Calendar Basics

Edward M. Reingold; Nachum Dershowitz

doi:10.1017/9781107415058.004

1 - Calendar Basics

Published online by Cambridge University Press: 22 March 2018

Edward M. Reingold and

Nachum Dershowitz

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

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Summary

A learned man once asked me regarding the eras used by different nations, and regarding the difference of their roots, that is, the epochs where they begin, and of their branches, that is, the months and years, on which they are based; further regarding the causes which led to such difference, and the famous festivals and commemoration-days for certain times and events, and regarding whatever else one nation practices differently from another. He urged me to give an explanation, the clearest possible, of all this, so as to be easily intelligible to the mind of the reader, and to free him from the necessity of wading through widely scattered books, and of consulting their authors. Now I was quite aware that this was a task difficult to handle, an object not easily to be attained or managed by anyone, who wants to treat it as a matter of logical sequence, regarding which the mind of the student is not agitated by doubt.

Abū-Raihān Muhammad ibn ‘Ahmad al-Bīrūnī: Al-Āthār al-Bāqiyah ‘an al-Qurūn al-Khāliyah (1000)

Calendrical calculations are ubiquitous. Banks need to calculate interest on a daily basis. Corporations issue paychecks on weekly, biweekly, or monthly schedules. Bills and statements must be generated periodically. Computer operating systems need to switch to and from daylight saving time. Dates of secular and religious holidays must be computed for consideration in planning events. Most of these calculations are not difficult because the rules of our civil calendar (the Gregorian calendar) are straightforward.

Complications begin when we need to know the day of the week on which a given date falls or when various religious holidays based on other calendars occur. These complications lead to difficult programming tasks—not often difficult in an algorithmic sense but difficult because it can be extremely tedious to delve into, for example, the complexities of the Hebrew calendar and its relation to the civil calendar.

The purpose of this book is to present, in a unified, completely algorithmic form, a description of over three dozen calendars and how they relate to one another.

Type: Chapter
Information: Calendrical Calculations
The Ultimate Edition
, pp. 1 - 52

DOI: https://doi.org/10.1017/9781107415058.004 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2018

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References

[1] Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, Her Majesty's Stationery Office, London, 1961.

[2] Goddard Earth Sciences Data Information Services Center website, National Aeronautics and Space Administration, disc.sci.gsfc.nasa.gov/ julian_calendar.html.

[3] The Larousse Encyclopedia of Mythology, Barnes & Noble Books, New York, 1994.

[4] J. P., Allen, Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphs, Cambridge University Press, Cambridge, 2nd edn., pp. 107-110, 2010.Google Scholar

[5] P. F. W., Bartle, “The Forty Days: The Akan Calendar,” Africa, vol. 48, pp. 80-84, 1978.Google Scholar

[6] B., Blackburn and L., Holford-Strevens, The Oxford Companion to the Year, Oxford University Press, Oxford, 1999.

[7] C. A., Boch, B., Ananthasubramaniam, A. M., Sweeney, F. J., Doyle, and D. E., Morse, “Effects of Light Dynamics on Coral Spawning Synchrony,” Biological Bulletin, vol. 220, pp. 161-173, 2011.Google Scholar

[8] M., Clagett, Ancient Egyptian Science: vol. 2, Calendars, Clocks, and Astronomy, American Philosophical Society, Philadelphia, 1995.

[9] L., Cope, “Calendars of the Indians North of Mexico,” American Archaeology and Ethnology, vol. 16, pp. 119-176, 1919.Google Scholar

[10] J., Davenport, T. T., Jones, T. M., Work, and G. H., Balazs, “Pink Spot, White Spot: The Pineal Skylight of the Leatherback Turtle (Dermochelys Coriacea Vandelli 1761) Skull and its Possible Role in the Phenology of Feeding Migrations,” Journal of Experimental Marine Biology and Ecology, vol. 461, pp. 1-6, 2014.Google Scholar

[11] N., Dershowitz and E. M., Reingold, “Modulo Intervals: A Proposed Notation,” ACM SIGACT News, vol. 43, no. 3, pp. 60-64, 2012.Google Scholar

[12] L. E., Doggett, “Calendars,” Explanatory Supplement to the Astronomical Almanac, P. K., Seidelmann, ed., University Science Books, Mill Valley, CA, pp. 575-608, 1992.Google Scholar

[13] J., Elkins, “On the Impossibility of Close Reading,” Current Anthropology, vol. 37, pp. 185-226, 1996.

[14] N., Fox, “A Bone Carved Calendar,” in Tel ‘Aroer: An Iron Age II Caravan Town and the Hellenistic-Early Roman Settlement. Avraham Biran (1975-1982) and Rudolph Cohen (1975-1976) Excavations, Y., Thareani, ed., Annual of the Nelson Glueck School of Biblical Archaeology, No. VIII, Jerusalem, pp. 255-258, 468, 2011.Google Scholar

[15] T., Galloway and W. S. B., Woolhouse, “Calendar,” The Encyclopædia Britannica, 11th edn., vol. 4, pp. 987-1004, The Encyclopædia Britannica Co., New York, 1910. The same article also appears in the 8th (1860) through the 13th (1926) editions.Google Scholar

[16] F. K., Ginzel, Handbuch der mathematischen und technischen Chronologie, J. C. Hinrichs'sche Buchhandlung, Leipzig, 1906 (vol. 1), 1911 (vol. 2), and 1914 (vol. 3). Reprinted by F. Ullmann, Verlag, Zwickau, 1958.

