AMUCHMA-NEWSLETTER-29

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)

in order to make this online edition easily
accessible, there are some differences from the original - **the pdf version** is the
same as the original.

TABLE OF CONTENTS

- Objectives of AMUCHMA
- Meetings, exhibitions, events
- Current Research Interests
- Notes and queries
- Theses
- Sources
- Reviews
- Have you read? (#
**432**-#**459**) - Announcements
- Addresses of scholars and institutions mentioned in this newsletter
- Suggestions
- Do you want to receive the next AMUCHMA-Newsletter
- AMUCHMA-NEWSLETTER website

Maputo (Mozambique), 30.07.2004

**2.1. Exploring mathematical concepts in
indigenous activities**

A workshop on "Exploring mathematical concepts in indigenous activities," organised by Queeneth Mkabela-Castiano, took place at the University of Zululand in Epamgeni (South Africa) on June 22-23, 2004. The following papers were presented:

- David Mtetwa (Zimbabwe): Framework for classroom practice involving indigenous knowledge systems.
- Paulus Gerdes (Mozambique): The ethnomathematics research programme and geometry in Africa.
- Sabelo Nxumalo & Herbert Khuzwayo (South Africa), Exploring KwaZulu-Natal games.
- Abdulcarimo Ismael (Mozambique): Exploring indigenous games: the case of tchadji.
- Mogege Mosimege (South Africa): Some traditional South Afrcan games and school mathematics.
- Marcos Cherinda (Mozambique): Developing mathematical ideas in the classroom by exploring a weaving board.

**2.2. Papers presented at recent meetings**

Ahmed Djebbar (Algeria) presented on May 8,
2004, at the Institute for the History of Science of the University
of Teheran (Iran) an invited paper on *"Mathematical activities
in the Maghreb and in Andalus (9th 15th century)*."

* Ahmed Djebbar (Algeria) gave on May 22 and
23, 2004, two lectures at the universities of Annaba and Tébessa
(Algeria), entitled "*Contribution of the mathematicians
of the Maghreb to the development of combinatorial analysis*"*
*and *"Mathematical activities in the Maghreb and in
Andalus (9th 15th century)*."

* At the fifth International Interdisciplinary
NEXUS conference on the Relationships Between Architecture and
Mathematics, held in Mexico City (June 19 - 23, 2004), Moussa
Muhammad Guizar Haider presented the paper "*Explicit and
Inplicit Geometric Orders in Mamluk Floors: Secrets of the Sultan
Hassan Floor in Cairo*" (Egypt).

Paulus Gerdes (Mozambique) is concluding a
book on Geometry, Symmetry and Basketry in various cultures from
Africa and the Americas, including several comparative studies.
The book will be published in September 2004 as a special issue
of the journal *Visual Mathematics* (http://members.tripod.com/vismath).

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.

* Query from Michael Morelli (USA) [AMUCHMA 23]:

"What do you know about math books in the 14th century university library of Timbuktu that was uncovered by Henry Louis Gates of Harvard University?"

Answer by Ahmed Djebbar:

The answer to the question may be found widely
in the following websites. The information that is on these websites
is given by Mr. Haidara, the responsible for one of the most important
libraries of manuscripts of Mali, the one that Henry Louis Gates
visited and that benefited from his support and from a grant from
Harvard University.

It is necessary to add that the libraries of Mali contain scientific
manuscripts but the majority of them have not yet been studied.

www.ebad.ucad.sn/.../les%20communications/A.aa.AKhaidara.colloqueBNdk.communicationenfrançais.04052003.doc

www.ebad.ucad.sn/sites_heberges/manifestations/colloque_BN_2003/Akhaïdara.htm

* Query from Muhammad Bello (Kano, Nigeria) [AMUCHMA 25]:

"Inconsistency in Arabic Writing? It is very common knowledge that Arabic writing is from right to left, as against Western writing that is left to right. When it comes to writing numbers, however, Arabic writing seems to be inconsistent writing from left to write. Thus, two thousand, eight hundred and seventy-five would be written left to right just as in the Western way: Is Arabic inconsistent when it comes to writing numbers, or is there an explanation for this?"

Answer by Ahmed Djebbar:

There is no contradiction between the writing of Arabic from left to right and the writing of the numbers in the western way. The reason is the following: In a text written in classic Arabic the number 1475 is read as "five and seventy and four hundred and one thousand," that is from right to left, just as the writing. But, it is true that in the current oral practice (maybe because of the contacts between various languages), there is a mixture of two readings. For example, when one speaks in popular Arabic, to pronounce the number 45, one says "five and forty." One never says "forty five." But if I want to pronounce, for instance, 1475, I say "one thousand and four hundred and five and seventy." In other words, the reading of the thousands and hundreds is done in the western way, from left to right (first the thousands and then the hundreds), whereas the reading of the tens and units continues to be done from the right to the left (first the units and then the tens).

* Query from Mohamed El Tom (Sudan) [AMUCHMA 25]:

"A colleague asked me about the origin
of Arabic numerals. India appears to be the origin of Arabic numerals:
1, 2, etc., and interestingly enough these are used only in the
Arab Maghreb and I have no idea about the origin of the numerals
used in the Arab Mashriq. Any idea?

