The Maya combine cycles of different lengths

Published on 4 April 2012, the paper interprets patterned notches on the Central African artifact as a calculating tool.

Repeated relationships among notches are used to test arithmetic, calendar and slide-rule interpretations.

It challenges assumptions that formal numerical reasoning began only in literate Eurasian civilizations.

The paper presents a hypothesis, not certainty, reminding users that archaeological objects can sustain multiple mathematical readings.

A 21 December 2012 article uses the end of a Long Count cycle to explain Maya calendrical mathematics.

Dots, bars and a shell-shaped zero made it possible to represent large numbers compactly.

It explains that the calendar's cycle ending was a mathematical rollover, not a prediction of the world's destruction.

The 7 October 2013 article examines an Indian temple inscription containing circular zero symbols.

Numbers in the inscription show zero functioning as a written positional digit in practical measurement and donation records.

It emphasizes that the so-called Arabic numerals reached Europe through a longer Indian-Arabic chain of transmission.