PHILOSOPHY OF MATHEMATICS EDUCATION JOURNAL 11 (1999)
Chairman: Paulus Gerdes (Mozambique)
Secretary: Ahmed Djebbar (Algeria)
Treasurer: Salimata Doumbia (Côte d'Ivoire)
Members: Kgomotso Garegae-Garekwe (Botswana), Maassouma Kazim (Egypt), Cornelio Abungu
(Kenya), Ahmedou Haouba (Mauritania), Mohamed Aballagh (Morocco), Ruben Ayeni (Nigeria),
Abdoulaye Kane (Senegal), David Mosimege (South Africa), Mohamed Souissi (Tunisia), David
Universidade Pedagógica (UP), Maputo (Mozambique), 25.08.1998
The African Mathematical Union Commission on the History of Mathematics
in Africa (AMUCHMA), formed in 1986, has the following objectives:
a. to improve communication among those interested in the history of
mathematics in Africa;
b. to promote active cooperation between historians, mathematicians,
archaeologists, ethnographers, sociologists, etc., doing research in, or related to, the
history of mathematics in Africa;
c. to promote research in the history of mathematics in Africa, and the
publication of its results, in order to contribute to the demystification of the
still-dominant Eurocentric bias in the historiography of mathematics;
d. to cooperate with any and all organizations pursuing similar
The main activities of AMUCHMA are as follows:
a. publication of a newsletter;
b. setting up of a documentation centre;
c. organization of lectures on the history of mathematics at national,
regional, continental and international congresses and conferences.
2. MEETINGS, EXHIBITIONS, EVENTS
2.1 International Colloquium in Béjaïa (Algeria)
The Study Group for the History of Mathematics in Béjaïa (GEHIMAB) organised
(University Centre of Béjaïa, November 9-11, 1997) an international colloquium on
"Béjaïa and environment during the ages: History, Society, Sciences, Culture".
Related to the history of mathematics the following papers were presented:
* Mustapha Abdelkader-Khaddaoui,
E.N.S. d'Alger (Algeria): Arithmetic and its methods in Bougie;
* Moktadir Zerrouki, E.N.S. d'Alger (Algeria): Some mathematical algorithms used in the
science of inheritance by two mathematicians who lived in Bougie;.
* Michel Ballieu, LouviËre (Belgium) & Djamal A'ssani, UniversitÈ de Bougie
(Algeria): The mathematical knowledge available in the Small Kabylia in the 19th century;
* Djamel Eddine Mechhed, UniversitÈ de Bougie (Algeria): The alphabetical numeration
in the manuscripts of the Small Kabylia
* Bernard Rouxel, UniversitÈ de Bretagne Occidentale (France) & Djamel A'ssani,
UniversitÈ de Bougie (Algeria): The geometer Albert Ribaucourt in Bougie;
* Rachide Bebbouchi, UniversitÈ d'Alger (Algeria): The geometrical reflections of the
EugËne Dewulf in Bougie;
* Ettore Picutti, U.M.I., Milan (Italy): Leonardo of Pisa and his "Liber
* Jacques SÈsiano, Ecole Polytechnique de Lausanne (Switzerland): The algebra of
Leonardo of Pisa and its influence in medieval Europe;
* Gino Arrighi, Lucca (Italy): Towards a better knowledge of the Latin versions of
2.2 Papers presented at recent meetings
* At the Conference in Honor of the 65th Birthday of Ubiratan D'Ambrosio (the 'father
of ethnomathematics'), realized on January 6, 1998 in Baltimore (USA), two talks were
related to the history of mathematics in Africa. Paulus Gerdes spoke about the historical
development of ethnomathematical research in Mozambique and D'Ambrosio's influence. Nkechi
Agwu (City University of New York) presented the paper "Mathematical teaching
techniques inherent in Nigerian cultures".