A second less difficult question is why this difference between
the numerals used between the two sets of Arab countries? Is it
the Andalus connection on the one hand, and the Indian proximity,
on the other?"

Answer by Ahmed Djebbar:

The historians of mathematics agree to say
that the Arabic numerals of the East and the Arabic numerals of
West (the Maghreb and Andalus) have the same origin: they are
Indian figures that were adopted by the mathematicians of the
countries of Islam since the 8th century.

But, since at least the 11th century, the Indian figures used
in Moslem Spain (Andalus) and in the Maghreb were transformed
(for reasons which we do not know) and distinguished themselves
gradually from Indian figures of the East. The manuscripts which
reached us show that in the 12th century, the figures of West
are very different from those of the East (at least some of them).

It is necessary finally to indicate that it is the European translators
of the 12th century who made the figures of the West known. As
they had found them in mathematics books written in Arabic, they
called them "Arabic numerals."

Today, the same distinction exists: in the countries of the Maghreb
one uses the figures called "Arabic," that is those
that were used in the Moslem West since at least the 12th century.
Whereas in the East (from Egypt onwards), one has kept the figures
which were used there since the 8th century.

None were reported.

**6.1 Examples of Books published by African
Mathematicians (2)**

To give the readers of the AMUCHMA Newsletter an impression of books and booklets published by African mathematicians, we continue in this issue to present examples. Any reader who has information on books not yet referred to in the AMUCHMA Newsletter, please contact the editors.

Adler, Jill (South Africa):

* *Teaching mathematics in multilingual classrooms*, Kluwer,
Dordrecht (Netherlands), 2001, 169 p.

Ahmad, Khalil (Morocco):

* (together with Pamy Manchanda & A.H. Siddiqi) (Eds.): *Current
trends in industrial and applied mathematics*, Anamaya Publishers,
New Delhi (India), 2002, 263 p.

Alvarinho, Ida (Mozambique):

* (together with Serguei Vodopianov): *Geometria Euclidiana*
[Euclidian Geometry], textbook, Universidade Eduardo Mondlane,
Maputo (Mozambique), 1982, 103 p.

Animalu, A. O. E.; Iyahen, Sunday O. &
Tejumola, Haroon O. (Nigeria) (Eds.):

* *Contributions to the development of mathematics in Nigeria*,
National Mathematical Centre, Abuja (Nigeria), 2000, 302 p.

Assani, Idris (Benin):

* (together with Wiener Wintner): *Ergodic Theorems*, World
Scientific, River Edge NJ (USA), 2003, 216 p.

Banyaga, Augustin (Rwanda):

* *The structure of classical diffeomorphism groups*, Kluwer,
Boston (USA); Boston, 1997, 197 p.

* (Ed. together with H. Movahedi-Lankarani & R. Wells) *Topics
in Low-Dimensional Topology*, World Scientific, Singapore,
1999.

* (Ed. together with J. Leslie, T. Robart) *Infinite Dimensional
Lie groups in Geometry and Representation Theory*, World Scientific,
Singapore, 2002.

Beirão, João Carlos (Mozambique)

* (together with Rodeon Alexandrov) *Problemas de análise
matemática: Funções reais de várias
variáveis *[Problems of mathematical analysis: Real
functions of various variables], Textbook, Universidade Eduardo
Mondlane, Maputo (Mozambique), 1982, 163 p.

* (together with Rodeon Alexandrov) *Problemas de análise
matemática: Séries* [Problems of mathematical
analysis: Series], Textbook, Universidade Eduardo Mondlane, Maputo
(Mozambique), 1982, 134 p.

* (together with Rodeon Alexandrov) *Problemas de análise
matemática: Integrais múltiplas* [Problems of
mathematical analysis: Multiple integrals], Textbook, Universidade
Eduardo Mondlane, Maputo (Mozambique),1983, 263 p.

* *Análise Matemática* [Mathematical Analysis],
Textbook,, Instituto Superior Pedagógico, Maputo (Mozambique),
1992, Vol. 1, 194 p.; Vol. 2, 230 p.

* *Funções de variável complexa* [Functions
of complex variable], Textbook, Instituto Superior Pedagógico,
Maputo (Mozambique), 1993, 175 p.

Cadete, Manuel D. O. (Angola):

* *Mathematical models for the management of education in countries
with an economy in transition*, Ph.D. thesis, Tula State Pedagogical
University, Tula (Russia), 1999, 115 p. (in Russian).

Chidami, Mohamed (Morocco):

* (together with Curto, R., Mbekhta, M., Vasilescu, F.-H., Zemánek,
J. (Eds.)): *Operator theory and Banach algebras. Proceedings
of the international conference in analysis held in Rabat, Morocco,
April 12--14, 1999*, Theta, Bucharest (Hungary), 2003, 161
p.

Chukwu, Ethelbert Nwakuche (Nigeria):

* *Stability and time-optimal control of hereditary systems.
With application to the economic dynamics of the U.S.*, Academic
Press, Boston MA (USA), 1992, 508 p. [2nd edition: Series on Advances
in Mathematics for Applied Sciences, Vol. 60. World Scientific
Publishing, River Edge NJ (USA), 2001, 495 p.]

