Have You Read ?

Notes and Queries



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7. Have You Read ?

Readers are encouraged to submit contributions to 'Have you read?'.

N.B. Supply complete bibliographic information: names of author(s), complete titles of books or of both the article and journal; for journals include both the volume and date; for books, edition, copyright date, publisher, place and country of publication.

#1. Almeida, António de: Sobre a matemática dos Indígenas da Guine Portuguesa, in: Boletim Cultural da Guine Portuguesa, Lisbon (Portugal), Vol.6, 1947, 389-440.

Deals with numerals, arithmetic operations, measurement, monitary system and time reckoning in Guine Bissau.

#2. Crowe, Donald: The geometry of African art I. Bakuba art, in: Journal of Geometry, München (Western Germany), Vol.1, 1971, 169-182; The geometry of African art II. A catalog of Benin patterns, in: Historia Mathematica, New York (USA), Vol.2, 1975, 253-271;

The geometry of African art III.The smoking pipes of Begho, in: C. Davis, B. Grünbaum, F.Sherk (ed.), The geometric vein, the Coxeter Festschrift, Springer Verlag, New York, 1982, 177-189;

Symmetry in African art, in: Ba Shiru, Journal of African Languages and Literature, Vol.11, no. 1, 1982, 57-71.

These papers investigate the repeated patterns found in African art, classifying them on the basis of the 24 plane crystallographic groups. Of these, seven admit translations in only one direction (the corresponding patterns are called strip patterns), while the remaining 17 admit two independent translations (so-called plane patterns).

#3. Djebbar, A.: Enseignement et recherche mathématiques dans le Maghreb des XIIIe-XIVe siecles (étude partielle), Publications Mathématiques d'Orsay, Vol.81-02, Paris (France), 1981, 146 pp.

Partial study on mathematical education and research in the Maghreb countries during the 13th and 14th centuries. Contains chapters on algebra (classification of equations, solution of quadratic equations), symbolism and algebra (symbolism in the 14th century, examples of the use of symbols) and on number theory and combinatorics (combinatorics before the 13th century, combinatorics in the Maghreb and examples of combinatoric problems).

#4. Djebbar, A: L'analyse combinatoire au Maghreb: l'exemple d'Ibn Mun'im (XIIe-XIIIe s.), Publications Mathématiques d'Orsay, Vol.85-01, Paris (France), 1985, 124p.

Contains a commentary and a translation of section XI of 'Fiqh al-Hisab', a manual written by Ibn Mun'im (Maghreb) between 1207 and 1212. On the basis of some linguistic problems (number of Arabic words of given length etc.), Ibn Mun'im develops his combinatorics. He presents an arithmetic triangle (the so-called Pascal's triangle) and deduces the equivalents of formulas like
(we canot represent these for the web).
centuries before Cardano, Tartaglia, Mersenne, Frenicle, etc., in Europe.

#5. Gerdes, Paulus: Three alternate methods of obtaining the ancient Egyptian formula for the area of a circle, in: Historia Mathematica, New York (USA), Vol.12, 261-268.

New conjectures on the origin of the ancient Egyptian formula for the area of a circle are formulated on the basis of an examination of old African craft techniques, e.g. the transformation of an elongated rectangle in the form of a coiled rope into a circle.

#6. Gerdes, Paulus: How to recognize hidden geometrical thinking: a contribution to the development of anthropological mathematics, in: For the Learning of Mathematics, Montreal (Canada), Vol. 6, 1986, no. 2, 10-12, 17.

Deals with a method for recognizing geometrical thinking 'hidden' in the forms of traditional - African - objects, like baskets, pots, fish traps, houses.

#7. Giacardi, Livia and Tullio Viola: Il calcolo del volume del tronco di piramide nella matematica egizia (Discussione sulle ipotesi piu importanti gia proposte), in: Atti della Accademia delle Scienze di Torino, Torino (Italy), Vol.111, 1976-1977, 441-453.