* At the 76th Annual Meeting of the National Council of Teachers of Mathematics (2-4
April 1998, Washington DC, USA), various papers were presented which are related to
mathematics in or from Africa:
Ron Eglash & Gloria Gilmer: African hairstyle designs;
Arthur Powell: Out-of-school application of ethnomathematics: the game of oware;
Daniel Ness: Ethnomathematics and Asante kete drumming;
Beatrice Lumpkin: Some mathematical gems from Egypt;
John Sims: Designs from the Kuba (Congo) and the teaching of mathematics to arts
Paulus Gerdes: Exploring geometrical ideas from Southern Africa;
Nelson Sanz: Problem solving and 'aha' calculation experiences with the Rhind
Anthony Stevens & Janet Sharp: Learning about fractions and ratios by using African
rhythms played on drums.
3. CURRENT RESEARCH INTERESTS
* Franz Gnaedinger (Zurich, Switzerland) is concluding a book
entitled "Geometrie und Mathematik im alten Ägypten" (Geometry and Mathematics
in ancient Egypt).
* Milo Gardner (Sacramento, USA) is analysing fractions in Ancient
Egypt and prepared several manuscripts on "'false position' arithmetic that 'picked a
number' to solve Egyptian fraction problems".
4. NOTES AND QUERIES
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
* Mathematical manuscripts from Mali?
Mike Morelli (University of Wisconsin-Stout) has the following query "A while
back, the Chronicle of Higher Education printed an article which stated that Dr. Henry
Louis Gates, while in Mali, discovered 4000 books from a 14th century university library
(Timbuktu?). I have been trying to get more information about this important discovery.
What do you know about this? In what language are the books written? Were any of them math
5. HAVE YOU READ?
5.1 On the History of Mathematics in Africa
#248 Bashakova, I.: Diophantus and Diophantine Equations,
Mathematical Association of America, Washington, 1997, 104 pp.
Presents the works of Diophantus of Alexandria, focusing on Diophantus'
general methods of obtaining rational solutions of indeterminate equations of the second
and third order. The second part of the book considers the evolution of the theory of
Diophantine equations from the Renaissance to the middle of the 20th century.
#249 Kielland, Else Christie: Geometry in Egyptian Art, Alec
Tiranti, London, 1955, 214 pp.
Presents a brief survey of Egyptian geometry based on the papyri that
have been found, followed by the interpretations which scholars placed on the geometric
marks found on the Egyptian works of art. Finally, Lange's law of frontality is discussed,
with its revision by Schäfer.
#250 Lumpkin, Beatrice: From Egypt to Benjamin Banneker: African
origins of false position solutions, in: Ronald Calinger (ed.), Vita Mathematica,
Historical Research and Integration with Teaching, MAA Notes (MAA = Mathematical
Association of America), 1996, Vol. 40, 279-289
Describes the use of the rule of false positions in ancient Egypt, in
the work of later Alexandrian mathematicians, like Diophantus (c. 250), and of Abu Kamil
(born 850), the influence on mathematicians in Europe and later on Benjamin Banneker
(1731-1806), one of the first African American who dedicated himself to mathematics (cf. #
#251 Robins, Gay: Proposition and style in Ancient Egyptian Art,
University of Texas Press, Austin, 1994, 279 pp.
"It has long been known that much Egyptian art executed in two
dimensions as painting or relief was conceived and carried out on a squared grid, which
helped to determine the proportions of the human figure. Although there have been several
previous studies of the Egyptian grid, these have been almost entirely limited to single
standing or seated male figures... In this book I have attempted to base my own ideas ...
primarily on observations carried out on the actual monuments. I have considered female
figures as well as male, other postures besides standing and sitting... I show that the
squared grid had an important influence on the composition of scenes as a whole and in
helping to determine the characteristic style of a particular period. I consider the
effects of the major change in the grid that occurred in the twenty-fifth dynasty and
persisted thereafter, and elaborate my discovery of the grid system adopted during the
Amarna period." (Preface, p. vii)
5.2 Publications on the History of Mathematics, Ethnomathematics and
#252 Ascher, Marcia: Malagasy Sikidy: A Case in
Ethnomathematics, in: Historia Mathematica, New York, 1997, Vol. 24, 376-395
"Sikidy is a system of divination that plays a significant
role in the lives of the people of Madagascar. Here we focus on the mathematical ideas
which it embodies. Formal algebraic algorithms are applied to initial random data, and
knowledge of the internal logic of the resulting array enables the diviner to check for
and detect errors. Sikidy and the mathematical ideas within it are placed in their
cultural and historical contexts".
