## Braille Mathematical Notations

Various Braille codes for mathematics have been developed in different countries. Here is the information I collected about existing Braille Mathematical Notations. This is not complete. If you have any information which could help, please post a comment down here or to this blog entry.

The biggest source of information was the survey done by UNESCO and published in 1990 [1].

### Mathematical and/or Scientific Braille notations

#### France

The Braille Mathematical code was ﬁrst adapted to Mathematics in 1922 by *Louis-Auguste Antoine*. Antoine was teaching Mathematics in secondary school until 1914 when he was mobilized. He became blind after being wounded at the face. After the war he adapted the Braille code to Mathematics and presented a PhD. Then he became professor at University of Rennes.

This code was revised a ﬁrst time in 1971. It was then deeply revised in 2001, in the goal of improving the collaboration between sighted and blind and facilitating automatic transcription. Another revision was done in 2007.

According to [1], in 1990 this code was also used in Madagascar and in Portugal.

*Notation Mathématique Braille (Mise à jour de la notation mathématique en braille de 1971)*, by*Commission Évolution du Braille Français*. INJA and AVH, Paris, France. Septembre 2001. Download the document « Notation Mathématique Braille, 2001″ (PDF version, in French).*Notation Mathématique Braille*, by Commission Évolution du Braille Français. INJA and AVH, Paris, France. Janvier 2007. Download the document « Notation Mathématique Braille, 2007″ (PDF version, in French).

#### Marburg

Marburg is used in German speaking countries. It was designed in 1955 in the Marburg school for the Blind in Germany by *Helmut Epheser*, *Karl Britz* and *Friedrich Mittelsten Scheid*. A heavily reworked and revised edition was published in 1986.

This code is at least used in Germany, Austria and Poland (with minor variations). According to [1], in 1990 it was also used in Denmark, The Netherlands, Norway and former Yougoslavia.

*Neufassung und vervollständigung des systems der internationalen mathematikschrift für blinde*, by H. Epheser, K. Britz and F. M. Scheid. Marburg/L.: Ständige Arbeitsgemeinschaft*“Mathematikschrift”*, Deutsche Blindenstudienanstalt e.V. 1986

#### Stuttgart Maths Notation

This notation is the only notation based on a 8-dot pattern (execpt the Lambda linear code). It has been used at least in Stuttgart.

*Stuttgarter Mathematikschrift für Blinde*, by W. Schweikhardt. Report Nr.3/87, Institut für Informatik, Universität Stuttgart, 1987.

*8-Dot-Braille for writing, reading, and printing texts which include mathematical characters*, by W. Schweikhardt. ICCHP ’98 – Computers and assistive technology, Vienna, Budapest, 31 August – 4 September 1998. IFIP world computer congress N^{o}15. OCG, Vienna, Austria, ISBN 3-85403-118-1, pp. 324-333, 1998.

#### British Braille

The British notation is used in United Kingdom and in Ireland. It was ﬁrst designed in 1970, and a deeply revised version was published in 1987. This was slightly revised in 2005.

According to [1], in 1990 this code was used (various releases according to the different countries) in Australia, Barhein, Hong-Kong, Iran, Ireland, Jordan, Kenya, Nigeria, Saudi Arabia, Sierra Leone, Singapore, UK and Zimbabwe.

*Braille mathematics notation*, by Braille Autority of the United Kingdom. RNIB, Peterborough, UK. 2001. Download the document « Braille mathematics notation » (PDF version).

#### Nemeth

The Nemeth Code for Braille Mathematics was published and accepted as the standard code for representing math and science expressions in Braille in 1952. It was designed in 1946 by Abraham Nemeth so that he could complete his PhD in mathematics. The 1972 revision is the current official code in use in the US. Note that Nemeth was adopted in a number of Southeast Asian countries (like India, Thailand, Malaysia, Indonesia, Cambodia, Vietnam).

According to [1], in 1990 this code was also used in Canada, India, Iran, Israel, Lebanon, New Zealand, Pakistan, Saudi Arabia, Sri Lanka, Thailand, USA and Western Samoa.

*The Nemeth Braille code for Mathematics and Science notation, 1972 revision*, by A. Nemeth. American Printing House for the Blind, USA. 1972- Here is a scan in PDF: The Nemeth Braille code for mathematics and science notation, 1972 revision

The Nemeth code is also in use in Quebec, the French speaking state of Canada. Here is a translation of the Nemeth code in French.

*Code pour la transcription en Braille de la notation Mathématique*, by Comité de normalisation du braille français en éducation, Gouvernement du Québec, Ministère de l’Éducation. Mai 2001. Download the document « Code pour la transcription en Braille de la notation Mathématique » (PDF version, in French).

Greece is using an adaptation of the Nemeth code, where the roles of Roman letters and Greek letters are in a sense reversed. Here is a document, in Greek, about the merits of Nemeth code, and the decription of the Nemeth code for Greece:

- Scientific Braille symbols for Greece, by Georges Kouroupetroglou and Evangelos Florias,
*Centre*for the*Education and Rehabilitation of the Blind, Athens*2003

#### Unified English Braille

The International Council on English Braille is developing a Unified English Braille which was implemented yet in 4 countries: *Australia, New Zealand, Nigeria* and *South Africa*. The UEB Mathematics Committee is completing the assignments of symbols for technical materials and any rules necessary for their use.

