Astronomical year numbering
Cassini gave the following reasons for using a year 0:
Fred Espanak of NASA lists 50 phases of the moon within year 0, showing that it is a full year, not an instant in time. Jean Meeus gives the following explanation:
Although he used the usual French terms "avant J.-C." (before Jesus Christ) and "après J.-C." (after Jesus Christ) to label years elsewhere in his book, the Byzantine historian Venance Grumel used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He did so possibly to save space and put no year 0 between them.
New Year
March 1 was the first day of the numbered year in the Republic of Venice until its destruction in 1797, and in Russia from 988 until 1492 (Anno Mundi 7000 in the Byzantine calendar). September 1 was used in Russia from 1492 (A.M. 7000) until the adoption of the Anno Domini notation in 1700 via a December 1699 decree of Tsar Peter I.