AMUCHMA-NEWSLETTER-24

Chairman: Paulus Gerdes (Mozambique)

Secretary: Ahmed Djebbar (Algeria)

Members:

Cyprien Gnanvo (Benin) |
Salimata Doumbia (Côte d'Ivoire) |

Nefertiti Megahed (Egypt) |
Mohamed Aballagh (Morocco) |

Abdoulaye Kane (Senegal) |
David Mosimege (South Africa) |

Mohamed Souissi (Tunisia) |
David Mtwetwa (Zimbabwe) |

Associate Members: José Barrios (Canary Islands, Spain), Scott Williams (USA)

TABLE OF CONTENTS

Fifth PAN-AFRICAN CONGRESS OF MATHEMATICIANS

2. Meetings, exhibitions, events

5. Theses

6. Sources

7. Reprints

8. Have you read? (#297-#322) --- - 2nd web page

9. Announcements - 2nd web page

10. Addresses of scholars and institutions mentioned in this newsletter - 2nd web page

11. New recipients - 2nd web page

Do you want to receive the next AMUCHMA-Newsletter

Universidade Pedagógica (UP), Maputo (Mozambique), 11.16.2000

**Fifth PAN-AFRICAN
CONGRESS OF MATHEMATICIANS**

During the Fifth Pan-African Congress of Mathematicians (Cape Town, South Africa, 23-28 January 2000), the General Assembly of the African Mathematical Union analysed the activities of the AMU during the last five years, and elected the members of the new Executive Committee and the chairpersons of the AMU Commissions.

The new Executive Committee of the AMU has the following composition:

President: Prof. Jan Persens (South Africa)

Secretary-General: Prof. Jean-Pierre Ezin (Benin)

Treasurer: Prof. Paulus Gerdes (Mozambique)

Vice-President for Southern Africa: Prof. Patrick
Phiri (Swaziland)

Vice-president for Eastern Africa: Prof. Verdiana Masanja (Tanzania)

Vice-President for North Africa: Prof. Mohamed Chidami (Morocco)

Vice-President for West Africa: Prof. Akry Koulibaly (Burkina
Faso)

Vice-President for Central Africa: Dr. M. Mawanda (Dem. Rep. Congo)

Members at large:

Dr. Sami Baraket (Tunisia)

Prof. Patrick Mangheni (Uganda)

Prof. Mary Teuw Niane (Senegal)

Prof. Hassan Nsar (Egypt)

Immediate Past President: Prof. Ahmed Kerkour (Morocco)

The following professors are the chairpersons
of the AMU Commissions elected by the General Assembly: Nouzha
El Yacoubi (Morocco): Chairperson, AMU Commission on Pan-African
Mathematics Olympiads; Verdiana Masanja (Tanzania): Chairperson,
AMU Commission on Women and Mathematics; Juma Shabani (Burundi):
Chairman, AMU Commission on Mathematics Education;

Paulus Gerdes (Mozambique): Chairman, AMU Commission on the History
of Mathematics in Africa (AMUCHMA) [reelected]; Daouda Sangare
(Mali): Editor-in-Chief of the AMU Journal "Afrika Mathematika"[reelected].

The newly elected Executive Committee of AMU completed the composition of AMUCHMA in the following way:

Chairman: Paulus Gerdes (Mozambique)

Secretary: Ahmed Djebbar (Algeria)

Members: Cyprien Gnanvo (Benin), Salimata Doumbia (Côte
d'Ivoire), Nefertiti Megahed (Egypt), Mohamed Aballagh (Morocco),
Abdoulaye Kane (Senegal), David Mosimege (South Africa), Mohamed
Souissi (Tunisia), David Mtwetwa (Zimbabwe)

Associate Members: José Barrios (Canary Islands, Spain),
Scott Williams (USA)

2. MEETINGS, EXHIBITIONS, EVENTS

**3.1 Papers presented at PACOM 2000**

At the Fifth Pan-African Congress of Mathematicians (Cape Town, South Africa, 23-28 January 2000; see 2), the following papers concerning the history of mathematics in Africa were (intended to be) presented:

* Paulus Gerdes (Mozambique) presented a plenary lecture entitled
"*On mathematical ideas in cultural activities in the history
of Africa south of the Sahara*".

