From the earliest times onwards humans in Africa have created and developed mathematical ideas. For an annotated bibliography of mathematics in African history and cultures, see Gerdes and Djebbar (2004, 2007).
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References
Djebbar, Ahmed (2001), Une histoire de la science arabe. Editions du Seuil, Paris. Djebbar, Ahmed (2003), A Panorama of Research on the History of Mathematics in al-Andalus and the Maghreb between the Ninth and the Sixteenth Century, in: Jan P. Hogendijk & A. Sabra (Eds.), The Enterprise of Science in Islam, New perspectives, MIT Press, Cambridge MA, 309-350.
Djebbar, Ahmed (2005), L’algèbre arabe: Naissance d’un art, Vuibert, Paris.
Eglash, Ron (1999), African Fractals. Modern Computing and Indigenous Design, Rutgers University Press, New Brunswick NJ.
Fauvel, John & Gerdes, Paulus (1990), African Slave and Calculating Prodigy: Bicentenary of the Death of Thomas Fuller, Historia Mathematica, New York, Vol. 17, 141-151.
Favilli, Franco, Maffei, Laura & Venturi, Irene (2002): SONA Drawings: From the Sand to the Silicon, in: Sebastiani Ferreira E. (Ed.), Proceedings of the II International Congress on Ethnomathematics, Summary Booklet, Ouro Preto, p. 35.
Gerdes, Paulus & Bulafo, Gildo (1994), Sipatsi: Technology, Art and Geometry in Inhambane, Universidade Pedagógica, Maputo, 112 pp.
Gerdes, Paulus & Djebbar, A. (2004), Mathematics in African History and Cultures. An Annotated Bibiography, African Mathematical Union, Cape Town. New edition: Lulu.com, 2007, 340 pp. [ISBN 978-1-4303-1537-7].
Gerdes, Paulus & Djebbar, A. (2007), Les mathématiques dans l’histoire et les cultures africaines. Une bibliographie annotée, Université de Lille, 332 pp.
Gerdes, Paulus (1990), On ethnomathematical research and symmetry, Symmetry: Culture and Science, Budapest, 1(2), 154-170.
Gerdes, Paulus (1995), Une tradition géométrique en Afrique - Les dessins sur le sable, L’Harmattan, Paris (3 volumes) [ISBN 2-7384-3552-8, 2-7384-3553-6, 2-7384-3654-4].
Gerdes, Paulus (1996), Lunda Geometry — Designs, Polyominoes, Patterns, Symmetries, Universidade Pedagógica, Maputo, New expanded edition, 2007, lulu.com, Morrisville NC, 152 pp.
Gerdes, Paulus (1997a), Ethnomathematik dargestellt am Beispiel der Sona Geometrie, Spektrum Verlag, Berlin/Heidelberg/Oxford, 1997, 436 pp. [ISBN 3-82740201-8].
Gerdes, Paulus (1997b), Recréations géométriques d’Afrique - Lusona - Geometrical recreations of Africa, L’Harmattan, Paris, 127 pp. [ISBN 2-7384-5168-3].
Gerdes, Paulus (1998), Women, Art and Geometry in Southern Africa, Africa World Press, Trenton NJ, 200 pp. [ISBN 0-86543-601-0 (hardback), ISBN 0-86543-602-9 (paperback)].
Gerdes, Paulus (1999a), Geometry from Africa: Mathematical and Educational Explorations, The Mathematical Association of America, Washington DC, 210 pp. [ISBN 0-88385-715-4].
Gerdes, Paulus (1999b) On Lunda-designs and some of their symmetries, Visual Mathematics, Belgrade, 1(1).∗ 2
Gerdes, Paulus (1999c), On the geometry of Celtic knots and their Lunda-designs, Mathematics in School, Leicester, 28(3), 29-33.
Gerdes, Paulus (2000a), Le cercle et le carré: Créativité géométrique, artistique, et symbolique de vannières et vanniers d’Afrique, d’Amérique, d’Asie et d’Océanie [The circle and the square: Geometric, artistic and symbolic creativity of basket weavers from Africa, America, Asia and Oceania], L’Harmattan, Paris, 301 pp. [ISBN 2-7384-9235-5].
Gerdes, Paulus (2000b), On Lunda-designs and the construction of associated magic squares of order 4p, The College Mathematics Journal, Washington DC, 31(3), 182-188.
Gerdes, Paulus (2002a), Symmetrical explorations inspired by the study of African cultural activities, in: István Hargittai & Torvand Laurent (Eds.), Symmetry 2000, Portland Press, London, 75-89.
