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Multiplication table for Mangarevan arithmetic

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posted on 2014-04-23, 13:33 authored by Hsin-Hao YuHsin-Hao Yu

Bender & Beller (2014; PNAS vol 111 no 4; "Mangarevan invention of binary steps for easier calculation") describes an unique arthemtic system used by people living on Mangareva, a small island in French Polynesia. This system is not too different from the decimal system that we're using today, except that a number in the Mangarevan language can contain a small segment of binary code, which employs four numerals to represent 10 multiplied by the first four powers of 2. The numerals are takau (10), paua (20), tataua (40), and varu (80), and they are abbreviated as K, P, T, and V respectively by the authors. For example, 273 is decomposed as 3VPK3 (3*80+20+10+3, pronounced "toru varu paua takau toru"). The paper unfortunately does not contain a multiplication table. I wrote a program to generate it, which is presented in here.