* Dirk Huylebrouck (Belgium) and Vladimir Pletser (European
Space Agency) were unable to come to South Africa to present their
paper "*Research and Promotion: about the first mathematical
artifact: The Ishango bone*". The authors' abstract of
the paper:

"In 1950, the Belgian Prof. J. de Heinzelin discovered a bone at Ishango, a village at the sources of the Nile, on the border of Congo and Uganda. The 20000 years old artifact has patterned notches, making it the first tool showing logic reasoning. In the present communication, four demonstrations of the mathematical skills in pre-colonial Africa will be given as additional circumstantial evidence for its mathematical properties. Furthermore, the Ishango bone is still a research object, because other dating methods are applied on it and because new interpretations are proposed for it, like Pletser's "slide rule"-reading. It rejects former "arithmetic game" and "calendar" explanations, but confirms de Heinzelin's archaeological evidence about relationships between Egypt, West Africa and Ishango. It points towards the use of the base 12, which anthropologist Thomas had studied in West Africa some 80 years ago. It shows that the Ishango artifact is the missing link Thomas was looking for. The fact that the dawn of mathematics originated in Africa is not always well known. The authors aim to make it better known, through an extraordinary link between Africa and the space adventure. Indeed, a scene from the movie "2001: A Space Odyssey" offers a very strong image that facilitates the communication with the largest audience. It is about a human ancestor who throws a bone in the air that turns into a space ship. The sequence can be considered as a metaphor to illustrate the progress of mankind, from apparently very simple discoveries up to the technology of the space age. If the African artifact would continue its Kubrick-like voyage, weightlessly floating in space, it would stand for the contributions made by different civilisations to the development of mathematics and physics, and thus to the conquest of space. A satellite conference about science, with schools in Africa, would focus the attention on mathematics in Africa, and this would certainly be successful, as the authors could experience in 1993, when they assisted in the organization of a scientific event by the University of Burundi."

* José Barrios (Canary Islands) was also unable to come
to cape Town to present his paper entitled "*On the place
of the Canary Islands in the studies of the ancient history of
African mathematics*". Here follows the author's abstract:

"Through my earlier research, evidence have arisen suggesting that the ancient Berber inhabitants of Grand Canary Island in 14th-15th centuries (the centuries just preceding the Spanish conquest of the Islands), systematically recorded numerical astronomical and calendrical data by mean of certain geometrical figures, named 'tara', painted in white, read and black on wood planks and on the wall of certain caves. In this paper, I summarise part of this evidence, stressing the peculiar position as well as the potential importance of the Canarian studies for the mainstream investigation the ancient history of African mathematics."

**3.2 Papers presented at recent meetings**

* At the Third Luso-Brasilian Meeting on the History of Mathematics
(University of Coimbra, Portugal, 7-12 February 2000), Paulus
Gerdes (Mozambique) presented a plenary lecture entitled "*On
some geometrical ideas in the history of central and southern
Africa*".

* At the Conference "Mathematics and Culture" (University
of Milano-Bicocca, Italy, 14 April 2000), Paulus Gerdes (Mozambique)
presented the keynote address entitled "*Mathematical inspiration
in / from African cultures*".

* At the International Colloquium on "2000 Years Transmission
of Mathematical Ideas: Exchange and Influence from Late Babylonian
Mathematics to Early Renaissance Science" (Rockefeller Study
and Conference Centre, Bellagio, Italy, 8-12 May 2000), Ahmed
Djebbar (Algeria) presented the paper entitled "*The circulation
of mathematics between the Islamic East and West: Old interrogations
and new elements*".