In April 2010, UEB was adopted by the Canadian Braille Authority.

#### Italy

There is an Italian Braille code. Here is the official 2003 specification and an online course, both in Italian:

#### Spain and spanish speaking countries

[NEW] 10/2009

Braille Code Unified Mathematics (CMU) for the spanish speaking countries, set up by the Spanish Braille Commission :

- CMU in PDF format
- CMU in ASCII file at the Quick Braille format (Braille editing program used by ONCE)

Older information: [1] (1990) states that a unified code was approved by the « Conferencia Iberoamericana para la Unification del Sistema Braille » in Buenos Aires. 3 documents which seem to be different releases of this code are mentionned by different countries:

*Simbologia Cientificca Braille*, by Della Barca, Juan José, y Judith A Varsavsky. Approved by the Conferencia Iberoamericana para la Unification del Sistema Braille. Buenos Aires 1973 (this is the reference given for Boliva, Chile and Cuba, [1]).*Unificación del código matematico*, Fundación Braille de Urugay (this is the reference given for Argentina, Colomba, Nicaragua, Spain and Uruguay, [1]).*Notacion « U » del Sistema Braille*, by Rodrigo Dominguez, Francisco. 3d ed. experimental. ONCE, Madrid 1978 (this is the reference given for Ecuador, El Salvador, Guatemala and Nicaragua, [1]).

Two books are available in Spanish:

- Braille y matemática, by José Enrique Fernández del Campo Sánchez. Publicación: Madrid : Organización Nacional de Ciegos Españoles, Dirección de Educación, 2004. ISBN: 84-484-0143-3. Braille y matemática (PDF version, zipped)
- Matematica Braille, (Guía para estudiantes, maestros y padres), by Ignacio L. Robles. Editorial: Trillas Editorial. ISBN: 978-968-24-5537-7

#### Japanese Mathematical Braille

The current Japanese Mathematical Braille notation was published in 2001 by the Japan Braille Committee. It is an important revision of the 1981 formal speciﬁcation of Japan Mathematical Notation, itself based on the notation published in 1956 by Japan Braille Research Group (“Nihon Tenji Kenkyukai”).

*Explanation of Braille Mathematics Symbols*, by Japan Braille Committee. Japan Braille Committee. Tokyo, 1981.

#### China

It seems a specific code was developed in China, based on the Marburg code (according to [1]).

*Braille Mathematical and Scientific Symbols*. Experimental ed. Beijing Braille Publishing Co. Beijing, 1979

#### Bharati Braille Code for Mathematics (India)

*Bharati Braille Code for Mathematics*, by National Association for the Blind. National Association for the Blind. Bombay, 1978

#### The Netherlands

A set of rules, inspired by the Marburg code, was set up in the Netherlands in 1983.

A revised version of the notation in use was released by Dedicon in October 2009 . Information is available at wiskunde.dedicon.nl (in Dutch – the site provides lots of examples). The new version is closer to the notation used in the printed copy of a book. That way it facilitates understanding and cooperation between for instance a sighted teacher and a non-sighted student when both using a computer. Another consideration taken into account regarded best practices from (international) notation used when linearizing math for computer purposes, e.g. in spreadsheets, calculating software or even plain e-mail traffic.

#### Woluwe code

The *Woluwe* code was developed in the sixties for the Dutch speaking part of Belgium. It is based on the Marburg code. The developer of the Woluwe code was a former teacher at the Royal Institute for Deaf and Blind people (Koninklijk Instituut Woluwe), in Sint-Lambrechts-Woluwe, a suburb of Brussels.

*Handleiding Braillesymbolen wiskunde*(Manual for mathematics Braille), ed. by Gilbert Notaert, Marc Suij and Emmanuel Vandekerkhove, G.on Woluwe, 1984.- The mathematical Woluve code, chapter of a document from the Maths project, where this code is described in english. This is a PDF version of a scanned document.

#### Sweden

*Matematiska Symboler I Punktskrift*. Stig Becker, ed, in cooperation with Gunilla Stenberg, Bengt Lindqvist and Nils Trowald. Uppsala School of Education, Pedagogical Institute. Uppsala, 1972

According to [1], in 1990 this code was also used in Iceland.

#### Finland

*Finnish Braille Committee’s Approved Mathematics, Physics and Chemistry Notation*, by Central Union of the Blind. Central Union of the Blinde. Helsinki, 1979

#### Denmark

*Mathematics and Scientific Notation in Braille*. Institutet for Blinde og Svagsynede. 1984

According to [1], in 1990 this code was also used in Norway.

#### Russia

It seems that the 2 following references are translations in Czech and in English of the same document.

