The Table of Sixty-One Headings as a Tool for Finding the Intervals between the Recurrence of Year Codes in the Jewish Calendar

Abstract

This paper presents an additional mathematical tool that can be used to analyze the Jewish calendar. The table of sixty-one headings was prepared in France, seven hundred and fifty years ago as a tool for finding the year codes for the 19-years of a particular cycle of Jewish years. This unique table demonstrated that there are only 61 possible arrangements of the year codes in these 19-year cycles. The table can be used to calculate the intervals between the appearances of a pair or any series of particular year codes.

The paper is divided into three parts. The first part will explain the use of the table of sixty-one headings, the second part will present an improved version of the table that will demonstrate the repetitiveness of the SIMAN HASHANA. The third part will demonstrate a new method with which one can understand the intervals at which a pair of year codes appear and the mathematical logic of these intervals. This method will be demonstrated on two cases.