* *Differential models and neutral systems for controlling the
wealth of nations*, Series on Advances in Mathematics for Applied
Sciences, Vol. 54. World Scientific, River Edge NJ (USA), 2001,
513 p.

* *Optimal control of the growth of wealth of nations. Stability
and Control: Theory, Methods and Applications*, Taylor &
Francis, London (UK), 2003, 384 p.

Esogbue, Augustine O. (Nigeria):

* (together with R. Bellman & I. Nabeshima) *Mathematical
aspects of scheduling and applications*, Pergamon, Oxford (UK),
1982, 329 p.

* *Dynamic programming for optimal water resources systems analysis*,
Prentice Hall, Englewood Cliffs NJ (USA), 1989, 435 p.

* (together with Liu, Baoding) *Decision criteria and optimal
inventory processes*, Kluwer, Boston (USA), 1999, 210 p.

Fatunla, Simeon Ola (Nigeria):

* (Ed.): *Computational mathematics I* [Proceedings of the
first international conference on numerical analysis and its applications
held in Benin City (Nigeria), November 2-4, 1983], Boole Press
Conference Series, Vol. 8,. Boole Press, Dún Laoghaire
(Ireland), 1985, 141 p.

* (Ed.): *Computational mathematics II *[Proceedings of the
Second International Conference on Numerical Analysis and its
Applications held in Benin City (Nigeria), January 27-31, 1986],
Boole Press Conference Series, Vol. 11. Boole Press, Dún
Laoghaire (Ireland), 1987, 221 p.

* *Numerical methods for initial value problems in ordinary
differential equations*, Computer Science and Scientific Computing,
Academic Press, Boston MA (USA), 1988, 295 p.

Guidy Wandja, Joséphine & Sah Bi,
Jess (Côte d'Ivoire):

* *Yao crack en math* [Yao crack in mathematics], Nouvelles
Editions Africaines, Abidjan (Côte d'Ivoire), 1985, 28 p.
(in French)

Hounkonnou, Mahouton Norbert (Benin):

* (together with Jan Govaerts & William Lester Jr.) (Eds.):
*Contemporary Problems in Mathematical Physics*, World Scientific,
River Edge NJ (USA), 2000, 377 p.

Jenda, Overtoun M. G. (Malawi):

* (together with Edgar Enochs): *Relative Homological Algebra*,
De Gruyter Expositions in Mathematics, Vol. 30, Walter de Gruyter,
Berlin (Germany), 2000.

Kuku, Aderemi O. (Nigeria) (continuation):

* *Abstract Algebra*, Ibadan University Press, Ibadan (Nigeria),
1980.

* *Axiomatic Theory of Induced Representation of Finite Groups*,
CIMPA, Nice (France), 1986.

* *Basic Computative Algebra*, Lecture Notes Series, National
Mathematical Centre, Abuja (Nigeria), 1994.

* *Topics in Algebraic K-Theory*, Lecture Notes Series, National
Mathematical Centre, Abuja (Nigeria), 1997.

Makinda, Olewole D. (Nigeria) & Sibanda,
Precious (Zimbabwe):

* *A mathematical introduction to incompressible flow*, Textbook,
University of Zimbabwe Press, Harare (Zimbabwe), 2000.

Nguiffo Boyom, Michel (Cameroon)

* (edited together with J.-M. Morvan & L. Verstraelen): *Geometry
and topology of submanifolds*, World Scientific, Teaneck NJ
(USA), 1990, 412 p.

Okikiolu, George Olatokunbo (Nigeria):

* *Aspects of the theory of bounded integral operators in Lp-spaces*,
Academic Press, London (UK), 1971, 522 p.

* *Special integral operators. Vol. I. Weierstrass operators
and related integrals*, Okikiolu Scientific and Industrial
Organization, London (UK), 1980, 306 p.

* *Special integral operators. Vol. II. Poisson operators, conjugate
operators, and related integrals*, Okikiolu Scientific and
Industrial Organization, London (UK), 1981, 507 p.

Olayi, Gabriel Atah (Nigeria):

* *Introductory Numerical Methods*, ABU Press, Zaria (Nigeria),
2000, 185 p.

* *Mathematicall Methods*, Bachudo Publ., Calabar (Nigeria),
2001, 135 p.

* *Complex Analysis, A Computational Approach*, Bachudo Science
Comp., Calabar (Nigeria), 2000, 164 p.

Seydi, Hamet (Senegal):

* *La théorie des anneaux japonais *[The Theory of
Japanese Rings], Colloque d'Algèbre Commutative, Université
de Rennes, Rennes (France), Vol. 12, 1972, 82 p.

Shonhiwa, Temba (Zimbabwe):

* *Introduction to Vector Analysis*, Textbook, University
of Zimbabwe Publications, Harare (Zimbabwe), 2000.

Vithal, Renuka (South Africa):

* *In Search of a Pedagogy of Conflict and Dialogue for Mathematics
Education*, Kluwer, Dordrecht (Netherlands), 2003, 416 p.

Uko, Livinus Ugochukwu (Nigeria):

* *Matematicas Amenas* [Mathematics for Leisure], Editorial
Universidad de Antioquía, Medellin (Colombia), 2000, 125
p. (in Spanish).