#253 Doumbia, Salimata: Maths et Cultures: Pythagore en Afrique,
in: Bulletin Harmonisation des Programmes de mathématiques des pays francophones
d'Afrique et de l'Océan Indien, Abidjan, 1997, Vol. 3, 6-11
Gives examples of Pythagorical figurative numbers in West Africa and
presents some ideas of Paulus Gerdes' book "African Pythagoras" on African
crafts and the Pythagorean theorem (cf. # 108, 182).
#254 Eglash, Ron: Scaling hexagons in a Bassari initiation mask,
in: Mathematics Teacher, Reston VA, 1995, Vol. 88, No. 7, pp. 618, 620
Short note that analyses the presence of a scaling series of hexagons
in a mask from the Bassari (eastern Senegal) and compares it with the use of the number
six in other contexts (time reckoning, string tallies, divination).
#255 Eglash, Ron: Bamana Sand Divination - Recursion in
Ethnomathematics, in: American Anthropologist, Arlington VA, 1997, Vol. 99, No.
Reflecting on his fieldwork realized among Bamana (or Bambara)
diviners, the author compares their use of recursion, where the iterative function is
addition modulo 2, with Cantor's recursion (cantor set), and hypotheses that an African
concept of self-generated fecundity is the shared origin of both the Bamana divination and
transfinite set theory.
#256 Eglash, Ron; Christian Sina Diatta and Nfally Badiane: Fractal
structure in Jola material culture, in: Ekistics, Athens, 1994, Vol. 368,
Discusses self-similarity in altar, house, and village structures among
the Jola in the Lower Casamance region in southern Senegal.
#257 Eglash, Ron: The African heritage of Benjamin Banneker, in:
Social Studies of Science, London, 1997, Vol. 27, 307-315
"Benjamin Banneker (1731-1806) is well known for his accomplishments in
early American applied science, as well as for his seminal role in African-American
science history. Historical and linguistic evidence suggests that his grandfather was of
Wolof origin, and that his father was from the area between what is now Ghana and Nigeria.
This cultural heritage may have emerged in some of his mathematical thinking"
(p.307). (cf. # 32, 82)
#258 Eglash, Ron: Geometric algorithms in Mangbetu design, in: Mathematics
Teacher, Reston, 1998, Vol.91, No.5, 376-381
Analyzes an ivory hat pin from the Mangbetu (northeastern Zaire /
Congo) and the geometric algorithm involved in its production. The top of the pin is
composed of four scaled, similar heads (forming isosceles right triangles in photographic
#259 Gerdes, Paulus: On culture and mathematics teacher education,
in: Journal of Mathematics Teacher Education, Dordrecht, 1998, Vol. 1, No. 1, 33-53
Presents a short history of mathematics teacher education in Mozambique
since independence in 1975, highlighting the multicultural context and the role of the
history of mathematics and of ethnomathematics in teacher education.
#260 Huylebrouck, D.: The bone that began the space odyssey, in:
The Mathematical Intelligencer, New York, 1996, Vol. 18, No. 4, 56-60
Describes the Ishango bone (Congo / Zaire) as a Mesolithic mathematical
artifact, some interpretations of the notches, and uses. Shallit remarks in a letter to
the editor (Vol. 19, No. 3, p. 7) that papers by A.S.Brooks present a date of 20,000 years
ago (not 11,000 years ago as stated by Huylebrouck) for the bone (cf. #20, 99, 162)
#261 Middleton, John (Ed.): Encyclopedia of Africa South of the
Sahara, Charles Scribner's Sons, New York, 1997, 4 volumes
This encyclopedia contains two short articles by Paulus Gerdes:
Geometries, Vol. 2, 224-227;
Number systems, Vol. 3, 346-348.
#262 Wilson, Eva: The interlacing and geometrical art of the Kuba,
in: Eva Wilson, Ornament 8,000 years, Harry N. Abrams, New York / British Museum
Press, London, 1994, 195-196
Short article on (a)symmetries in Kuba art (cf. #2, 105, 182).