* At the occasion of the International Year of Mathematics,
the Houari Boumédiène University organised a national
colloquium on mathematics (Alger, Algeria, 21-24 May 2000). More
than 300 Algerian teachers and scholars, coming from all regions
from Algeria and from abroad, took part in the colloquium. The
opening address was given by Ahmed Djebbar (Algeria) and was entitled
"*From the 9*th* to the 19*th* century, thousand
years of mathematical activities in the Maghreb*". Other
papers concerning the history of mathematics were the following:

* Djamil Aïssani: "

The stay of the famous mathematician François Arago (1808-1809) in Algeria";

* Abdelmalek Bouzari: "The theory of conic sections in the mathematical tradition of Andalusia and the Maghreb";

* Youcef Guergour: "Al-Mu'taman Ibn Hud and his Kitab al-istikmal";

* Moktadir Zerrouki: "Mathematics and heritage in the Maghreb through the commentary of al-`Uqbani".

* At the Peruvian Bilingual Educational Research Programme, Paulus Gerdes (Mozambique) conducted a workshop on the methodology of ethnomathematical and historical research, illustrated by examples from the Amazonia and from Africa south of the Sahara (Iquitos, Peru, May-June 2000).

* Ahmed Djebbar (Algeria) gave a series of lectures at the University of Zaragossa (Zaragossa, Spain, 12-14 June 2000). The lectures were about the history of algebra, the history of combinatorics and the history of mathematical activities in the Maghreb and in Spain.

* At the third Mathematical Summer School of Safi (Safi, Morocco, 11-14 July 2000), two papers were presented concerning the history of mathematics:

* Mohamed Akkar (Morocco): "

Mathematics and society";

* Ahmed Djebbar (Algeria): "Birth and development of Arabic mathematics (9th-15thcentury)".

* Ahmed Djebbar (Algeria) was member of the Programme Committee of the International Francophone Colloquium on "Mathematics education in Francophone countries in the 20th century and perspectives for the beginning of the 21st century" (Grenoble, France, 15-17 July 2000). The following African scholars presented papers at the colloquium:

Mohamed Akkar (Morocco): "

Mathematics education in the Maghreb";

Saliou Touré (Ivory Coast): "Mathematics education in Subsaharan Africa";

Rachid Bebbouchi (Algeria): "Didactical Research: A possible transition between mathematics education and mathematical research";

Ahmed Daif (Morocco): "History of the introduction and the evolution of didactics in Morocco. Today's teaching of didactics at teacher training colleges (ENS, CPR, ERI)";

Khalil Sammad (Morocco): "Mathematics and other subjects. Their different roles. Examples of experimentation";

Abdelkader Khelladi (Algeria): "Mathematical symbolism in a non-Latin graphic environment, neither from the left nor from the right";

Moncef Zaki (Morrocco): "Conception of a mathematical module of expression in French for Moroccan students";

Abderrahman Aït Ouassarah (Morocco): "Use of Cabri to visualise certain qualitative properties of dynamic systems".

* At the International Symposium "Symmetry 2000"
(Stockholm, Sweden, 13-17 September 2000), Paulus Gerdes (Mozambique)
presented the paper "*Symmetrical explorations inspired
by the study of African cultural activities*".

* At the International Colloquium "From China to the West: Ways between Arithmetic and Algebra" (Toulouse, France, 22-23 September 2000), the following African scholars presented papers:

Ahmed Djebbar (Algeria): "

Mathematics and Society: Some problems in medieval Maghrebian mathematical writings";

Ezzaim Laabid (Morrocco): "Arithmetical procedures that may replace algebra: Examples from the heritage tradition in the medieval Maghreb";

Abdelmalek Bouzari (Algeria): "Procedures and circulation of 'thought numbers' from the Islamic East to the West";

Mohamed Souissi (Tunisia): "Algorithms of different operations by al-Qalasadi. Some remarks".