Vithal, Renuka & Adler, Jill (South Africa):

* (editors together with Christine Keitel) *Mathematics Education
Research in South Africa: Perspectives, Practices and Possibilities*,
Human Sciences Research Council, Pretoria (South Africa), 2004.

None were received

**8.1 Publications on the History of Mathematics
in Africa**

#432 Abdeljaouad, Mahdi: *Ibn al-Hâ'im,**
***Sharh al-Uujûza al-Yâsamîniyya**, Association
Tunisienne des Sciences Mathématiques, Tunis (Tunisie),
427 p.

Edition, accompanied by commentaries in Arabic and in French,
of a work by the Egyptian mathematician Ibn al-Hâ'im (1352-1412).
This work is entirely dedicated to a detailed commentary of the
algebraic poem *al-Yâsamîniyya* of the Maghrebian
mathematician Ibn al-Yâsamîn (d. 1204).

#433 Barrios García, José: **Investigaciones
sobre matemáticas y astronomía Guanche. Parte I:
Señales para recuerdo** [Research on Guanche mathematics
and astronomy. Part 1: Signs for recording], in: Morales Padrón,
F. (Ed.), *XIV Coloquio de Historia Canario-Americana* (Las
Palmas 2000), Cabildo, Las Palmas de Gran Canaria (Canary Islands,
Spain), 2002, 508-517 (in Spanish) (CD-ROM).

"The first part of this paper opens with a very brief summary
of what is known about the Guanches (ancient Berber inhabitants
of Tenerife island) in the 14th - 15th centuries, and goes on
analyzing the archaeological and ethnographical evidence documenting
their use of marks on the mummies, strings of clay beads, as well
as marks and pictures on wood planks and stones for recording
several kind of data, mainly calendrical and numerical ones."

#434 Barrios García, José: **Investigaciones
sobre matemáticas y astronomía Guanche. Parte II:
Sistemas de numeración** [Research on Guanche mathematics
and astronomy. Part 2: Numeration systems], in: Morales Padrón,
F. (Ed.), *XV Coloquio de Historia Canario Americana* *(Las
Palmas 2002)*, Cabildo, Las Palmas de Gran Canaria (Canary
Islands, Spain), 2002 (in Spanish) (CD-ROM).

"The second part of this paper studies the numeral systems
used by the ancient inhabitants of Tenerife Island to perform
several economical and socio-cultural practices as mentioned in
the written ethnographic sources. On this ground an hypothesis
is formulated about the numeral systems used, the name of the
numbers and the scope of the system."

#435 Furlong, David: ** Sekeds and the Geometry
of the Egyptian Pyramids** (Available on-line at:

www.kch42.dial.pipex.com/articles_frame_earth_sekeds.htm)

#436 Imhausen, Annette: **The Algorithmic
Structure of the Egyptian Mathematical Problem Texts**, in:
John Steele & Annette Imhausen (Eds.), *Under One Sky: Astronomy
and Mathematics in the Ancient Near East, Proceedings of the Conference
held in the British Museum, London, June 2527, 2001*,
Alter Orient und Altes Testament Vol. 297, Ugarit Verlag, Münster
(Germany), 2002, 147-166.

#437 Imhausen, Annette: **Ägyptische
Algorithmen. Eine Untersuchung zu den mittelägyptischen mathematischen
Aufgabentexten** [Egyptian Algorithms. A Study of Middle Egyptian
Mathematical Problem Texts], Verlag J. B. Metzler, Wiesbaden (Germany),
2003, 388 p. (in German).

"This technical analysis of ancient Egyptian mathematical
algorithms is based on a catalogue of Middle Egyptian mathematical
texts. The study considers the presentation of Egyptian mathematics
as collections of algorithms, and the application of mathematical
texts in everyday life and business. The catalogue presents the
texts in hieroglyphs with a transcription and commentary."

#438 Imhausen, Annette: **Egyptian Mathematical
Texts and Their Contexts**, *Science in Context*, Cambridge
(UK), 2003, Vol. 16, 367-389..

"The extant sources for ancient Egyptian mathematics are
extremely limited. It is therefore necessary to read the few sources
carefully and use additional information from further Egyptian
sources in order to achieve the most detailed picture possible.
Traditional approaches to Egyptian mathematics have provided only
a superficial account of mathematical practices and almost no
information about the role of mathematics within Egyptian culture.
To enlarge our knowledge it is crucial to use a different methodological
approach in the analysis of ancient mathematical techniques. In
addition, it is indispensable to contextualize the mathematical
problems with sources that are not specifically mathematical per
se. In this article I discuss several possibilities for these
additional sources, such as administrative texts, reliefs found
in tombs, and other archaeological evidence. I exemplify the use
of these sources with two problems from the Moscow mathematical
papyrus."

#439 Imhausen, Annette: **Calculating the
Daily Bread: Rations in Theory and Practice**, *Historia Mathematica*,
New York (USA), 2003, Vol. 30, No. 1, 3-16.