5.3 Other publications on the
History of Mathematics by African mathematicians
#263 Djebbar, Ahmed: La rédaction de L'istikmal
d'al-Mu'taman (XIe s.)
par Ibn Sartaq, un mathématicien des XIIIe-XIVe
siècles, Historia Mathematica, New York, 1997, Vol. 24, 185-192
The author presents a "14th-century manuscript which has not been
studied before. It contains a complete redaction of the Kitab al-Istikmal by the
Andalusian mathematician, al-Mu'taman ibn Hud (11th century), and informs us about the
missing pieces of al-Mu'taman's book and about the content of his initial project that had
never been completed".
#264 Hitchcock, Gavin: Teaching the Negatives, 1870-1970: A Medley
of Models, For the Learning of Mathematics, Vancouver, 1997, Vol. 17, No. 1,
Six snapshots of important representative moments in the teaching of
the negatives are represented in historical sequence as classroom scenes.
6.1 First International Congress on Ethnomathematics
The International Study Group on Ethnomathematics organizes from 2 to 5 September 1998
in Granada (Spain) the First International Congress on Ethnomathematics. For more
Maria Luisa Oliveras, Dpto. de Didáctica de la Matemática. Facultad de Ciencias de la
Educación, Universidad de Granada, 18071 Granada - Spain (Fax: 34-58-246359
/34-58-243949; E-mail: oliveras@platon. ugr.es)
6.2 Web sites that may interest the readers of the
* AMUCHMA website
Scott Williams (Buffalo, USA) has been so kind to set a webpage for
the English language edition of the AMUCHMA-Newsletter:
See also Williams' web page "Mathematicians of the African
* African Indigenous Knowledge Systems website
Gloria Emeagwali (New Brittain, USA) has created a website on
African Indigenous Knowledge Systems:
* ISGEm website
The official website of the International Study Group on
Ethnomathematics is maintained by Ron Eglash. It contains the ISGEm-Newsletter and several
useful links, including to 'African mathematics':
* Indigenous Knowledge and Development Monitor website
The Indigenous Knowledge and Development Monitor is now also
available directly from the web:
E-mail addresses of African centres:
Cameroon Indigenous Knowledge Organisation: firstname.lastname@example.org
Centre for Cosmovisions and Indigenous Knowledge: email@example.com
Kenya Resource Centre for Indigenous Knowledge: firstname.lastname@example.org,
South African Resource Centre for Indigenous Knowledge: email@example.com
* Benjamin Banneker Association website
The Benjamin Banneker Association [BBA] (cf. # 32, 82, 257),
founded in 1986, provides a forum for mathematics educators, mathematicians, and other
interested people to discuss the learning and teaching of mathematics for African-
American children. The BBA recently created its website, managed by its president Carol
7. ADDRESSES OF SCHOLARS, INSTITUTIONS AND PUBLISHERS MENTIONED IN THIS NEWSLETTER
Mustapha: E.N.S., Vieux Kouba, 16050 Kouba, Algeria
* Agwu, Nkechi: Department of
Mathematics, Borough of Manhattan Community College, City University of New York, 199
Chambers Street, New York, NY 10007, USA (E-mail: firstname.lastname@example.org)
* A'ssani, Djamal
: UniversitÈ de Bougie, Laboratoire LAMOS, 06000 Bougie, Algeria
* Badiane, Nfally: Enda Tiers Monde,
Relais pour le developpement Urbain Participe (RUP),BP. 3370, Dakar, Senegal (Tel.: (221)
822 09 42, Fax: (221) 823 51 57, E-mail : email@example.com)
Rachid : DÈpartement de mathÈmatiques, USTHB, Bab Ezzouar, Alger, Algeria
* Benjamin Banneker Association:
Post Office Box 2686, Durham, NC 27715, USA
* Diatta, Christian Sina: Institut Technologie Nucleaire Appliquée,
Université Cheikh Anta Diop, Dakar, Senegal (E-mail: firstname.lastname@example.org)
