Abstract
During Lean’s (1992) analysis of counting systems in Papua New Guinea (PNG) using Salzmann’s (1950) notions of frame pattern, cycle, and operative pattern (see Chapter 1, pp. 20–21 for more details), he found that the most prominent cycle to be 2. Further analysis showed that there were a number of modified 2-cycle systems that he denoted by 2ʹ and 2ʺ as they had a non-compound word for 3 or 4 respectively. Furthermore, many of these systems had additional cycles especially 5- and 5- and 20- cycle systems. He also noted some that had 4- and 8- and 10- cycles. His map of the spatial occurrences of these types of systems is given in Figure 3.1. Further data (Mimica, 1988; C. Muke, 2000) and that obtained by Owens indicate that these systems were developed from cultural beliefs and practices to incorporate large numbers.
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Owens, K., Lean, G., Muke, C. (2018). 2-Cycle Systems Including Some Digit Tally Systems. In: History of Number. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-45483-2_3
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