"This article discusses the handling of rations in Middle
Kingdom Egypt (2119-1794/93 BC) as it is displayed in three types
of texts: mathematical problem texts, administrative ration texts
("real" ration texts), and literary texts. The example
of handling rations is used to examine the relation between mathematical
problem texts-which served according to the opinio communis to
educate scribes- and administrative texts, the actual documents
from the professional life of scribes. Using one specific example,
the use of a mathematical technique from the problem texts within
a ration text is demonstrated. The presentation is complemented
by passages from literary texts referring to rations."

#440 Imhausen, Annette: **Zahl, II. Ägypten**
[Number, II, Egypt], in: Hubertus Cancik & Helmuth Schneider
(Eds.), *Der Neue Pauly. Enzyklopädie der Antike*, Vol.
12/2 Ven-Z, Stuttgart (Germany), 2003, 668-669 (in German).

#441 Imhausen, Annette: ** Mathematical
Fragments from Lahun**, University College of London, London
(UK) (online available at: www.petrie.ucl.ac.uk/digital_egypt/lahun/mathintro.html)

"Among the Lahun papyri a small number of fragments can be identified as mathematical texts, i.e. texts that have been written to record a mathematical procedure or used to carry out a mathematical procedure. Very few sources of ancient Egyptian mathematical texts are still extant. Of these, the mathematical fragments of the Lahun papyri hold a significant place. They contain both table texts and problem texts. While they are in many respects like the two major sources, the Rhind (mathematical) papyrus and the Moscow (mathematical) papyrus, they also show a number of significant details that are not seen in any other text."

#442 Imhausen, Annette & Ritter, James:
**Mathematical fragments: UC 32114, UC 32118, UC 32134, UC 32159
- UC32162**, in: Mark Collier & Stephen Quirke (Eds.), *The
UCL Lahun Papyri*, Archaeopress, Oxford (UK), 2004, Vol. 2,
71-96.

#443 Lumpkin, Beatrice: **Ancient** **Egyptian
Mathematics and Forerunners: Some Hints from Work Sites**, in:
A. K. Eyma & C. Bennett (Eds.), *A Delta-man in Yebu*,
Occasional Volume of the Egyptologists' Electronic Forum, Universal
Publishers / uPublish.com, 2003, No.1, 210-214.

#444 Omotunde, Jean-Philippe: ** Les nègres
: inventeurs du zéro en mathématique** [The
Blacks: inventors of the zero in mathematics], 2003 (Available
on-line at: www.africamaat.com/article.php3?id_article=105)

#445 Omotunde, Jean-Philippe: *L'Afrique
reste le berceau des sciences mathématiques**
*[Africa remains the cradle of the mathematical sciences],
2003 (www.africamaat.com/article.php3?id_article=117).

Discusses the Blombos stone (80 000 BC, South Africa), the Lebombo
(35 000 BC, Swaziland) and Ishango (20 000 BC, Congo) bones, and
the ancient Nile civilisations Nubia and Egypt.

#446 Rossi, Corinna: **Dimensions and Slope
in the Nineteenth and Twentieth Dynasty Royal Tombs**, *Journal
of Egyptian Archaeology*, London (UK), 2001, Vol. 87, 73-80.

**8.2 Publications on the History of Mathematics
in Africa, Ethnomathematics and / or Mathematics Education**

#447 Abdeljaouad, Mahdi: *Introduction à
l'arithmétique *[Introduction to arithmetic], Centre
des Publications Universitaires, Tunis (Tunisie) (in French).

In this handbook for first year university students the author
presents a chronology of arithmetic that gives its place back
to the contribution of the Arabs. Each chapter concludes with
an historical appendix that shows how each civilisation contributed
to the development of the concerned concepts.

#448 Akkar, Mohamed: **L'enseignement des
mathématiques dans l'enseignement secondaire maghrébin**
[Mathematics teaching in secondary schools of the Maghreb region],
*Zentralblatt für Didaktik der Mathematik - International
Reviews on Mathematical Education*, Karlsruhe (Germany), 2002,
Vol. 34, No. 4, 179-185 (in French).

Analyses "the following questions. Does the mathematics teaching
in the secondary schools in the Maghreb prepare to University
studies and more specifically does it initiate students to modern
science and technology? Is anyone able to understand mathematics
or is mathematics only accessible to the happy few. Is it a means
of selection? Is mathematics omnipresent in our modern society?
What relationships can one hope to find between mathematics and
other disciplines? Has mathematics evolved to such an abstract
and formal state that it seems difficult to relate it to any other
topic? All these questions are discussed in relationship with
the particular problems in the Maghreb, namely the mathematics
program as taught today in these countries."

#449 Brenner, Klaus-Peter: ** Die kombinatorisch
strukturierten Harfen- und Xylophonpattern der Nzakara (Zentralafrikanische
Republik) als klingende Geometrie eine Alternative zu Marc
Chemilliers Kanonhypothese** [The Combinatorically Structured
Harp and Xylophone Patterns of the Nzakara (Central African Republic)
as Sounding Geometry an Alternative to Marc Chemillier's
Canon-Hypothesi

#450 Gerdes, Paulus: **Interweaving Art and
Mathematics in African Design**, *International Review of
African American Artists*, Hampton VI (USA), Spring 2004, Vol.
19, No. 3, 44-47.

