## Calendar Problem The Date of Easter

There are many historically interesting calendric problems. Among these is the calculation of the date of Easter. The

21 This rule states that Easter will fall on the first Sunday after the 14th day of the Moon that occurs on or after March 21. The 14th day of the Moon, is, on average, slightly earlier than the precise date of full moon, in our reckoning of dates.

traditional statement is that Easter is the first Sunday after the first full moon22 following the vernal equinox. Neugebauer (1979) notes that astronomically, the solution requires the determination of the length of the tropical year and the ability to predict accurately the moment of full moon. In his study of an Ethiopian table giving the dates of Easter, Neugebauer found that the dates were simply computed from the dates of Passover (Easter would be a following Sunday). These dates were computed using the 19-year Metonic cycle, but without the refinements that the Babylonians employed (according to Neugebauer). The point to be made is that the computation of the dates of Easter usually involved computational schemes that sometimes differed in application among the ecclesiastical authorities. Moreover, the date of Easter can be different if one begins counting days from sundown, as in ancient Babylon [and in the later Jewish tradition (see Metzger and Coogan 1993, p. 744)], and controversies arose if some calculations indicated an Easter date that fell just one day after Passover. The question of the need to avoid a date prior to or coincident with Passover depends on the priority given one part of scripture over another. The distinction causes a difference between the dates of Easter as celebrated by Orthodox Christians, for whom the date of Easter must follow Passover, and by the Catholics and Protestants of the western churches, for whom Easter can precede Passover. Even among western churches, however, dates computed with different lunar theories have yielded different dates of Easter. Ginzel (1906) summarizes these difficulties and others. See Dershowitz and Reingold (1997) for a recent mathematical treatment.

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