Brazil, 2006
This edition of the Unified Language Code for the Portuguese Language was revised and updated according to the Braille the Portuguese Language, a document prepared by the Brazilian Commission the Braille Commission of Portugal and approved by the Ministry of Education by means of Ordinance 2.678, of September 24, 2002
Presentation book page 11
Introduction book page 13
Observations book page 17
Chapter 1 - Alphabetic prefixes and unifying signals book page 19
1.1 Alphabetic prefixes book page 19
1.2 Braille representation of the Greek alphabet book page 20
1.3 Auxiliary signals and parentheses book page 22
Chapter 2 - Superscripts and Subscripts book page 25
2.1 Index positions book page 25
2.2 Lower indices and higher indices book page 25
2.3 Trademarks book page 27
2.3.1 Marks to the right at the top index book page 27
2.3.2 Marks in superscript book page 29
2.4 Symbols with Multiple Indices book page 30
2.4.1 Lower indices and simultaneous higher indices book page 30
2.4.2 General case. book page 30
2.5 Indices displaced book page 32
2.6 Abbreviated Numeric Data book page 32
Chapter 3 - Numbers book page 33
3.1 Arabic characters or figures book page 33
3.2 Decimal and fractional numbers book page 34
3.3 Numbers represented on different bases book page 35
3.4 Types of numbers book page 36
3.5 Representation of the main number sets book page 36
3.6 Ordinal book page 36
3.7 Roman Numbers book page 37
3.8 Examples of transcripts of units of measurement book page 37
Chapter 4 - Basic Arithmetic Operations and Elementary Numeric Relations book page 41
4.l Signs of elementary arithmetic operations book page 41
4.2 Elementary numerical relationships book page 42
4.3 Negative relations book page 44
4.4 Other Arithmetic Representations book page 44
Chapter 5 - Fractions, Powers and Roots book page 47
5.1 Fractions book page 47
5.2 Powers book page 49
5.3 Roots book page 50
5.4 Examples of algebraic expression transcription book page 50
Chapter 6., Theory of Sets and Logic book page 53
6.1 Elementary representations book page 53
6.2 Logic book page 58
6.3 Other notations book page 60
6.4 Set theory notation examples book page 61
Chapter 7 - Applications (Functions) book page 63
7.1 Basic notes book page 63
7.2 Limits book page 65
7.3 Derivatives book page 66
7.4 Integrals book page 69
7.5 Notations on specific functions book page 70
7.5.l Successions, Progressions, and Matrices book page 70
7.5.2 Logarithmic functions book page 72
7.5.3 Trigonometric functions and their inverse book page 74
7.5.4 Hyperbolic functions and their inverse book page 74
7.6 Common symbols with different meanings book page 75
7.7 Illustrative examples book page 76
Chapter 8 - Geometry book page 79
8.1 Elementary notation, vectors and figures book page 79
8.2 Angular measurements book page 82
8.3 Relationships and Operations book page 83
Appendix I book page 85
Appendix 11 book page 87
Bibliography book page 89
The Unified Mathematical Code for the Portuguese Language the aspirations of Brazilian teachers and Ibero-America, who years have sought a unified solution adapted to the characteristics of of the Braille System used in Europe and Latin America. Much is due to professionals in the area of education of students with disabilities national and international bodies. Their efforts are crystallized in the existence of the Brazilian Commission Braille, which, when it reaches its great goal, offers today the Brazilian Educational Code The Unified Language Code for the Language Portuguese - CMU.
The invaluable support of the Brazilian government through the Ministry of Education / Special Education Secretariat and its represented partners especially by the Benjamin Constant Institute - IBC, the Dorina Nowill for Blind People - FDNC and the Brazilian Union of the Blind - UBC, demonstrate the importance of the joint effort that resulted in the preparation of an up-to-date and highly relevant document for the education of the blind in the computer age - the Mathematical Code Unified for the Portuguese Language. Claudia Pereira Dutra Secretary of Special Education - MEC
The application of the Braille System to Mathematics was proposed by Louis Braille version of the System edited in 1837. On that occasion, the basic symbols for figures and conventions for Arithmetic and Geometry.
This fundamental symbolism, however, was not always adopted in the countries that came to use the Braille System, more or less marked regional and local differences, to the point of prevailing, as today, several codes for Mathematics and sciences, all over the world.
In order to unify Braille symbology for Mathematics and the sciences, a congress was held in the city of Vienna in 1929, bringing together countries in Europe and the United States. Despite this effort, the lack of agreement meant that divergences continued to prevail, which were accentuated, in view of the need to adopt new symbols, determined by the technical and scientific evolution of the twentieth century.
The World Council for the Well-being of the Blind, today, the Union Blind World, with the support of UNESCO, started to worry about with the problem of the unification of the mathematical and scientific symbology, in the world.
For this purpose, the Spanish National Organization of the Blind (ONCE), in the beginning of the 70's, developed studies through of the analysis and comparison of different codes in use in the world for, finally, to propose a unified code that he called Notacion Universal.
