Braille writing rules for mathematics and science

The Swedish Braille script series contains the following titles:


Phonetics and Braille, by Lillemor Andersson and Catharina Johansson (2005)
Short Scripture. Level 1 and 2 (1997)
Short Scripture. Levels 3 and 4, for notes (1997)
Louis Braille - Creator of a writing system (2005), by Beatrice Christensen Sköld
Braille and its use (second edition, planned to be released in 2009)
Braille terms (2001)
Editing and Depreciation (1999)
Writing rules for mathematics and science (second edition, planned to be published in 2009)
Swedish writing rules for Braille (second edition, 2009)
Tactile maps - Guidelines for the production of maps for the visually impaired (2003), by Yvonne Eriksson, Gunnar Jansson and Monica Strucel
Tactile maps - Tutorial in map production (2003), by Yvonne Eriksson, Gunnar Jansson and Monica Strucel
Character table as the norm for Swedish eight-point script (1997)

Distribution: Speech and Braille Library
Box 5513
121 17 Johanneshov
Email: info@tpb.se
www.punktskriftsnamnden.se
www.tpb.se
© 2009


Contents


Preface to the second edition 7
Introduction 9
-- About this book 9
-- Blank character in mathematical braille 10
-- Arithmetic operators 10
-- -- Arrows 10
-- -- Line 10
-- -- Comparison Operators 10
-- -- Multidisciplinary and logic 10

Part 1 MATTERS AND WRITING RULES AND NATURAL SCIENCE
1 Special Braille characters 13
1.1 List 13
1.2 Blank sign 14
1.3 Help characters 14
1.3.1 Termination and separation signs 14
1.3.2 Warning signs 16
1.3.3 Continuing character 16
1.3.4 Auxiliary help 16
1.3.5 Fuse co-ordinator 16
1.4 Signs that do not have a defined typeface in Braille 17
1.5 Rules for line breaking 17
2 Letters 19
2.1 Latin letters 19
2.2 Greek letters 19
2.3 Single highlighted characters 22
2.4 Highlighted characters 23
3 Numbers 25
3.1 Arabic numerals 25
3.1.1 Blank characters in numerical sequences 25
3.1.2 Enter and point in numerical sequences 25
3.2 Roman numerals 26
4 Storages and devices 28
4.1 Some special unit signs 28
4.2 Other units 28
Arithmetic operators 30
6 Fraction 34
6.1 Figures and variables in fraction 34
6.2 Fractures in mixed form 36
6.3 Complicated fraction 36
6.4 Fractions with the main fraction 38
6.5 Fraction-like layouts 39
7 Exponents, Roots and Index 40
7.1 Upper and lower index 40
7.2 Root expression 45
8 Parentheses, dashes and arrows 47
8.1 Parentheses 47
8.2 Parentheses over several rows 48
8.3 Lines 51
8.4 Common arrows 54
8.5 Other arrows 55
9 Other operators and characters 57
9.1 Comparison operators 57
9.2 Multidisciplinary and logic 60
9.3 Geometric characters 63
9.4 Analysis (derivative and integrals) 64
9.5 Other characters 66
9.6 Characters in computer context 67

Part 2 EXAMPLE COLLECTION, SUBJECT ORDER
10 Mathematics 71
10.1 Arithmetic and algebra 71
10.2 Analysis 75
10.2.1 Some function types 75
10.2.2 Interval and boundaries 77
10.2.3 Derivator 78
10.2.4 Integrals 80
10.2.5 Differential Equations 80
10.2.6 Exponential and Logarithm Functions 81
10.2.7 Limit values, sequences and series 81
10.3 Complex numbers 83
10.4 Quantity teaching and logic 84
10.5 Geometry 86
10.6 Trigonometric Functions 87
10.7 Probability and statistics 88
11 Physics and Astronomy 90
12 Chemistry and biology 93
12.1 Chemical designations and formulas 93
12.2 Structural formulas 97
13 Programming and Internet 99

APPENDIX - changes in the second edition 102
Character with new look in Braille 102
Arrows with new look in Braille 105
New characters in Braille 106
Removed characters 108
Alphabetical register 109
Character register 129

Preface to the Second Edition

Braille's writing rules for mathematics and science are one collection of rules and recommendations for how to write mathematics and other science subjects in Swedish Braille.