Contains a brief analysis of the hypotheses of Gunn and Peet, Vogel, Neugebauer, Van der Waerden and Gillings on the origin of the ancient Egyptian formula for the volume of a truncated pyramid.

#8. Giacardi, Livia and Tuliio Viola: Saggio su un possibile calcolo dei volumi di alcuni poliedri nella matematica egizia, in: Atti della Accademia delle Scienze di Torino, Torino (Italy), Vol.111,1976-1977, 523-537.

Proposes a new deduction of the ancient Egyptian formula for the volume of a truncated pyramid, based on the successive determination of the volumes of particular pyramids and prisms.

#9. Lumpkin, Beatrice: Africa in the mainstream of mathematics history, in: I. van Sertima (ed.), Blacks in science; Transaction Books, New Brunswick NJ (USA) and London (UK), 1983, 100-109

"For thousands of years, Africa was in the mainstream of mathematics history. This history began with the first written numerals of ancient Egypt, a culture whose African origin has been reaffirmed by the most recent discoveries of archaeology. With a longer period of scientific work than any other area of the world, progress in mathematics continued on the African continent through three great periods, ancient Egyptian, Hellenistic and Muslim". "Although all peoples and continents have played a role in the history of mathematics, the contributions of Africa are still unacknowledged by western historians".

#10. Lumpkin, Beatrice: A young genius in old Egypt, Dusable Museum Press, Chicago (USA), 1979, 24 pp.

Booklet for children with information on ancient Egyptian number symbols and addition procedure.

#11. Mmari, Geoffrey: The United Republic of Tanzania: mathematics for social transformation, in: F. Swetz (ed.), Socialist Mathematics Education, Burgundy Press, Southampton PA (USA), 1978, 301-350.

Analyses the history of mathematics education in Tanzania before and after Independence.

#12. Njock, Georges E.: Mathématiques et environnement socio-culturel en Afrique Noire, in: Presence Africaine, New Bilingual Series no. 135, 3rd Quarterly, 1985, 3-21.

Stresses that it is very urgent to study the history of mathematics in Africa, as colonialism and neo-colonialism neglected the existence of mathematics in Black Africa. "Pure mathematics is the art of creating and imagining. In this sense black art is mathematics". The author gives a summary of the development of numeration systems, arithmetics and mathematical games in Africa.

#13. Robins, Gay and Charles C.D.Shute: Mathematical bases of ancient Egyptian architecture and graphic art, in: Historia Mathematica, New York (USA), Vol. 12, 1985, 107-122.

"Deals with the trigonometric basis of pyramid architecture and disposes of the erroneous notion that pyramidal dimensions intentionally incorporate irrational numbers".

#14. Santos, Eduardo dos: Sobre a matemática dos Ouiocos de Angola, in Garcia da Orta, Lisbon (Portugal), Vol 3 no. 2, 1960, 257-271.

Paper on the mathematics (numerals ,arithmetical operations, measures, coins, time reckoning and geometrical vocabulary) of the Tchokwe of North-East Angola.

#15. Shirley, Lawrence: History of mathematics in Nigerian mathematics classrooms: values and problems, in: Abacus, the Journal of the Mathematical Association of Nigeria, Ilorin (Nigeria), Vol. 12, 1986, 123-133.

Discusses the "problem of making the history of mathematics culturally relevant in the Nigerian setting when much of the recorded historical developments in mathematics have been Mediterranean, Arab and European".

#16. Souissi, Mohamed: Un texte d'Ibn al Banna sur les nombres parfaits, abondants, deficients et aimables, Hamdard National Foundation, Karachi (Pakistan), 1975, 14 pp.

Translation of a manuscript of Ibn al Banna' (1256-1321, Maghreb) on perfect, abundant, deficient and amicable (friendly) numbers.

