Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas

Challenges readers to think creatively about mathematics and ponder its role in their own daily lives Cultural mathematics, or ethnomathematics as it is also known, studies the relationship between mathematics and culture—with the ultimate goal of contributing to an appreciation of the connection between the two. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas integrates both theoretical and applied aspects of the topic, promotes discussions on the development of mathematical concepts, and provides a comprehensive reference for teaching and learning about multicultural mathematical practices. This illuminating book provides a nontraditional, evidence–based approach to mathematics that promotes diversity and respect for cultural heritages. Part One covers such major concepts as cultural aspects of mathematics, numeration and number symbols, kinship relations, art and decoration, games, divination, and calendars. Part Two takes those concepts and applies them to fascinating case studies of both the Otomies of Central Mexico and the Incas of South America. Throughout the book, numerous illustrations, examples, and motivational questions promote an interactive understanding of the topic. Each chapter begins with questions that encourage a cooperative, inquiry–based approach to learning and concludes with a series of exercises that allow readers to test their understanding of the presented material. Introduction to Cultural Mathematics is an ideal book for courses on cultural mathematics, the history of mathematics, and cultural studies. The book is also a valuable resource and reference for anyone interested in the connections between mathematics, culture, anthropology, and history.

Preface ix Introduction xi PART I General Concepts 1 Understanding the Culture in Mathematics 3 2 Numeration S ystems 24 3 Number Gestures and N umber S ymbols 39 4 Kinship and S ocial R elations 57 5 Art and D ecoration 73 6 Divination 103 7 Games 123 8 Calendars 142 PART II Case S tudies 9 Hñähñu Math: T he O tomies 181 10 Tawantinsuyu Math: T he Incas 211 Hints to S elected E xercises 253 Bibliography 273 Index 281

THOMAS E. GILSDORF, PhD, is Professor in the Mathematics Department at the University of North Dakota. He has long been interested in topics such as anthropology and languages, and he has traveled to archaeological sites and cultural centers of numerous pre–Hispanic and indigenous cultures to study mathematics in a cultural context. Dr. Gilsdorf has published and presented research on cultural mathematics, as well as locally convex spaces.