An ethnoarithmetic excursion into the Javanese calendar

Abstract

A perpetual calendar, a calendar designed to find out the day of the week for a given date, employs a rich arithmetical calculation using congruence. Zeller's congruence is a well-known algorithm to calculate the day of the week for any Julian or Gregorian calendar date. Another rather infamous perpetual calendar has been used for nearly four centuries among Javanese people in Indonesia. This Javanese calendar combines the Saka Hindu, lunar Islamic, and western Gregorian calendars. In addition to the regular seven-day, lunar month, and lunar year cycles, it also contains five-day pasaran, 35-day wetonan, 210-day pawukon, octo-year windu, and 120-year kurup cycles. The Javanese calendar is used for cultural and spiritual purposes, including a decision to tie the knot among couples. In this chapter, we will explore the relationship between mathematics and the culture of Javanese people and how they use their calendar and the arithmetic aspect of it in their daily lives. We also propose an unprecedented congruence formula to compute the pasaran day. We hope that this excursion provides an insightful idea that can be adopted for teaching and learning of congruence in number theory.