#17. Souissi, Mohamed: Présentation et analyse du traité "Somme des principes et des conclusions"par le savant astronome Marocain al-Hasan al Marrakusi (était vivant en1281), in: Cahiers de Tunisie, Tunis, (Tunisia), Vol.XXX, 1982, 273-286.

Analyses the treatise "Summary of principles and conclusions" by the Morrocan astronomer al-Hasan al-Marrakusi (13th century). This treatise may be considered the culmination of astronomic literature written in Arab. It gives a summary of the results obtained by al-Hasan's predecessors and adds his own observations and solutions.

#18. Williamson, John: Dabida numerals, in: African Studies, Vol.2, 1943, 215-216.

"While searching for Dabida ways of using arithmetics, for the purpose of making the early studies of young children easier and more interesting, it was discovered that several sets of 'numerals' exist'.' These sets are described. The Dabida inhabit the Taita hills in Kenya.

#19. Williamson, Kay & A. O. Timitimi: A note on ho number symbolism, in: African Notes, (Nigeria), Vol. 5, no. 93, 1970, 9-16.

"Among the Kolokuma Ijo of the Niger Delta odd numbers in general, and three in particular, are associated with men; while even numbers in general, and four in particular, are associated with women. The number seven is associated with the great divinities of the clan, such as Kolokuma Egbesu, and is therefore normally avoided". The paper gives examples.

#20. Zaslavsky, Claudia: Africa counts; Number and Pattern in Africa Culture, Prindle, Weber & Schmidt Inc., Boston (USA), 1973, 328p.; a recent paperback edition: Lawrence Hill & Co.,520 Riverside Av., Westport, Connecticut (USA); Hungarian translation Africa Szaniol, Gondalet, Budapest (Hungary), 1984.

Already classical introduction to the mathematical heritage of Africa south of the Sahara. Includes chapters on 'Numbers-words, gestures, significance', 'Numbers in daily life', 'Mathematical recreations', 'Pattern and shape', and two regional studies on southwest Nigeria and East Africa. Bibliography with 191 references.

Review by R. Wilder in: Historia Mathematica, New York, Vol. 2, 1975, 207-210.

#2l. Zaslavsky, Claudia: Count on vour finger African style, Harper & Row, New York (USA), 1980.

Picture book for ages 6-9 on traditional finger counting in the marketplace in Kenya, Sierra Leone, and in South Africa.


8. Notes and Queries

This section is reserved for questions that 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 Editor. If you are answering a question, make a clear reference to the question. All readers may send both questions and answers. Each will be published with the name of the sender.

9. Announcements

Ahmed Djebbar (Algeria) will present at the 6th International Congress on Mathematical Education to be held in Budapest (Hungary), July 27-August 3, 1988, a paper entitled "The contents of mathematics education in North Africa during the Middle Ages and its role in education today" .




1. Aballagh, Mohamed: Maison du Maroc, ch.306, 1 Bd. Jourdan, 75014 Paris, France.

2. Bebbouchi, Rachid: Université d'Oran, Institut des Mathématiques, B.P. 1524, Es-senia, Algeria.

3. Bouamrane, Cheikh: Institut de Philosophie, Université d'Alger, Karoubi, Algeria.

4. Bruins, E . M.: Joh. Verhulstraat 185, 1075 GZ Amsterdam, Netherlands.

5. Caveing, Maurice: 13, Bd. Beaumarchais, 75004 Paris, France.

6. Crowe, Donald: Mathematics Department, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706, USA.

7. Enukoha, I.: Faculty of Education, University of Calabar, Calabar, Nigeria.

8. Giacardi, Livia: Dipartimento di Matematica, Universita di Torino, Via Principe Amadeo 8, 10123 Torino, Italy.

9. Guergour, Youcef: Département de Mathématiques, E.N.S., 16050 Vieux Kouba, Alger, Algeria.

10. Guillemot, Michel: 10 Impasse de la Pelude, 31400 Toulouse, France.

11. Hadfi, Hamida: Institut Supérieur de la Formation Continue, 43 Rue de la Liberté, le Bardo, Tunis, Tunisia.

12. Hogbe-Nlend, Henri: Département de Mathématiques et Informatique, Université de Bordeaux 1, 351 Cours de la Libertation, 33405 Talence Cedex, France.