#451 Gerdes, Paulus: **Vinte cinco Anos de
Estudos Histórico-Etnomatemáticos em África
ao Sul da Sahara** [Twenty five Years of Historical-Ethnomathematical
Studies in Africa South of the Sahara], *LLULL, Revista Española
de História de las Ciencias y de las Técnicas*,
Zaragoza (Spain), Vol. 26, No. 56, 2004, 491-520 (in Portuguese).

Presents the development of historical and ethno-mathematical
studies in Africa South of the Sahara throughout the last quarter
of the 20th century by geographic region, from West Africa to
Southern Africa.

#452 Patel, Ramila: **Symmetry in Patterns
on Swazi grass mats**, *Symmetry: Culture and Science*,
Vol. 12, No. 1-2, Budapest (Hungary), 2003, 127-157.

Explores "the presence of symmetry in patterns on Swazi grass
mats made by women in Swaziland. The fundamental aim is to elucidate
and present basic explanations of the presence of symmetry in
the patterns on the Swazi grass mats. Symmetry in patterns on
other parallel Swazi material culture that admits patterning in
clay beer pots, beaded necklaces, grinding mats and more recently
baskets" are illustrated.

#453 Touré, Saliou: **L'enseignement
des mathématiques dans les pays francophones d'Afrique
et de l'Ocean Indien** [Mathematics teaching in the French-speaking
countries of Africa and the Indian Ocean], *Zentralblatt für
Didaktik der Mathematik - International Reviews on Mathematical
Education*, Karlsruhe (Germany), 2002, Vol. 34, No. 4, 175-178
(in French).

"Mathematics teaching in the French-speaking countries of
Africa and the Indian Ocean. We examine Mathematics teaching in
the French-speaking countries of Africa and the Indian Ocean,
starting from the consequences of the Colonial Period. At that
time, education was mainly aimed at preparing the civil servants,
and there was no organised structure for teaching. When they became
independent, these countries started with the French system and
methods, but they progressively realised that it was not totally
adapted to the aims and specificities of such countries. So progressively
new systems and curricula were designed. In this paper, we describe
some examples, and give some trends in the development of Mathematics
education in Africa and Indian Ocean, and perspectives for the
future."

**8.3 Other publications on the History of
Mathematics by African mathematicians**

#454 Djebbar, Ahmed: **Scientific Activities
and Inter-Cultural Relations in al-Andalus**, in: S. Osseiran
(Ed.): *Cultural Symbiosis in al-Andalus*, Regional Office
for Education in the Arab States, Beyrouth (Liban), 2004, 147-164.

**8.4 Publications on the History of Mathematics
and the African Diaspora**

#455 Agwu, Nkechi; Smith, Luell & Barry,
Aissatou:** Dr. David Blackwell, African American Pioneer**,
*Mathematics Magazine*, Vol. 76, No.1, February 2003, 3-14.

#456 Camara, Abdoulaye: Thomas Fuller (1710-1790)
Le grand calculateur [Thomas Fuller (1710-1790) The
great calculator], 2004 (http://www.africamaat.com/article.php3?id_article=92)
(in French).

Short article based on #83.

#457 Spangenburg, Ray *et al*.: **African
Americans in Science, Math, and Invention**, Facts on File Inc.,
New York (USA), 2003, 254 p.

**8.5 Reviews**

#458 Darvas, György: Paulus Gerdes' 'Awakening
of Geometrical Thought in Early Culture', *Symmetry: Culture
and Science*, Vol. 12, No. 1-2, Budapest (Hungary), 2003, 229-230*
*(cf. #388)

#459 Fleming, Steven: Paulus Gerdes' 'Awakening
of Geometrical Thought in Early Culture', *Nexus Network Journal,
*Vol. 6 No. 1 (Spring 2004), http://www.nexusjournal.com/reviews_v6n1-Fleming.html*
*(cf. #388)

**8.6 Mathematical books and documents published
in Africa**

None were reported (other than referred to in 6.1).

**8.7 Mathematical books published by Africans
outside Africa**

See 6.1.

**9.1 **Southern
African Ethnomathematics Study Group (SAEMSG

On June 22, 2004 in Richard Bay (South Africa)
the Southern African Ethnomathematics Study Group (SAEMSG), affiliated
to the International Study Group on Ethnomathematics (ISGEm),
was created. As first tasks for SAEMSG were formulated:

* Establish links with somehow regional associations or regional
branches of African or international organisations, so that at
their conferences, seminar and sub-conferences on ethnomathematics
may be held. The following organisations were identified: SAARMSTE,
SAMSA, AMU / AMUCHMA, AMESA, IKS, UNESCO-Harare, ICME-SA.

* Identify colleagues in the region who are interested in ethnomathematics
and circulate the information.

* Organise a scheme for joint supervision of masters and doctoral
theses in the field of ethnomathematics.

* Elaborate a regional ethnomathematics research agenda.