* At the sixth Congress of the Association of Francophone Circles
of History and Archaeology of Belgium (Mons, Belgium, 24-27 August
2000), Francis Buekenhout (Free University of Brussels, Belgium)
presented the paper entitled "*Polyhedra from Lucy to Jacques
Tits*", in which the prehistory and early history of the
concept of polyhedron in Africa in stone cutting activities is
analysed.

* At the Study days of the French Association of Teachers of
Mathematics in Public Schools (APMEP) on "Mathematics in
the Mediterranean" (Nice, France, 27-29 October 2000), Ahmed
Djebbar (Algeria) presented the opening address entitled "*Arabic
mathematics on both sides of the Mediterranean*". About
800 mathematics teachers took part in the event, among them teachers
from the Maghreb and from Subsaharan Africa.

* **Cameroon Research Group on Ethnomathematics**

The University of Yaoundé 1 set up a Research Group on Ethnomathematics. Its coordinator is Professor G. Edward Njock (cf. #12) [P.O. Box 623, Yaoundé, Cameroon (Tel./Fax. +237-216717; E-mail: enjock@uycdc.uninet.cm)].

This section is reserved for questions that readers would like
to have answered; these are the 'queries'. The answers will be
the 'notes'. If you have questions or answers about sources, dates,
names, titles, facts, or other such matters related to the history
of mathematics in Africa, frame them in clear and concise language
and send them to the editors. If you are answering a question,
make clear reference to that question. All readers may send both
questions and answers. Each will be published with the name of
the sender.

* Sidi Amar Assali (Algeria) defended successfully a 'Magister'
thesis in the History of Mathematics (École Normale Supérieure
d'Alger, June 25, 2000). His thesis is entitled "*The mathematical
instruments of astronomy through the work of al-Hasan al-Murrakushi
in the 'Book of principles and objectives of the science of time'*".

The Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University (Frankfurt am Main, Germany) collected and started the reprinting of a series of papers and books on "Islamic mathematics and science". Related to the history of mathematics in Africa are the following reprints:

**Volume 24**: ** Ibn Yunis Abu l-Hassan 'Ali ibn 'Abdarrahman
(d. 399/1009). Texts and Studies. Collected and reprinted**.

This volume contains the following papers:

* A letter from the Rev. Mr. Richard Dunthorne to the Rev.
Mr. Richard Mason F.R.S. and keeper of the Woodwardian Museum
at Cambridge, concerning the acceleration of the moon (1-10);

* George Costard: Translation of a passage in Ebn Younes, with
some remarks thereon (11-23);

* Jean Bernouilli: Examen des remarques de M. Costard sur les
éclipses d'Ibn-Jounes (25-36);

* Jean Bernouilli: Recherches sur une éclipse de lune observée
au caire en 979 et comparée avec les Tables de Mayer (37-53);

* Armand-Pierre Caussin de Perceval: Kitab az-Zij al-kabir al-hakimi
rasad as-saih Abi l-Hassan 'Ali ibn Ãbdarrahman ibn Ahmad
ibn Yunis / Le livre de la grande table Hakémite, observée
par le Sheikh Abdoulhassan Ali ibn Abderrahman, ebn Ahmad, ebn
Iounis (54-278).

**Volume 25**: ** Ibn Yunis Abu l-Hassan 'Ali ibn 'Abdarrahman
(d. 399/1009). Texts and Studies. Collected and reprinted**.
Vol. II. Edited by Fuat Sezgin in collaboration with M. Amawi,
C. Ehrig-Eggert, and E. Neubauer. 1997, VI, 318 pp.