13. Hogendijk, Jan: Mathematisch Instituut, Rijksuniversiteit Utrecht, Budapestlaan 6, 3508 TA, Utrecht, Netherlands.

14. Jaouiche, Khalil: 128 Rue de la Croix Nivert, 75015 Paris, France.

15. Kane, Abdoulaye E.: Département de Philosophie, Université de Dakar, Dakar-Fann, Senegal.

16. Kani, A.M.: Northern Nigeria History Research Scheme, Department of History, Ahmadu Bello University, Zaria, Nigeria.

17. Lumpkin, Beatrice: 7123 S.Crandon, Chicago IL 60649, USA.

18. Mmari, Geoffrey: Vice-Chancellor, Sokoine University of Agriculture, P.0.Box 3000, Horogoro, Tanzania.

19. Navez, Jacques: Département de Mathématiques, Université du Burundi, B.P. 2700, Bujumbura, Burundi.

20. Njock, Georges: Département de Mathématiques, B.P. 812, Université de Yaounde, Yaounde, Cameroun.

21. Ojoade, J.0.: Centre for Development Studies, University of Jos, Jos, Nigeria.

22. Rebstock, U.: Orientalisches Seminar, Universität Tübingen, Münzgasse 30, 7400 Tübingen 1, F.R. Germany.

23. Robins, Gay: Christ's College, Cambridge CB2 3BU, England UK.

24. Sadallah, Aboulkacim: Institut d'Histoire, Université d'Alger, Karoubie, Alger, Algeria.

25. Santos, Eduardo dos: Instituto de Investigação Científica Tropical, Rua da Junqueira 86, 1300 Lisbon, Portugal.

26. Seka, Beniel: Institute of Education, P.O.Box 35094, Dar es Salaam,Tanzania.

27. Sesiano, J.: 4 Avenue du Mail, 1205 Genève, Switzerland.

28. Shirley, Lawrence: Department of Education, Ahmadu Bello University, Zaria, Nigeria.

29. Souissi, Mohamed: 7 Rue de Teheran, 2000 Le Bardo, Tunis, Tunisia.

30. Taleb, K.: Universite d'Oran, Institut de Mathématiques, B.P. 1524, Es-Senia, Algeria.

31. Washburn, Dorothy: Department of Anthropology,University of Rochester, River Station, Rochester, New York 14627, USA.

32. Zaslavsky, Claudia: 45 Fairview Avenue, 13-1, New York, NY 10040,USA.

33. Zemouli, Touhami: Département de Mathématiques, ENS., 16050 Vieux Kouba, Alger, Algeria.


1. Centre de Recherches Juridiques et Historiques: 9 Rue Mahler, 75004 Paris, France.

2. African Mathematical Union (AMU)
President: Aderemi Kuku: Mathematics Department, University of Ibadan, Nigeria.
Secretary-General: Saliou Touré: Institut de Recherches Mathématiques, Université d'Abidjan 08 B.P. 2030 Abidjan 08, Ivory Coast (Côte d'Ivoire).

3. AMU Commission on the History of Mathematics in Africa (AMUCHMA~ Chairman: Paulus Gerdes: (Faculty of Mathematical Sciences, Eduardo Mondlane University), C.P. 915, Maputo, Mozambique.
Secretary: Ahmed Djebbar: Département de Mathématiques, Université Paris-Sud, 91405 Orsay Cedex, France.




This web page is the property of the African Mathematical Union. It was created and is maintained by

Dr. Scott W. Williams, Professor,
The Department of Mathematics,
State University of New York at Buffalo