# Braille transcription of mathematical documents

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## Introduction to braille

With in this document, I will discuss braille as if there is very little prior or even no knowledge of braille, although it might be of interest in some of the later sections to those have some knowledge. I will aim to introduce the basics of braille which will allow appreciation of the discussion later on, which will give an understanding of the possible difficulties for producing braille mathematical documents.

## Braille basics

Braille is a system of 6 raised dots, laid out in 3 rows and 2 columns, which is used by many blind people to read written materials. One braille character, normally called a cell, considering the spacing between cells, is about 6mm by 10mm. The typical braille page can contain 40 cells per line, and 25 lines, and the braille page is slightly larger than A4 paper. So if a straight forward substitution of letters, numbers and punctuation was to be done, braille would be extremely bulky. To reduce the number of cells in the document, contractions were made. Some of these contractions may be as simple as a letter or combination of letters on their own meaning a word. An example of this is the letters wd on their own mean would. Now this reduces the number of cells, but there is more that can be done.

## Contractions using prefix symbols

There is only a certain number of words we can contract in the way previously described, so how can we improve on this? The answer is to use some characters as prefixes for some of the other characters and the number of combinations increases greatly. You may ask, if we are going to do that, why not increase the braille cell to 12 dots? If we were to increase the braille cell, we would always need to make space for those extra dots, so increase the size of the document. If we only have prefixes, we only need to use them when those dots are needed. Another advantage to the prefixes is that these can be used in part of a word for common combination of letters, how many words can you think of in english that end with tion? As we now have all these combinations to hand, the lesser used symbols can now be given prefixes and those now free one cell combinations can be used for very common contractions such as a cell to mean the.

## Representing technical information such as equations

In the last section we in fact solved more than one problem by defining prefix cells, as well as making things more compact, the increase in number of combinations available allows more than just text to be represented. Unfortunately although there may be an increase in combinations, it is difficult to define all mathematical symbols, greek letters, etc using these prefixes. As you don't have all those words and combinations of letter in equations, we can simplify things, and compact things by not using all those prefixes that would be required, by redefining those contractions in equations. As an example, there is an one cell character for "the" which becomes integral in British braille.

## Braille in different countries

Up to now we have been discussing braille in general, but where examples of contractions have been given it has been of english words. In different countries, different combinations of letters and words are commonly used, so what may lead to compact braille in one, may lead to no reduction in number of cells in another. Due to this, different countries have different braille codes. You might think that braille for a particular language would be the same in any country which uses it as its first language, but you would be wrong, there is even differences between the British braille and the north American braille. The variation in the codes varies depending on the differences in the use. For languages which use the Roman alphabet the basics such as the letters, numbers and common punctuation is usually the same, and in the case of British braille and north American braille it is mainly the same except for technical codes such as maths.

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