For more information, contact:

Abdulcarimo Ismael, Universidade Pedagógica, Maputo, Mozambique
(abdulcarimoismael@hotmail.com)

**9.2 Web pages**

*** **An extensive
webpage on Ancient Egyptian mathematics has been organised**
by **John O'Connor and Edmund Robertson:

www-history.mcs.st-andrews.ac.uk/Indexes/Egyptians.html

* Webpage on 'Sacred Geometry' in Ancient Egypt:

www.egypt-tehuti.org/articles/sacred-geometry.html

**9.3 **Mathematics
in African History and Culture: An Annotated Bibliography

Paulus Gerdes and Ahmed Djebbar concluded an
annotated bibliography on Mathematics in African History and Cultures,
to be published in English, French, and Arabic. The first English
and French language versions will be launched at the 6th Pan-African
Congress of Mathematicians (PACOM 2004), to take place from September
1 to September 6, 2004, in Tunis, Tunisia. The English version
published by the African Mathematical Union (AMU) contains 371
pages and is entitled ** Mathematics in African History and
Culture: An Annotated Bibliography**. Prof. Jan Persens,
President of the AMU, wrote the preface the book. The bibliography
is organised in alphabetical order and includes the following
appendices: (1) On mathematicians of African descent / Diaspora,
(2) Publications by Africans on the History of Mathematics outside
Africa, (3) On Time-reckoning and Astronomy in African History
and Cultures, (4) String figures in Africa, (5) Examples of other
Mathematical Books and Booklets published by African Mathematicians,
(6) Board Games in Africa, (7) Some African mathematical pioneers
in the 20th century, (8) Note on Research Inspired by the Historical
Reconstruction of Mathematical Ideas in the 'Sona' Geometric Tradition
Of Southern-Central Africa. Included are indices by subject, country,
region, language and ethnic group, journal, author and mathematician.

**9.4 **One semester
course on the History of Mathematics in Tunis

The UNESCO chair for "Mathematics and Development" in Tunis organises a one-semester course on the history of mathematics co-ordinated by Roshdi Rashed (CNRS, Paris). The aim of the course at a masters level is to inform mathematicians about the history of mathematics and to introduce the historiography of mathematics as a field of research and of teaching. The following themes and topics will be presented:

A. History of algebra and of number theory

* History of diophantine analysis and the number
theory from Diophant to Lagrange (Rosdi Rashed);

* History of algebra: al-Khwârizmî and his Arab and
Latin successors (Marouane Ben Miled, Tunis);

* History of algebra since Galois. (Massimo Galuzzi, Milan, Italy)

* History of algebraic geometry, 20th century (Christian Houzel,
Paris, France)

B. History of calculus

* The Arab Archimedians (Pascal Crozet, Paris,
France);

* The beginning of differential calculus (Daniele Napolitani,
Pisa, Italy);

* History of differential calculus, 18th 19th century (Serge
Demidov, Moscow, Russia);

* History of differential geometry (Erhard Scholz, Wuppertal,
Germany);

* History of measure and integration theory (Alain Michel, Marseille,
France).

C. History of some applications of mathematics

* History of applications of mathematics: mechanics,
optics (Michel Blay, Paris, France);

* History of astronomy of Plotemy to Kepler (Régis Morelon,
Paris, France);

* History of Greek and Arab statics (Fayza Bancel, Paris, France).

For more information, see the webpage:

http://www.tn.refer.org/unesco/semestre2/semestre2-fr.htm

or contact: Marouane Ben Miled (marouane.benmiled@fss.rnu.tn)

**9.5 **Colloquia
in Alexandria

Two international colloquia will take place
in September 2004 at the Library of Alexandria (Alexandria, Egypt):

* International Colloquium on the Arab manuscripts in Alexandria
(26-28.09.04);

* International Colloquium on the Unknown Aspects of the History
of Arab Science (29-30.09.04).

For more information, contact:

Yousef Zaydan, Director of the Centre of Manuscripts and of the
Museum of Manuscripts, Library of Alexandria, Alexandria, Egypt
(Fax: +203 48 30 329).

**9.6 **University
of Blida (Algeria)

Ahmed Djebbar visited in May 2004 the University
of Blida within the context of an agreement between the University
of Lille 1 and the University of Blida. His mission was prepare
the introduction of history of science courses in the scientific
teaching of the University of Blida, within the framework of the
new LMD system (License, Master, Doctorate) which will start in
the next academic year.

The mission also allowed preparing the launch of a postgraduate
programme for the training of scientific journalists for Algeria.
In this training, programmes of history of mathematics, physics,
chemistry and biology are foreseen. This programme will start
at the beginning of the 2005-2006 academic year. But, the next
year will be one year of training for already exercising journalists
who would be interested in this training.