[17] A. T., Grafton, Joseph Scaliger: A Study in the History of Classical Scholarship, vol. II, Historical Chronography, Oxford University Press, Oxford, 1993.Google Scholar

[18] R. L., Graham, D. E., Knuth, and O., Patashnik, Concrete Mathematics, 2nd edn., Addison-Wesley Publishing Company, Reading, MA, 1994.Google Scholar

[19] G. H., Hardy, and E. M., Wright, An Introduction to the Theory of Numbers, 5th edn., Oxford University Press, Oxford, 1979.Google Scholar

[20] M. A., Harris and E. M., Reingold, “Line Drawing, Leap Years, and Euclid,” ACM Computing Surveys, vol. 36, pp. 68-80, 2004.Google Scholar

[21] O. L., Harvey, Calendar Conversions by Way of the Julian Day Number, American Philosophical Society, Philadelphia, 1983.Google Scholar

[22] J., Hastings, edn., Encyclopædia of Religion and Ethics, Charles Scribner's Sons, New York, 1908-1922.Google Scholar

[23] H., Henderson and B., Puckett, Holidays & Festivals Index, Omnigraphics, Detroit, MI, 1995.Google Scholar

[24] H., Henderson and S. E., Thompson, Holidays, Festivals & Celebrations of the World Dictionary, 2nd edn., Omnigraphics, Detroit, MI, 1997.Google Scholar

[25] J. F. W., Herschel, Outlines of Astronomy, 3rd edn., Longman, Brown, Green, Longmans, and Roberts, London, 1849.Google Scholar

[26] W., Horowitz, “The 360 and 364 Day Year in Ancient Mesopotamia,” Journal of the Ancient Near Eastern Society vol. 24 (1996), pp. 35-41.

[27] A. Ya., Khinchin, Continued Fractions, translated by P., Wynn, P., Noordhoff, Groningen, 1964. Reprinted by Dover Publications, Mineola, NY, 1997.Google Scholar

[28] D. E., Knuth, The Art of Computer Programming, vol. 2: Seminumerical Algorithms, 3rd edn., Addison-Wesley Publishing Company, Reading, MA, 1998.

[29] K., Konadu, “The Calendrical Factor in Akan History,” International Journal of African Historical Studies vol. 45, pp. 217-246, 2012.

[30] N., Kronfeld-Schor, D., Dominoni, Ḥde la, Iglesia, O., Levy, E. D., Herzog, T., Dayan, and C., Helfrich-Forster, “Chronobiology by Moonlight,” Proc. Royal Soc. B vol. 280, 20123088, 2013.Google Scholar

[31] F., Macler, “Calendar (Armenian),” vol. III, pp. 70-72, Encyclopædia of Religion and Ethics, J., Hastings, edn., Charles Scribner's Sons, New York, 1908-1922.Google Scholar

[32] A., Marshack, The Roots of Civilization, McGraw-Hill, New York, 1972.Google Scholar

[33] O., Neugebauer, A History of Ancient Mathematical Astronomy, Springer- Verlag, Berlin, 1975 (vol. 1, pp. 1-555, vol. 2, pp. 556-1058, vol. 3, pp. 1059-1457).Google Scholar

[34] Ø., Ore, Number Theory and Its History, McGraw-Hill., New York, 1948. Reprinted by Dover, Mineola, NY, 1987.Google Scholar

[35] O. K., Osei, A Discourse on Akan Perpetual Calendar (for Religious Ceremonies and Festivals), Domak Press Ltd., Accra, Ghana, 1997.Google Scholar

[36] F., Parise, ed., The Book of Calendars, Facts on File, New York, 1982.Google Scholar

[37] R. A., Parker, The Calendars of Ancient Egypt, University of Chicago Press, Chicago, 1950.Google Scholar

[38] R. L., Reese, E. D., Craun, and C. W., Mason, “Twelfth-Century Origins of the 7980-Year Julian Period,” Amer. J. Physics, vol. 51, p. 73, 1983.Google Scholar

[39] R. L., Reese, S. M., Everett, and E. D., Craun, “The Origin of the Year Julian Period: An Application of Congruences and the Chinese Remainder Theorem,” Amer. J. Physics, vol. 49, pp. 658-661, 1981.Google Scholar

[40] E. G., Richards, Mapping Time: The Calendar and its History, Oxford University Press, Oxford, 1998.Google Scholar

[41] R. G., Schram, Kalendariographische und chronologische Tafeln, J. C. Hinrichs'sche Buchhandlung, Leipzig, 1908.Google Scholar

[42] R. D., Skeel and J. B., Keiper, Elementary Numerical Computing with Mathematica, McGraw-Hill, New York, 1993.Google Scholar

[43] J., Speicher, L., Schreffler, and D., Speicher, “Lunar Influence on the Fall Migration of Northern Saw-whet Owls,” Wilson J. Ornithology, vol. 123, pp. 158-160, 2011.Google Scholar

[44] R. M., Stallman, GNU Emacs Manual, 13th edn., Free Software Foundation, Cambridge, MA, 1997.Google Scholar

[45] D., Steel, Marking Time: The Epic Quest to Invent the Perfect Calendar, John Wiley & Sons, New York, 2000.Google Scholar

[46] G. L., Steele Jr., Common LISP: The Language, 2nd edn., Digital Press, Bedford, MA, 1990.Google Scholar

[47] S. H., Taqizadeh, “An Ancient Persian Practice Preserved by a Non-Iranian People,” Bulletin of the School of Oriental Studies, vol. 9, no. 3, pp. 603-619, 1938.Google Scholar

[48] A., Troesch, “Interprétation géométrique de l'algorithme d'Euclide et reconnaissance de segments,” Theoret. Comp. Sci., vol. 115, pp. 291-319, 1993.Google Scholar

[49] B. L. van der, Waerden, “Tables for the Egyptian and Alexandrian Calendar,” ISIS, vol. 47, pp. 387-390, 1956.Google Scholar

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1 - Calendar Basics

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