Geometry from Africa

Mathematical and Educational Explorations

by Paulus Gerdes

Published 1999 by The Mathematical Association of America; Washington DC, 1999, xii + 210 pp. [Foreword by Arthur B. Powell] ISBN 0-88385-715-4

In this "beautifully illustrated" book, "our Mozambican colleague, Paulus Gerdes, elaborates and presents us a rare mathematical gift. Through him, we learn of the diversity, richness, and pleasure of mathematical ideas found in Sub-Saharan Africa. From a careful reading and working through this delightful book, one will find a fresh approach to mathematical inquiry as well as encounter a subtle challenge to Eurocenctric discurses concerning the when, where, who, and why of mathematics" [Prof. Arthur B. Powell, Rutgers University, Newark NJ]

The book presents geometrical ideas from Africa south of the Sahara, with suggestions on how they can be explored both mathematically and in mathematics education (secondary school, teacher education, university).

The book is organised in the following parts:
Preface: Geometrical and educational explorations inspired by African cultural activities);
Part 1: On geometrical ideas in Africa south of the Sahara [overview, pp.2-53];
Part 2: From African designs to discovering the Pythagorean Theorem [pp.54-87];
Part 3: Geometrical ideas in crafts and possibilities for their educational exploration [Explores ideas from house building, wall decoration, mat and basket weaving, pp.88-155];
Part 4: The 'sona' sand drawing tradition and possibilities for its educational use [pp.156-204].

above: Textiles woven by the Tellem people in an area that is now in the Republic of Mali, for example, feature intricate combinations of white and indigo cotton threads to produce symmetric strip and planar patterns of various types.

right: The following sand drawing illustrates a fable: Sambálu, the rabbit (positioned a point B), discovers a salt mine (point A). Immediately, the lion (point C), the jaguar (point D), and the hyena (point E) demand possession, asserting the rights of the strong. The rabbit, affirming the inviolable rights of the weak, then quickly makes a fence to isolate the mine from all usurpers.
Note that only from B can one go to point A, without going beyond the line that represents the fence.

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