Addresses of scholars and institutions and publishers mentioned in this Newsletter

Abdeljaouad, Mahdi: I.S.E.F.C., 43 rue de la
Liberté, 2019 Le Bardo, Tunis, Tunisia (E-mail: mahdi.
Abdeljaouad@isefc.rnu.tn)

Adler, Jill: School of Education, University of the Witwatersrand,
Private bag 3, P O Wits 2050, Johannesburg, South Africa (E-mail:
adlerj@educ.wits.ac.za)

Agwu, Nkechi; Mathematics Department, Borough of Manhattan Community
College, City University of New York, 199 Chambers Street, New
York, NY 10007 (USA) (E-mail: nagwu@bmcc.cuny.edu; Web-page: http://www.bmcc.cuny.edu/dptfac/matfac/agwu/index.html)

Akkar, Mohamed: Département de Mathématiques, Université
Bordeau I, 351 Cours de la libération, 33405 Talence Cedex,
France (E-mail: Alkhawar@post.club-internet.fr, Mohamed.Akkar@math.u-bordeaux.fr)

Alvarinho, Ida: Faculdade de Ciências, Universidade Eduardo
Mondlane, C. P. 257, Maputo, Mozambique

Assani, Idris: Mathematics Department, University of North Carolina,
Chapel Hill NC 27599-3250, USA (E-mail: assani@math.unc.edu)

Barrios García, José: Depto. de Análisis
Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife),
Islas Canarias, Spain (E-mail: josebarrios@telefonica.net; webpage:
http://webpages.ull.es/users/jbarrios/page/)

Banyaga, Augustin: Mathematics Department, Pennsylvania State
University, University Park, State College, PA 16802, USA (Web-page:
www.math.psu.edu/banyaga/; E-mail: banyaga@math.psu.edu)

Beirão, João Carlos: Departamento de Matemática,
Universidade Pedagógica, C.P. 4040, Maputo, Mozambique

Ben Miled, Marouane: Lamsin Enit, 1002 Tunis Belvedere,
Tunisia (Tel. +216 71 87 10 22, Fax: +216 71 87 27 29; E-mail:
marouane.benmiled@fss.rnu.tn)

Brenner, Klaus-Peter: Musikwissenschaftliches Seminar der Georg-August-Universitaet
Goettingen, Kurze Geismarstrasse 1, D-37073 Goettingen, Germany
Tel. +49-551-39-5075; Fax: 49-551-39-9353; E-mail: musik@gwdg.de)

Cadete, Manuel D.O.: Ministério de Ciência e Tecnologia,
Ilha do Cabo, C.P. 034, Luanda, Angola (Fax: 00 244 23 09 794;
E-mail: mdocadete@hotmail.com, mdocadete@yahoo.com.br)

Camara, Abdoulaye: E-mail: abdoulaye@africamaat.com.

Chidami, Mohamed: Université Mohamed V-Agdal, Faculté
des Sciences, Département de Mathématique et Informatique,
B.P. 1014, Rabat, Morocco (E-mail: chidami@fsr.ac.ma)

Darvas, György: Symmetrion, P.O.Box 994, Budapest, H-1245
Hungary (E-mail: darvasg@iif.hu)

Esogbue, Augustine O.: School of Industrial and Systems Engineering,
Georgia Institute of Technology, Atlanta GA 30332-0205, USA, (E-mail:
Augustine.Esogbue@isye.gatech.edu)

Fleming, Steven: The Department of Architecture, University of
Newcastle, Newcastle, Australia (E-mail: arspf@cc.newcastle.edu.au)

Hounkonnou, Mahouton Norbert: Institut de Mathématiques
et de Sciences Physiques (IMSP), Unité de recherche en
Physique Théorique (URPT), B.P. 2628, Porto-Novo, Benin
(E-mail: hounkonnou@yahoo.fr)

Imhausen, Annette: Trinity Hall, Trinity Lane, Cambridge CB2
1TJ, United Kingdom (E-mail: ai226@cam.ac.uk)

Jenda, Overtoun M. G.: Department of Mathematics, Auburn University,
AL 36849-5310, USA (E-mail: jendaov@auburn.edu)

Nguiffo Boyom, Michel: Département de Mathématique,
Université des Sciences et Techniques de Languedoc, 34060
Montpellier, France (E-mail: Boyom@darboux.math.univ-montp2.fr)

O'Connor, John: School of Mathematical and Computational Sciences,
University of St Andrews, St Andrews, Fife KY16 9SS, Scotland,
UK joc@st-andrews.ac.uk).

Olayi, Gabriel Atah: Mathematics, Statistics & Computer Science
Department, University of Calabar, Calabar, Nigeria

Omotunde, Jean-Philippe: Institut Khepera / Shabaka, Paris (France)
(E-mail: Agor@frica.com)

Patel, Ramila: Waterford Kamhlaba, United World College of Southern
Africa, P.O. Box 52, Mbabane, Swaziland (ramila@waterford.sz;
www.waterford.sz)

Ritter, James: Département de Mathématiques, Université
de Paris 8, 2 Rue de la Liberté, 93526 Saint Denis Cédex
02, France (E-mail: jim@univ-paris8.fr)

Shonhiwa, Temba: Department of Mathematics, University of Zimbabwe,
PO Box MP 167, Mount Pleasant, Harare, Zimbabwe (E-mail: temba@maths.uz.ac.zw)

Touré, Saliou: Institut de Recherche Mathématiques,
08 B.P. 2030, Abidjan 08, Côte d'Ivoire (E-mail: saliou_toure2002@yahoo.fr)

Uko, Livinus Ugochukwu: Universidad de Antioquía, Medellin,
Colombia

Vithal, Renuka: School of Educational studies, University of
Kwazulu-Natal, Private bag X54001, Durban 4000, South Africa (E-mail:
vithalr@ukzn.ac.za)

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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**