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Geometry from Africa: Mathematical and Educational Explorations

Geometry from Africa: Mathematical and Educational Explorations

By Paulus Gerdes

Print ISBN: 978-0-88385-715-1
224 pp., Paperbound, 1999
List Price: $49.00
Member Price: $36.75
Series: Classroom Resource Materials

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The peoples of Africa south of the Sahara constitute a vibrant cultural mosaic, extremely rich in its diversity. Among these peoples interest in creating and exploring forms and shapes has blossomed in diverse cultural and social contexts with such an intensity that with reason it may be said that “Africa Geometrizes.” Gerdes presents examples of geometrical ideas in the work of wood and ivory carvers, potters, painters, weavers, and mat and basket makers. He analyzes geometrical ideas inherent in various crafts and explores possibilities for their educational use. Using as examples African ornaments and artifacts from Senegal to Madagascar, he shows how students may be led to discover the Pythagorean Theorem and to find proofs of it. He also explores connections to Pappus’ Theorem, similar right triangles, and Latin and magic squares as well as the geometrical ideas inherent in mat and basket weaving, house building, and wall decoration.

The author presents the geometry of a sand drawing tradition—called sona in the Chokwe language (predominately northeast Angola). Through the knowledge of sona, passed from generation to generation via beautiful, often symmetric, designs made in the sand, Gerdes uncovers mathematical ideas and presents examples of how they may be used in teaching mathematics. He underscores the mathematical potential of the sand drawing tradition by developing the geometry of a new type of design/pattern, which he calls Lunda-designs.

Table of Contents

Preface: Geometrical and educational explorations inspired by African cultural activities
1. On geometrical ideas in Africa south of the Sahara
2. From African designs to discovering the Pythagorean Theorem
From woven buttons to the Theorem of Pythagoras
From decorative designs with fourfold symmetry to Pythagoras
From a widespread decorative motif to the discovery of Pythagoras’ and Pappus’ theorems and an infinity of proofs
From mat weaving patterns to Pythagoras, and Latin and magic squares
3. Geometrical ideas in crafts and possibilities for their educational exploration
Wall decoration and symmetries
Rolling up mats
Exploring rectangle constructions used in traditional house building
A woven knot as a starting point
Exploring a woven pyramid
Exploring square mats and circular basket bowls
Exploring hexagonal weaving: Part 1
Exploring hexagonal weaving: Part 2
Exploring finite geometrical designs on plaited mats
Decorative plaited strips
From diagonally woven baskets and bells to a twisted decahedron
4. The ‘sona’ sand drawing tradition and possibilities for its educational use
Introduction: The Chokwe and their sand drawing tradition
Some geometrical aspects of the sona sand drawing tradition
Examples of mathematical-educational explorations of sona
Excursion: Generation of Lunda-designs

About the Author

Paulus Gerdes received his doctorates in mathematics, the history of mathematics, and mathematics education from the Universities of Dresden and Wuppertal (Germany). He has been a professor of mathematics at the Eduardo Mondlane University, and the Universidade Pedagógica in Mozambique for many years, serving as president from 1989-1996. He was a visiting professor at the University of Georgia from 1996 to 1998. He has served the African Mathematical Union as chair of the Commission on the History of Mathematics in Africa since 1986, and was the secretary of the Southern African Mathematical Sciences Association 1991-1995. Among his books published in English are: Women, Art and Geometry in Southern Africa; Lusona: Geometrical Recreations of Africa; Lunda Geometry—Designs, Polynominoes, Patterns, Symmetries; Ethnomathematics and Education in Africa; African Pythatgoras: A Study in Culture and Mathematics Education; and Culture and The Awakening of Geometrical Thinking (with a preface by Dirk Struik).