This volume contains the following papers:

* Jean-Baptiste Joseph Delambre: Ebn Younis et Aboul Wefa (1-96);

* Louis-Amélie Sédillot: La grande Table hakémite
(97-101);

* Armin Wittstein: Die von Ibn Junis in Kairo beobachteten Mond-
und Sonnenfinsternisse. Nach Theodor von Oppolzer's "Kanon
der Finsternisse" berechnet (102-104);

* Carl Schoy: Das 20. Kapitel der grossen haekemitischen Tafeln
des Ibn Yunis: Ueber die Berechnung des Azimuts aus der Hoehe
und der Hoehe aus dem Azimut" (105-119);

* Carl Schoy: Ueber eine arabische Methode, die geographische
Breite aus der Hoehe der Sonne im 1. Vertikal ("Hoehe ohne
Azimut") zu bestimmen (120-129).

* Carl Schoy: Die Bestimmung der geographischen Breite eines Ortes
durch Beobachtung der Meridianhoehe der Sonne oder mittels der
Kenntnis zweier anderen Sonnenhoehen und den zugehoerigen Azimuten
nach dem arabischen Text der haekimitischen Tafeln des Ibn Yunus
(131-149).

* Carl Schoy: Beitraege zur arabischen Trigonometrie (Originalstudien
nach unedierten arabisch-astronomischen Manuscripten) (150-185).

* Carl Schoy: Ueber den Gnomonschatten und die Schattentafeln
der arabischen Astronomie. Ein Beitrag zur arabischen Trigonometrie
nach unedierten arabischen Handschriften (187-215).

* Carl Schoy: Die Gnomonik der Araber (217-315).

* J. H. Reynolds: The Hakemite Tables of Ebn Younis (316-317).

**Volume 41**: ** Traité des instruments astronomiques
des Arabes composé au treizième siécle par
Abu l-Hasan 'Ali al-Marrakushi (VII/XIII s.) intitulé Jami'
al-mabadi' wa-l-ghayat. Partiellement traduit par Jean-Jacques
Sédillot et publié par Louis-Amélie Sédillot.
Tome I-II**. Reprint of the Edition Paris 1834-1835. Edited
by Fuat Sezgin. Introduction in French and Arabic, 1998, X, 619,
4 pp., 38 plates

**Volume 42**: ** Al-Marrakushi Abu 'Ali al-Hassan ibn
'Ali ibn 'Umar (7**th

This volume contains the following papers:

* Dominique François Jean Arrago and Charles Mathieu:
Rapport sur un Mémoire de M. Am. Sédillot, sur les
instruments astronomiques des Arabes (1-3);

* Jean-Baptiste Biot: Sur un mode d'énonciation des longitudes
terrestres, particulier à certaines écrivains arabes
(Review of: Louis-Amélie Sédillot, Traité
des instruments astronomiques des Arabes, composé au XIIIe
siècle par Abdoul-Hassan-Ali de Maroc. Paris 1834 (5-43);

* Louis-Amélie Sédillot: Mémoire sur les
instruments astronomiques des Arabes (45-312);

* Edward J. Stone: On Aboul hhassan's catalogue of 240 stars (3142-316);

* Carl Schoy: Die geschichtliche Entwicklung der Polhoehenbestimmungen
bei den aelteren Voelkern (317-350);

* August Wedemeyer: Der Mittagshafir und halazun von Abul
Hassan. Die aelteste Messkarte zur bestimmung von Sonnenhoehen
(with remarks by Carl Schoy) (352-364).

(to be continued)

**8.**
Have you read?** - 2nd
web page**

**9.** Announcements**
- 2nd web page**

**10.** Addresses
of scholars and institutions mentioned in this newsletter**
- 2nd web page**

**11.** New
recipients** - 2nd web page**

Thanks to Scott Williams, the English language
edition of all issues of the **AMUCHMA Newsletter** is also
accessible on the following website: **http://www.math.buffalo.edu/mad/AMU/amuchma_online.html**

Please note the address of the above website
changed to the present with AMUCHMA 21.

The English version of AMUCHMA
24 is reproduced and distributed

with financial support from **SIDA**-**SAREC** (Sweden)