The Ibero-American Conference for the Unification of the Braille, held in Buenos Aires in 1973, was an attempt to establish a unique code for Spanish-speaking and Portuguese-speaking countries. At the opportunity, three papers were presented, respectively, by Spain, Argentina and Brazil. The marked divergence between the codes made impossible a desirable agreement.
The Executive Committee of the World Council for the Well-Being of Cegos, meeting in the city of Riyadh, Saudi Arabia (1977), created the Subcommittee on Mathematics and Sciences, composed of representatives Spain, the United States, the Soviet Union, West Germany and England, with the main purpose of promoting, in different countries, studies and experiences at national and regional levels, aiming to unification of the various codes in use.
The Castilian-speaking countries finally reached an agreement for the unification of mathematical symbology in 1987 in the city of Montevideo, during a meeting of press representatives braille of the countries that speak the language. This meeting was attended by two Brazilian representatives, as observers.
Specialists in the Brazilian Braille System, especially related to the The Benjamin Constant Institute and the Dorina Nowill Foundation for the Blind people, from the 70's, began to worry about the advantages the unification of scientific codes, since the Taylor Table, adopted in Brazil since the 1940s, no longer came braille transcript, especially after introduction of the symbols of Modern Mathematics, especially in the which referred to Mathematics at the higher level.
Brazil participated initially and subsequently accompanied the studies developed by the ONCE in the Unified Mathematical Code (CMU).
In 1991 the Commission for Study was created; Updating the Braille System in Use in Brazil, with the participation of specialists representatives of the Benjamin Constant Institute of the Dorina Foundation Nowill for Blind, the Brazilian Council for the 'Well-Being of the Blind', of the Brazilian Association of Educators of the Visually Impaired and the Brazilian Federation of Blind Entities, with the support of the Brasileira de Cegos and the sponsorship of the Economic Cooperation Fund for Ibero-America - ONCE-ULAC.
The work of that committee was completed on May 18, 1994, and included in the main resolutions to be adopted in Brazil. Unified Mathematical Code for the Spanish Language, with the necessary adaptations to the Brazilian reality. Under guidance of the Brazilian Blind Union (UBC), the Commission Braille, a technical body subordinated to it, established a strategies for the implantation, throughout the national territory, of the new unified mathematical symbology.
The present edition represents one of the more concrete actions in this sense.
The Unified Mathematical Code for the Portuguese Language excellent options for the representation of symbols of the common system, up to now without adequate representation in the Braille System, as indexes and brands. An outstanding alternative is the application of auxiliary brackets, Braille representation feature in cases where that linear writing hinders the understanding of mathematical expressions. The CMU also has symbols available for new representations in Braille.
Any doubts that may arise with the application of this work may be settled with the Brazilian Braille Commission.
-- Brazilian Braille Commission - CBB
The use and application of this Mathematical Code does not offer greater difficulties to the user, whether this person is blind or the sighted.
Its implementation and editing, far from being an obstacle, transforms into a medium that will unify for all (teachers, transcribers, users ...) the way of using a mathematical language common.
To further facilitate this task, we offer the following recommendations:
1. Mathematical expressions are usually written without cells empty intermediates. Nevertheless, in some cases, for reasons of clarity, it is necessary to leave blank spaces before and after some symbols that are expressly indicated in corresponding tables (example: "therefore", see item 6.3).
In the same way, this exception applies in some cases to other such as equality in the case of tables or graphs. (see item 7.5.1).
2. In exact and natural science texts, it is recommended not to use braille stenography, in order to avoid possible confusion in the reading.
3. The transcription of a form contained in a common text shall be obey the following rule: leave two cells blank before formula and, likewise, two empty cells after it.
4. In order to facilitate the reading and comprehension of the text, expressions and short sentences, when they do not fit at the end of a line, transferred in full to the next line, spaces on the top line are neglected. Already the expressions and sentences when they do not fit in a line, will be cut, preferably, in a ratio signal (equal to, different from, greater than, etc.) or in an operation signal (more, less, times, divided by) as in ink, that is, by writing the signal at the end of the line and repeating it, the beginning of the next line. The start of a next line to cut an expression or sentence two cells should be left after or two cells before the cell that corresponds to the beginning of the upper line, in the which the cut was made. In successions, progressions, in the sets represented element by element, etc., the cut will be made after the signal punctuation (comma, period, colon) later.a term, without repetition of this signal on the next line. Cutting an expression between parentheses should be avoided, even if blank cells are abandoned end of line. Where this is unavoidable, it shall be previously, that is, the expression will be cut off in an operation signal; repeated, necessarily, on the next line. Where these if possible, the signal shall be used; (point 5), which will not be repeated on the next line.
5. It is recommended (especially to the editors) that in the texts of mathematics and of exact sciences, in general, tables with the signs used and their respective meanings are included, besides the graphic representation (as it is in ink) of the signography and the graphs.
6. Special attention should be given to the application of auxiliary brackets, which have no correspondents in the common system, as they constitute a particular feature of Braille. Its diverse applications should be well explained to teachers, transcribers, reviewers and users of the Braille System.