Instituto Superior Pedagógico, Maputo, Mozambique, 07.9.1992
Chairman: Paulus Gerdes (Mozambique)
Secretary: Ahmed Djebbar (Algeria)
Members: Hilda Lea (Botswana), George Njock (Cameroon), Salimata Doumbia (Côte d'Ivoire), Maassouma Kazim (Egypt), John Mutio (Kenya), Mohamed Aballagh (Morocco), Peter Lassa (Nigeria), Abdoulaye Kane (Senegal), Geoffrey Mmari (Tanzania), Mohamed Souissi (Tunisia), Venie Timkumanya (Uganda)
TABLE OF CONTENTS NEWSLETTER #8
Note of the Chairman
5. Have you read? (#86-#105)
The Secretary of the A.M.U. Commission on the History of Mathematics in Africa (AMUCHMA), Prof. Ahmed Djebbar, has been appointed on 19.7.1992 Minister of National Education of the Democratic and Popular Republic of Algeria. On behalf of AMUCHMA, I would like to congratulate Prof. Djebbar and wish him success in his new and very responsible position.
2.1 Third Pan-African Congress of Mathematicians
The 3rd Pan-African Congress of Mathematicians was held at the Kenyatta Conference Centre, Nairobi (Kenya), August 20-28, 1991. The following were contributed papers concerning the history of mathematics in Africa:
* Gerdes, P.: On the History of Mathematics in Subsaharan Africa, an overview of recent research;
* Ismael, A.: On the origin of the concepts of 'even' and 'odd' in Macua culture (Northern Mozambique);
* Doumbia, S.: African games and mathematics.
The General Assembly of the African Mathematical Union honoured during the Congress the following three mathematicians who have pioneered the development of mathematics in their countries and their subregion: Attia Ashour (Egypt), Chike Obi (Nigeria) and Paul Mugambi (Uganda). In his address to the Congress, Mugambi described the historical development of mathematics in Uganda.
2.2 Lectures on the History of Arabic Mathematics at the University of Khartoum (Sudan)
The University of Khartoum invited Ahmed Djebbar to give a series of
lectures on the History of Mathematics. The following papers were presented:
2.3 Papers presented at recent meetings
* At the 14th International Conference on the Psychology of Mathematics
Education [PME] (Mexico City, Mexico, July 1990) Hilda Lea presented a paper
entitled 'Spatial concepts in the Kalahari'.
* Gizachew Atnaf (Dresden, Germany) started research for a Ph.D. dissertation
on the cultural history of mathematics in Ethiopia.
This section is reserved for questions to which readers would like to have answers; 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 the question. All readers may send both questions and answers. Each will be published with the name of the sender.
4.1 Fractal geometry and traditional African architecture
Ron Eglash and Peter Broadwell (University of California, USA) concluded a research report on Fractal Geometry in Traditional African Architecture (The Dynamics Newsletter, Santa Cruz Ca., July 1989, 3-8) and would like to know of other researchers who would be interested in studies concerning fractal architectural designs in Africa.
4.2 Numerical representations in San (Bushmen) rock art
Annemarie Martinson (University of the Witwatersrand, SA) started a research project of looking for numerical representations in San (Bushmen) rock art. She writes:
At the South African Art Research Association Conference (August 1991, Drakensberg) she presented a paper entitled 'The role of rock art in mathematics education'.
#86 Actes du Premier Colloque International d'Alger sur l'Histoire des Mathématiques Arabes, La Maison des Livres (12 rue Ali Boumendjel), Alger (Algeria), 1988.
Proceedings of the first International Colloquium on the History of Arabic
Mathematics, held in Alger, Algeria (1986) [cf. AMUCHMA
1: 2.2]. It includes the following contributions:
#87 Actes du Deuxième Colloque Maghrebin sur l'Histoire des Mathématiques Arabes, Maghreb-Éditions (5 rue Borj Bourguiba), Tunis, 1991, 206 p.
Proceedings of the second Maghrebian Colloquium on the History of Arabic
Mathematics, held in Tunis, Tunesia (1988) [cf. AMUCHMA
4: 2.1]. It includes the following contributions:
#88 Benoit, P.; Chemla, K. & Ritter, J. (ed.): Histoire de fractions, fractions d'histoire, Birkhäuser Verlag, Basel (Switserland), 1992, 436 p.
Proceedings of the international colloquium on the History of Fractions held in Paris, France (1987) [cf. AMUCHMA1: 2.3]. The following chapters concern the history of mathematics in Africa:
* J.Ritter: Metrology and the prehistory of fractions (pp.19-35);
#89 Bronshtehn, V.A.: Claudius Ptolemy. Second Century A.D.(in Russian), Nauka, Leningrad, 1988, 24p.
Edited with a preface and an afterword by A.Gurshtein. An overview which, besides the contributions of Ptolemy to astronomy, includes discussions of his work in optics, music, geography, and astrology.
