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9 - The Ecclesiastical Calendars

from I - Arithmetical Calendars

Published online by Cambridge University Press:  22 March 2018

Edward M. Reingold
Affiliation:
Illinois Institute of Technology
Nachum Dershowitz
Affiliation:
Tel-Aviv University
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Summary

We send you the good news concerning the unanimous consent of all in reference to the celebration of the most solemn feast of Easter, for this difference also has been made up by the assistance of your prayers, so that all the brethren in the East, who formerly celebrated this festival at the same time as the Jews, will in future conform to the Romans and to us and to all who have from of old kept Easter with us.

Synodal Letter of the Council of Nicæa to the Church of Alexandria (325 c.e.)

The calculation of the date of Easter has a fascinating history, and algorithms and computer programs abound (for example, [1], [2], [9], [10], [14], and [17]); there are also oddities such as the “finger algorithm” shown in the frontispiece of this chapter and the nomogram of Figure 9.1.Many of the computations rely on the formulas of Gauss [5], [6] (see also [8]). Our fixed-date approach allows considerable simplification of “classical” algorithms.

The history of the establishment of the date of Easter is long and complex; good discussions can be found in [3], [7], and [12]. The Council of Nicæa convened in 325 c.e. by Constantine the Great, was concerned with uniformity across various Christian groups. At the time of Nicæa, almost everyone in the official Church agreed to the definition that Easter was the first Sunday after the first full moon occurring on or after the vernal equinox [3] (a rule promulgated by Dionysius Exiguus and the Venerable Bede, who attributed it to the Council of Nicæa). By this definition, Easter is delayed one week if the full moon is on a Sunday, lessening the likelihood of its being on the same day as the Jewish Passover. This was contrary to the practice of the Quartodecimans, who celebrated Easter on the day of the full moon, 14 days into the month, regardless of the day of the week.

The concern that the date of Passover would influence the date of Easter goes back to the earliest days of Christianity. For example, Eusebius (Vita Constantini, book iii, pp. 18-20) gives a letter of the Emperor sent to those not present at the Council of Nicæa:

Type
Chapter
Information
Calendrical Calculations
The Ultimate Edition
, pp. 143 - 154
Publisher: Cambridge University Press
Print publication year: 2018

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References

[1] E. R., Berlekamp, J. H., Conway, and R. K., Guy, Winning Ways, vol. 2, Games in Particular, Academic Press, New York, 1982.Google Scholar
[2] R., Bien, “Gauß and Beyond: The Making of Easter Algorithms,” Archive for History of Exact Sciences, vol. 58, no. 5, pp. 439-452, July 2004.Google Scholar
[3] G., Declercq, Anno Domini: The Origins of the Christian Era, Brepols Publishers, Turnhout, Belgium, 2000.Google Scholar
[4] J. K., Fotheringham, “The Calendar,” The Nautical Almanac and Astronomical Ephemeris, His Majesty's Stationery Office, London, 1931-1934; revised 1935-1938; abridged 1939-1941.Google Scholar
[5] C. F., Gauss, “Berechnung des Osterfestes,” Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde, Herausgegeben vom Freiherrn von Zach (August 1800). Reprinted in Gauss's Werke, Herausgegeben von der Königlichen Gesellschaft der Wissenschaften, Göttingen, vol. 6, pp. 73-79, 1874.Google Scholar
[6] C. F., Gauss, “Noch etwas über die Bestimmung des Osterfestes,” Braunschweigisches Magazin (September 12, 1807). Reprinted in Gauss's Werke, Herausgegeben von der Königlichen Gesellschaft der Wissenschaften, Göttingen, vol. 6, pp. 82-86, 1874.
[7] J. L., Heilbron, The Sun in the Church: Cathedrals as Solar Observatories, Harvard University Press, Cambridge, MA, 1999.Google Scholar
[8] H., Kinkelin, “Die Berechnung des christlichen Osterfestes,” Zeitschrift für Mathematik und Physik, vol. 15, pp. 217-228, 1870.Google Scholar
[9] D. E., Knuth, “The Calculation of Easter,” Communications of the ACM, vol. 5, pp. 209-210, 1962.Google Scholar
[10] D. E., Knuth, The Art of Computer Programming, vol. 1, Fundamental Algorithms, 3rd edn., Addison-Wesley, Reading, MA, 1997.Google Scholar
[11] J., Meeus, Mathematical Astronomy Morsels, Willmann-Bell, Richmond, VA, 1997.Google Scholar
[12] A. A., Mosshammer, The Easter Computus and the Origins of the Christian Era, Oxford University Press, Oxford, 2008.Google Scholar
[13] G., Moyer, “The Gregorian Calendar,” Scientific American, vol. 246, no. 5, pp. 144-152, May 1982.
[14] T. H., O'Beirne, Puzzles and Paradoxes, Oxford University Press, Oxford, 1965. Reprinted by Dover Publications, New York, 1984.Google Scholar
[15] D., Roegel, “The missing new moon of A.D. 16399 and other anomalies of the Gregorian calendar,” INRIA internal report A04-R-436, 2004. Available at hal.inria.fr/inria-00099868/document.
[16] World Council of Churches, “The Date of Easter: Science Offers Solution to Ancient Religious Problem,” Press release, March 24, 1997.
[17] J. V., Uspensky and M. A., Heaslet, Elementary Number Theory, McGraw-Hill, New York, 1939.Google Scholar

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