Marcia Ascher

Graphs in cultures: A study in ethnomathematics

Abstract Western culture is but one of several with an interest in continuous figure-tracing. This paper elaborates evidence of that interest in Oceania with emphasis on the dieas of the Malekula. Included are the figures, with cultural context, and with associated geometric and topological ideas. For many Malekula figures there is a record of actual order and direction of the tracing of each edge. This enables us to analyze their procedures and to show that basic procedures were transformed and combined into larger systematic procedures.

Recognizing the Emergence of Man Specific courses of action are necessary for identifying the traces of early man

Recognition of early human industries takes on significance with the realization that commitment to tools is the novel adaptive design accounting for the emergence of man. The most abundant evidence for the emergence of man consists of the stones that he refashioned. But recognizing these objects is a problem, as they are both rare and similar to the stones of the environments in which they occur. Because the validity of a procedural, or course-of-action, approach to the problem of recognition can be demonstrated, such an approach is preferable to the intuitive and heuristic approaches that have dominated attempts to deal with the possible traces of early man.

The Logical-Numerical System of Inca Quipus

Quipus, used by the Incas during the sixteenth century, were sophisticated devices for recording and transmitting codified information. They are a part of the global history of data handling and computation. This paper describes the logical-numerical system expressed through these multicolored spatial arrays of knotted cords. included are basic ideas about the logical structures of some quipu formats and the means of encoding quantitative and nonquantitative data. Several specific examples are given of quipus containing arithmetic and logical relationships.

Cycling in the Newton‐Raphson Algorithm

Summary To better understand the Newton‐Raphson algorithm more attention should be given to cases of non‐convergence, in particular to cases that lead to cycling iterates. The values of cycling iterates have been shown to be crucial to separating regions of convergence and divergence. This paper summarizes what has been written about cycling iterates and provides further examples of the Newton‐Raphson algorithm cycling when being used to solve for the zeroes of f(z). The examples include families of functions for which an initial value can be selected to initiate a cycle of any given length preceded by any given number of non‐cycling values and families of functions for which the cycle length is fixed and does not depend on the initial value. In each example, the regions of convergence and divergence are also delineated.

Ethnomathematics: A Multicultural View of Mathematical Ideas

Introduction Numbers: words and symbol Tracing graphs in the sand The logic of kin relations Chance and strategy in games and puzzles The organization and modeling of space Symmetric strip decorations In conclusion: Ethnomathematics