Gerdes, Paulus (2002b), From Liki-designs to cycle matrices: The discovery of attractive new symmetries, Visual Mathematics, 4(1).*
Gerdes, Paulus (2002c), New designs from Africa, Plus Magazine, 19 (http://plus.maths.org/issue19/features/liki/index.html)
Gerdes, Paulus (2002d), m-Canonic mirror curves, Visual Mathematics, 4(1).*
Gerdes, Paulus (2002e), Helix matrices, Visual Mathematics, 4(2).*
Gerdes, Paulus (2002f ), Cylinder matrices, Visual Mathematics, 4(2).*
Gerdes, Paulus (2002g), A note on chessboard matrices, Visual Mathematics, 4(3).*
Gerdes, Paulus (2002h), Variazioni sui disegni Lunda, in: Michele Emmer (Ed.), Matematica e Cultura 2002, Springer, Milan, 135-146.
Gerdes, Paulus (2003a), Awakening of Geometrical Thought in Early Culture, MEP Press, Minneapolis MN, 184 pp. [ISBN 0-930656-75-X].
Gerdes, Paulus (2003b), Sipatsi: Cestaria e Geometria na Cultura Tonga de Inhambane [Sipatsi: Basketry and Geometry in the Tonga culture of Inhambane], Moçambique Editora, Maputo, 176 pp. [ISBN 902-47-9908-2].
Gerdes, Paulus (2004), Basketry, Geometry, and Symmetry in Africa and the Americas, E-book, Visual Mathematics, Belgrade, 2004 [on-line available at: www.mi.sanu.ac.yu/vismath/]
2 The papers marked by* are available at: http://members.tripod.com/vismath/pap.htm or http://www.mi.sanu.ac.yu/vismath/pap.htm.
Gerdes, Paulus (2005), Lunda Symmetry where Geometry meets Art, in: Michele Emmer (Ed.), The Visual Mind II, MIT Press, Boston, 335-348.
Gerdes, Paulus (2006a), Sona geometry from Angola: Mathematics of an African tradition, Polimetrica, Monza, 232 pp. [ISBN 978-88-7699-055-7].
Gerdes, Paulus (2006b), Symmetries of alternating cycle matrices, Visual Mathematics, 8(2).*
Gerdes, Paulus (2006c), On the representation and multiplication of basic alternating cycle matrices, Visual Mathematics, 8(2).*
Gerdes, Paulus (2007a), African Doctorates in Mathematics: A Catalogue, Lulu.com, London, etc., 384 pp. [ISBN 978-1-4303-1867-5].
Gerdes, Paulus (2007b), Adventures in the World of Matrices, Nova Science Publishers, New York (in press).
Gerdes, Paulus (2007c), Drawings from Angola: Living Mathematics, Lulu.com, Morrisville NC, 72 pp. [ISBN 978-1-4303-2313-6].
Jablan, Slavik (1995), Mirror generated curves, Symmetry: Culture and Science, Budapest, 6(2), 275-278.
Jablan, Slavik (2001), Mirror curves, in: Sarhangi, R. & Jablan, S. (Eds.), Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Southwestern College, Winfield [reproduced in: Visual Mathematics, 3(2)* ].
Jaritz, Wolfgang (1983), Über Bahnen auf Billardtischen - oder: Eine mathema-tische Untersuchung von Ideogrammen Angolanischer Herkunft, Berichte der mathematisch-statistischen Sektion im Forschungszentrum Graz, Graz, 207, 1-22.
Njock, Georges Edward (1985), Mathématiques et environnement socio-culturel en Afrique noire, Presence Africaine, Paris, No. 135, 3-21.
Obenga, Théophile (1985), La géométrie égyptienne. Contribution de l’Afrique antique à la Mathématique mondiale, L’Harmattan, Paris.
Peterson, Ivars (2001), Sand Drawings and Mirror Curves, Science News, Washington DC (available at: http://www.sciencenews.org/20010922/mathtrek.asp).
Rossing, Nils & Kirfel, Christoph (2003), Matematisk beskrivelse av taumatter [Mathematical description of rope mats], NTNU, Trondheim.
Schlatter, Mark (2000), Mirror Curves and Permutations (available at: http://personal.centenary.edu/∼mschlat/sonaarticle.pdf ).
Schlatter, Mark (2001), Sona sand drawings and permutation groups, in: R. Sarhangi & S. Jablan (Eds.), Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, Southwestern College, Winfield (USA) [reproduced in: Visual Mathematics, 3(2)* ].
Schlatter, Mark (2004), Permutations in the sand, Mathematics Magazine, 77(2), 140-145.
Schlatter, Mark (2005), How to create monolinear mirror curves, Visual Mathematics, 7(2).*
Sica, Giandomenico, ed. What mathematics from Africa? Monza: Polimetrica, 2005. Vitturi, Mattia de Michieli & Favilli,
Franco (2006), Sona drawings, mirror curves and pattern designs, Proceedings of the 3 rd International Congress on Ethnomathematics (in press).
Zaslavsky, Claudia (1999), Africa Counts: Number and Pattern in African Cultures, Lawrence Hill, Westport [First edition 1973].
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Gerdes, P. (2008). From the African sona Tradition to New Types of Designs and Matrices. In: Konaté, D. (eds) Mathematical Modeling, Simulation, Visualization and e-Learning. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74339-2_20
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