To expand search, see Oceania. Laterally related topics: Indo-Malay Archipelago, The Philippines, New Zealand, The Malekula of Vanuatu, New Guinea, The Hawaiians, The Marshall Islands, Kiribati (The Gilbert Islands), The Caroline Islands, Australia, The New Hebrides, and Polynesia.
The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Ascher, Marcia. Graphs in cultures: a study in ethnomathematics. Historia Math. 15 (1988), no. 3, 201--227. (Reviewer: M. P. Closs.) SC: 01A10, MR: 90d:01002.
As the author observes, the philosopher Wittgenstein pointed to the problem of tracing graphs or figures as one that everyone can recognize as mathematical. Related problems have occurred in a variety of cultures. In western Europe, problems of tracing graphs or figures have occurred in Danish folk puzzles, where they were used as an alternative to dancing. Two patterns that are traced out are said to be similar to those on an artifact from Viking times, and are said to have mystical significance; and two others are said to be useful in witchcraft. Similar problems occur in other cultures as well. The article focuses on the context of the puzzles and the methods used to solve them in New Ireland and the Republic of Vanuatu, especially on the island of Malekula. A number of designs from Vanuatu have mythic significance. There is a tradition that one must complete a certain diagram to enter the Land of the Dead; failure results in being eaten. The methods used to draw the diagrams are also very interesting. In many cases, Ascher shows how individual drawing elements are transformed by processes such as reflection and rotation and are combined in systematic ways to draw the figure. Other types of mathematical ideas from Malekula include a drum signaling system with rhythms for each clan, rank, grade of pig, and special phrases, and a six-class marriage system which the elders explained with diagrams in the sand. Closely related topics: Continuous Tracing Problems, The Malekula of Vanuatu, Storytelling Traditions, The Philosophy of Mathematics, and Denmark Folk Tradition.Modify notes on this entry Modify bibliography entry Make comment on this entry
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