This second revised edition has been produced by Ulf Aldener, Lillemor Andersson, Stig Becker, Fredrik Larsson, Björn Nyqvist, Anders Sennerö and Björn Westling. The previous edition was published in 1997.

The new edition, among other things, has a new sign for mathematical characters ] (dots 12456) introduced. A list of changes made at the sign level is towards the end of the book. Changes have been made to make it easier to use mathematically Braille. The appearance of the mathematical characters in Braille has been chosen to be easier to remember than before. The It is further recommended that greater attention be paid to it mathematical braille layout, among other things by using blank characters can be used to create better readability in a succession of characters and that each equation in an equation system should be written on new line.

A basic prerequisite for the design of the mathematical Braille is to get so much conformity with writing rules for other Braille as possible. This has succeeded in principle fully and can serve as a model for the construction of corresponding writing rules for Braille in other countries. That, for example, 3 × 4 m² is written in the same way in Braille in one novel as in a scientific article we think is very important for the Braille to be readable and accessible.

Johanneshov, August 2012; Björn Westling

Introduction

About this book

Braille's writing rules for mathematics and science are one compilation of rules and associated examples for Braille in mathematics and science.

The script consists of two parts. Nine chapters in the first part are presented writing rules and different groups of characters and symbols. IN the second part is given examples sorted in four chapters for different areas or subjects.

The writing rules for mathematics and science are based on and are an extension of the writing rules described in Swedish writing rules for Braille.

The Braille's writing rules for mathematics and science cover the need for Braille characters up to and including high school and in many cases also the college level. Based on how the Braille characters If designed, it is possible to create further if necessary Braille characters so as to completely cover the need for Higher literature.

Black print books often have a layout that gives the eye a quick look overview of quite complicated connections. Such a layout can be difficult to reproduce in braille and can sometimes become more obstacles than help for Braille reader.

Typical typefaces in black print that are difficult to exactly imitate Braille is, for example, layouts where you can arrows show a cross-flow, the "staircase" that illustrates division calculation as well as atomic and molecular structures in chemistry. Such black-and-white illustrations should be commented on and can also be supplemented with relief images.

The examples in the Braille's writing rules for mathematics and science are essentially authentic and have been chosen to illustrate phenomena that are not always clear from the text. Note that the examples in some cases introduce typos and characters that are taken up later in the book.

Blank character in mathematical Braille

In most cases, blank characters do not have any meaning-bearing function in mathematical Braille but can be used to create one better readability for longer character sequences. In some cases, Braille characters must be surrounded by whitespace to avoid misunderstandings.

Arithmetic operators

Arithmetic operators (Chapter 5) can be written in black print with or without blank characters on either side.

Arrows

Braille characters for different arrows are presented in section 8.4 and 8.5.

The representations that ordinary arrows (section 8.4) have in Braille are meant to graphically mimic the appearance of the characters in black writing. This principle does not apply to most other characters. All Braille characters that represent common arrows must be surrounded by whitespace.

Other arrows (section 8.5) are represented in Braille by using the meaning of the sign is written within the auxiliary service - in an abbreviated form

Line

Lines are presented in section 8.3. Two simple lines alongside each other should be separated by whitespace so as not to be misinterpreted as one double stroke.

Comparison

Comparison operators are presented in section 9.1. It is often appropriate and sometimes necessary to have these Braille characters surrounded of whitespace.

Multidisciplinary and logic

The characters and symbols used in volume theory and logic are presented in section 9.2. Even for them, it is often appropriate that the corresponding Braille characters are surrounded by blank characters.