* Djebbar, Ahmed: Département de Mathématiques, Bâtiment 425,
Université de Paris-Sud, 91405 Orsay Cedex, France (Fax: 33-1-47015917; E-mail:
* Eglash, Ron: Comparative Studies, Ohio State University, Columbus OH
43210, USA (E-mail: email@example.com)
* Ekistics: Athens Technological Organization, 24 Strat. Syndesmou
Street, 106 73 Athens Greece
* Emeagwali, Gloria: History Department, Central Connecticut State
University, 1615 Stanley Street, New Britain, CT 06050, USA (E-mail: firstname.lastname@example.org)
* Frankenstein, Marilyn: CCPS, University of Massachusetts Boston, 100
Morrisey Boulevard, Boston Ma 02125-3393, USA (E-mail: email@example.com)
* Gardner, Milo: Sacramento, CA, USA (E-mail: firstname.lastname@example.org)
* Gerdes, Paulus: Universidade Pedagógica, C.P. 915, Maputo,
Mozambique (Fax: 258-1-422113; E-mail: email@example.com)
* Gilmer, Gloria: Math Tech, 9155 North 70 Street, Milwaukee, WI 53223,
USA (E-mail: firstname.lastname@example.org)
* Gnaedinger, Franz: Hafnerstrasse 60, CH-8005 Zürich, Switzerland
* Hitchcock, Gavin: Department of Mathematics, University of Zimbabwe,
P.O.Box MP 167, Zimbabwe (E-mail: email@example.com)
* Jama, Jama Musse: Via di Pretale 103F, 56100 Pisa, Italy (E-mail:
* Lumpkin, Beatrice: 7123 S. Crandon, Chicago, IL 60649, USA (E-mail: Bealumpkin@aol.com)
* Mechhed, Eddine
Djamel: UniversitÈ de Bougie, Laboratoire LAMOS, 06000 Bougie, Algeria
* Morelli, Mike: Department of
Mathematics, Statistics, and Computer Science, 237c Harvey Hall, University of
Wisconsin-Stout, Menomonie, WI 54751 (E-mail: morellim@UWSTOUT.EDU)
* Powell, Arthur B.: Academic Foundations Department, University
Heights, 175 University Avenue, Newark NJ 07102 (E-mail:
* Rouxel, Bernard:
UniversitÈ de Bretagne Occidentale, 29200 Brest, France
* SÈsiano, Jacques: Ecole Polytechnique de Lausanne, Lausanne,
* Shallit, Jeffrey: Department of
Computer Science, University of waterloo, Waterloo, Ontario N2L 3G1, Canada (E-mail:
* Sims, John: Mathematics Coordinator, Ringling School of Arts and
Design, 2700 North Tamiani Trail, Sarasota, Florida 34234-5895 (E-mail: firstname.lastname@example.org)
* Social Studies of Science: SAGE
Publications, 6 Bonhill Street, London EC2A 4PU, UK (editor: David Edge, E-mail:
* Williams, Scott: Department of Mathematics, South Campus, State
University of New York at Buffalo, Buffalo NY 14214, USA (E-mail: email@example.com;
Moktadir: E.N.S., Vieux Kouba, 16050 Kouba, Algeria
What are your suggestions for improving the AMUCHMA Newsletter?
What are your suggestions for other activities of AMUCHMA?
Send your suggestions, comments, information, questions and any other contributions to
the chairman or secretary of AMUCHMA.
Send articles, books and manuscripts for the AMUCHMA Documentation Centre to the
Chairman or Secretary.
9. DO YOU WANT TO RECEIVE THE NEXT AMUCHMA-NEWSLETTER?
The AMUCHMA Newsletter, published in Arabic, English and French, is available free of
charge upon request.
Send requests to the Chairman
Paulus Gerdes: Universidade Pedagógica, C.P. 915, Maputo, Mozambique (Fax:
258-1-422113; E-mail: firstname.lastname@example.org)
for the English version;
or to the Secretary
Ahmed Djebbar: Département de Mathématiques, Bâtiment 425, Université de Paris-Sud,
91405 Orsay Cedex, France (Fax: 33-1-47015917; E-mail: Ahmed.Djebbar@wanadoo.fr)
for the French and Arabic versions.
Readers who would like to receive the AMUCHMA Journal in Portuguese should
contact the chairman, C.P. 915, Maputo, Mozambique.
The English version of AMUCHMA 20 is reproduced and distributed
with financial support from SIDA-SAREC (Sweden)
© The Authors 1999