*Systém Matematických, Fyzikálních, Astronomických a Chemických znaků ve Slepeckém Písmu*, by A. G. Bykov, A.F. Golubčikov, F.B. Morozova and I.V. Proskurjakov. Stāni Pedagogickē Nakladatelstvi. Prague, 1980.*System of Symbols for Math, Physics, Chemistry, and Astronomy: A Learning Aid*, by A. G. Bykov, M.I. Egorov, F.B. Morozova and I.V. Proskurjakov. Edited by Proskurjakov and Bykov. Committee fr Exact Sciences for All Russia Association for the Blind. 2nd ed, rev and enl. The All Russia Association for the blind. Moscow, 1982.

According to [1], in 1990 this code was also used in Bulgaria, former Czechoslovakia (and I guess now Czech republic and Slovakia), and Denmark.

#### Romania

*Sistemul de Notatie Matematica in Scierea din Romania*. 1981

#### Israel

An Israeli code exists. Some bibliographic found on clfb.org.il:

- Mathematics in Braille (1991), by Rivka Rosenzweig
- Mathematics in Braille – improved edition (2001), by Rivka Rosenzweig
- A Guide for Learning Mathematics in Braille (1998, 2002), by Rivka Rosenzweig
- Familiarity with Mathematics for writers of Braille (2002), by Rivka Rosenzweig

And here is the Israeli code, in Hebrew.

#### Czech republic

Here is some information, in Czech language about Czech braille codes. Any information in English welcome!

### Other notations

#### HRTeX

HRTeX (Human Readable TeX) is a code developed at the Johannes Kepler Universität Linz, Austria, with the intention to supply teaching materials in a way more easily readable than TEX or LATEX. HRTeX is derived from TeX, although not compatible with it. These are some of the most important differences:

- Many symbols are abbreviated. For instance, the symbols for Greek letters are composed of the ﬁrst two characters, e.g., al instead of alpha, be instead of beta, etc.
- The names of standard functions are written like variables, but in upper case letters, e.g., SIN instead of sin, LOG instead of log, etc.
- Alternative notation for fractions: The fraction bar is represented by two slashes – // -, and the whole fraction is written as a group. For instance, {a+b // c+d} instead of frac{a+b}{c+d}.

#### AMS

The ASCII Maths Notation (AMS) has been developed in University of Karlsruhe by Mr Schönberg in 1993. It uses exclusively the 128 characters of the 7-bit standard ASCII, which makes it platform independant. AMS is used in Germany, Austria and some eastern european states.

- ASCII-Mathematikschrift AMS – Anleitung zur Umsetzung mathematischer Formeln, nov 2001 (in German)
- AMS TeX – text file in english

#### Lambda

Lambda is a mathematical reading and writing system designed for blind students. The software was developed in a pro ject of the same name, whose meaning is in full: “Linear Access to Mathematics for Braille Device and Audio Synthesis”. The Lambda software is mostly referred to as the “Lambda Editor” – it is an editor that enables a blind student to input and to edit mathematical expressions in a rather comfortable way.

The main characteristics of the Lambda pro ject is that it is built on a brand new code. This code is an XML code speciﬁcally designed for supporting the Braille transcription into 8-dot pattern national codes. Each Lambda national code has the lambda structure and a Braille character dictionary as close as possible to the official national code.

As for output, Lambda supports these modalities:

- Braille output in a special, though customisable 8 dot code
- speech synthesis – mathematical symbols are verbalised in a descriptive language
- visual presentation in a linear code (a speciﬁc font in which each Braille character is represented by a visual symbol)
- graphical rendering – not synchronous to input, the graphical rendering is built when the user presses a key. This view is then static. The graphical view is obtained by conversion of the Lambda code to MathML.

To learn out more about Lambda:

*LAMBDA: a European System to Access Mathematics with Braille and Audio Synthesis*, by W. Schweikhardt, C. Bernareggi, N. Jessel, B. Encelle and M. Gut. In K. Miesenberger, J. Klaus, W. Zagler, and A. Karshmer editors, Proc. ICCHP 2006 (10th International Conference on Computers Helping People with Special Needs), volume 4061 of LNCS, pages 1223–1230, Linz, Austria. Springer.- http://www.lambdaproject.org

### References

[1] *World Braille usage*, UNESCO, Paris 1990, ISBN 92-3-102323-3/US Library of Congress, Washington D.C. 1990, ISBN 0-8444-0676-7. (Link to original on UNESCO server)

### Acknowledgements

Many thanks to:

- Pr Gerhard Weber, from Technische Universität Dresden, Germany.
- Pr Mazakazu Suzuki, from Kyushu University, and leader of the Infty Project, Japan.
- Bernhard Stöger, from Johannes Kepler Universität Linz, Austria.
- Emilia Persoon, from Dedicon, The Netherlands.
- Pr Jan Engelen, from Katholieke Universiteit Leuven, Belgium.
- Christope Strobbe, from Katholieke Universiteit Leuven, Research Group on Document Architectures, Belgium.
- Jaroslaw Urbanski, from Harpo, Poland.
- Antonio Quatraro, Italy.
- David Holladay, Duxbury Systems
- Gerhard Jaworek, Universität Karlsruhe (TH), Studienzentrum für Sehgeschädigte (SZS), Germany.
- Pedro Ruiz, Technical Secretary of the Spanish Braille Commission, Spain.

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