. The ink print page and dot image page are obtained from the same word processor file by a font change. A sighted computer user with no knowledge of braille can prepare such pages.
Ideally, all dotsplus documents would have raised images overprinted by the ink print equivalent as illustrated in Figure 3. This technique allows both visual and tactile reading by visually-impaired people and enhances communication between blind students and their sighted peers and teachers.
The author believes that dotsplus could become the preferred method for printing advanced mathematical and scientific literature for blind people. Portions of several high school and college textbooks are presently being prepared in dotsplus for testing by students who are using those books in their classes. The design of dotsplus has been developed after extensive testing and criticism by blind scientists, educators, and braille authorities in the US and several foreign countries. Blind scientists had little difficulty learning the capitalization and greek indicator convention but believe that some practice will be required for users to become familiar with dotsplus numbers and use of subscripts, superscripts, etc.
* Research program supported in part by the US National Science Foundation.
Figure 1. Dotsplus braille cell conventions.
Figure 2. Dotsplus raised image page transcribed from Advanced Algebra (University of Chicago School Mathematics Project), Scott Foresman Publishers, Glenview, Illinois.
Figure 3. Raised image from Figure 2 in light gray with equivalent ink print in dark gray. Ideal dotsplus literature would have inkprint as well as raised images, so it can be read easily by sighted and blind readers.