#90 Christianidis, Jean: 'Aristhmetikè Stoicheíosis': Un traité perdu de Diophante d'Alexandrie?, in: Historia Mathematica, New York (USA), Vol.18. No.3, 1991, 239-246
"The author suggests a conjecture about the existence of a lost theoretical treatise of Diophantus, entitled Teaching of the Elements of Arithmetic His claims are based on a scholium of an anonymous Byzantine commentator".
#91 Doumbia, Salimata (ed.): Mathématiques dans l'environne-ment socio-culturel Africain, Vol. 1: Jeux, Institut de Recherches Mathé-matiques, Abidjan (Côte d'Ivoire), 1984, 240p.
Studies mathematical aspects of traditional games of Côte d'Ivoire:
#92 Dundas, Charles: Chagga Time-Reckoning, in: Man, London (UK), Vol.87-88, 1926, 140-143
Describes pre-colonial time-reckoning among the Wachagga (Kilamanjaro-region, east Africa): the year is divided into twelve months; each month has thirty days and is divided into six periods of five days each. Describes also the belief in the influence of the day and the hour in which a person is born, on his character and life.
#93 El-Abbadi, Mostafa: The life and fate of the ancient Library of Alexandria, UNESCO, Paris, 1990, 250p. (published in English, French and Arabic)
Describes the background and the history of the Library of Alexandria: from its creation in the early third century B.C. to the destruction of the Royal Library in 48 B.C. and of the Daughter Library in 391. Particular attention is given to the type of scholarship cultivated at Alexandria. Eratosthenes of Cyrene, author of 'On the Measurement of the Earth', was the chief librarian from 245 to 204/1 B.C. Other mathematicians that are referred to, are Euclid (86), Heron (90), Claudius Ptolemy (141), Theon and Hypathia (159).
#94 Euclid of Alexandria: Les Élements (traduits du texte de Heiberg): Vol.1, Livres I-IV: Géométrie plane, Presses Universitaires de France, Paris, 1990, 531p.
General introduction by Maurice Caveing. Translation and commentary by Bernard Vitrac of Euclid's Elements based on the text by Heiberg.
#95 Gerdes, Paulus: Ethnogeometrie. Kulturanthropologische Beiträge zur Genese und Didaktik der Geometrie (Ethnogeometry. Cultural-anthropological contributions on the genesis and the didactics of geometry), Franzbecker Verlag, Bad Salzdethfurth (Germany), 1991, 360p.
After a critical analysis of the phenomenon of curriculum export from the North to the South, the author stresses the need to incorporate mathematics education into the cultural/scientific contexts of Africa. The book is intended to contribute towards this aim by studying the (historical) relationships between (the development of) geometrical knowledge and socially important activities as mat and basket weaving, pot making and house building. In the second part of the book hypotheses on the early development of geometrical thinking are formulated. The last part presents examples of didactical experimentation with the aforementioned incorporation. Peter Damerow (Max Planck Institute for Educational Research, Berlin, Germany) wrote the preface, entitled 'Ethnomathematics and Curriculumexport'.
#96 Gerdes, Paulus: On Mathematical Elements in the Tchokwe "Sona" Tradition, in: For the Learning of Mathematics, Montreal (Canada), Vol.10, No.1, 1990, 31-34
#97 Gerdes, Paulus: On mathematical elements in the Tchokwe drawing tradition, in: Discovery and Innovation, Journal of the African Academy of Sciences, Nairobi (Kenya), Vol.3, No.1, 1991, 29-36
#98 Gerdes, Paulus: On Mathematical Elements in the Tchokwe 'Sona' tradition, in: Afrika Mathematika, Journal of the African Mathematical Union, Ibadan (Nigeria), Series 2, Vol.3, 1991, 119-130
These three related papers present a summary of the author's research findings on the mathematics in the sanddrawing ('sona') tradition of the Tchokwe people (Angola): symmetries and monolinearity, classes and geometrical algorithms, rules for the construction of monolinear 'sona'; and discuss the educational and mathematical potential of this tradition. The examples given in the papers vary.
The author states in chapter 1 that the "standard treatment of the history of non-European mathematics exhibits a deep-rooted historiographical bias in the selection and interpretation of facts, and that mathematical activity outside Europe has as a consequence been ignored, devalued or distorted" (p.3). In the subsequent chapters he contributes to an alternative perspective. With respect to Africa, it is noted that "Much research needs to be done..." (p.22). Information is given on the Ishango bone (23-27), on Egyptian mathematics (57-90, 125-129), on the Zulu counting system (43-44) and on Yoruba arithmetic (44-46).
#100 Klein, Herbert Arthur: The science of measurement, a historical survey, Dover, new York (USA), 1988, 736p.
Contains little information on measurement in Africa: Egyptian length measures ('cubit' and 'foot', 59-61); Egyptian weigth 'ratl' (86); 'Cape foot' from South Africa (63).
#101 Lea, Hilda: Informal Mathematics in Botswana: Mathematics in the Central Kalahari, Faculty of Education, University of Botswana, 1990, 9 p.
"A good example of what mathematical ideas were used before recorded history, can be seen today in the daily activities of Bushman society. They carry out mathematical activities suitable for their traditional way of life, and their highly developed spatial abilities are very necessary for survival in their harsh environment" [p.1]. The paper describes counting (one, two, two-one, two-two, two-two-one etc.), measurement, time reckoning, classification, tracking and mathematical ideas in technology and craft. "Bushmen have the oldest pattern of life found in the world today... A hunting and gathering community does not have need of counting precise measurement though requires basic skills for survival, and very special skills to interpret the environment. They need very good visual discrimination and visual memory" [p.7].
#102 Lea, Hilda: Informal Mathematics in Botswana: Spatial concepts in the Kalahari, Faculty of Education, University of Botswana, 1990, 9 p.
"Hunters and herdsmen in the Kalahari, who have never been to school and who have lived in very remote areas all their lives, were interviewed on two occasions to ascertain how far their spatial concepts have developed. When asked how they recognised animal footprints, and how they found their way in the desert, they were seen to have a very good visual memory, and to be aware of the minutest detail in recognising shapes. When given a visual thinking test, they performed with a high degree of skill on items related to their environment".
#103 Mann, Adolphus: Notes on the Numeral System of the Yoruba Nation, in: Journal of the Anthropological Institute of Great Britain and Ireland, London (UK), Vol.16, 1886, 59-64
Explains how the addition, multiplication and subtraction principles are used to form the Yoruba (Nigeria) numerals: 15 = 5 less 20, 40 = 20 x 2, 170 = (20 x 9) - 10, 185 = (200 - 10) - 5, 5000 = 200 x 25, etc. The author suggests the origin of this system is found in "the way in which large sums of money (cowries) are counted".
#104 Pater, C.de: Was Augustine Mathematics-Hostile?, in: Nieuw Archief voor Wiskunde, Amsterdam (Netherlands), Vol.8, No.1, 1990, 43-45
Criticizes an article by H.Beckers  in the same journal, in which it is asserted that Augustine (354-430), bishop of Hippo (North Africa), warned that "good christians should beware of mathematicians, because the danger exists that they have made a pact with the devil". On the contrary says the author Augustine warned against astrologers: the Latin mathematicus also means astrologer. Augustine considered geometry and arithmetic as useful disciplines.
#105 Washburn, Dorothy: Style, classification and ethnicity: design categories on Bakuba raffia cloth, American Philosophical Society, Philadelphia (Box 40098, Philadelphia, PA 19106, USA), 1990
"The study shows that while two kinds of features are used for category definition (object-specific features and basic perceptual properties) the style of a culture is primarily defined by the way the basic properties are specifically manipulated. This thesis is illustrated by a study of named pattern categories on Bakuba raffia cloth. One of the basic perceptual properties is symmetry. Chapter 5 details how a symmetry analysis of the raffia patterns can differentiate patterns produced by the different Bakuba groups".
Prof.Evert Bruins of the University of Amsterdam, Netherlands (see AMUCHMA 1: 2.3; 4: 2.1; 7: 5) died 20.11.1990 (born 4.1.1909). E.Knobloch (Technical University Berlin, Germany) wrote an 'In memoriam' (Historia Mathematica, New York, Vol.18, 381-389, 1991) with a bibliography of scientific books and articles compiled by J.Hogendijk. The bibliography includes the following publications refering to the history of mathematics in Africa:
1945 On the approximation of f(;4) in Egyptian geometry (in Dutch), in:
Indagationes Mathematica, Vol.7, 11-15
7.1 Study Group on the History of Mathematics at Béjaia during the Middle Ages
A Study Group on the History of Mathematics at Béjaia during the
Middle Ages (GEHIMAB) has been created (December 1991) in Béjaia
(Algeria). The Study Group published a first brochure, that treats the following
7.2 Information Bulletin of the Ibn al-Haytham Seminar on the History of Arabic Mathematics
The Department of Mathematics of the 'École Normale Supérieure'
(ENS) at Kouba (Algeria) published in December 1991 the first number of
its information bulletin called 'Cahier du Séminaire Ibn al-Haytham
sur l'Histoire des Mathématiques Arabes': 36 p. with articles mostly
in Arabic. The bulletin is directed foremost to students and former students
of the ENS at Kouba, who take part in the Ibn al-Haytham Seminar, that started
in 1986 (cf. AMUCHMA 1:5), but it is hoped
that the Bulletin may be useful to all in Algeria and elsewhere interested
in the history of Arabic mathematics. The number includes information on
Ahmed Djebbar is responsible for the 'Cahier' and Youcef Guergour and Touhami Zemouli form the secretariat . Adress: ENS de Kouba, Département de Mathématiques, B.P.92, 16050 Vieux Kouba, Alger, Algeria, tel. 581135; telex: 62567).
* Aissani, D.: LAMOS, Centre Universitaire de Béjaia, 06000, Algeria
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The Department of Mathematics,
State University of New York at Buffalo