Contents

Mathematical algorithms for perpetual Ethiopian calendar(e.c.) and similar calendars

Author(s): Aschale Moges Belay1, Snehashish Chakraverty2
1Department of Mathematics, Debark University, P.O.Box 90, Ethiopia
2Department of Mathematics, NIT Rourkela, India
Copyright © Aschale Moges Belay, Snehashish Chakraverty. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study focused on developing mathematical algorithms for the perpetual Ethiopian calendar and similar calendars. The primary objective was to demonstrate the methodology for creating these algorithms. The research identified that arithmetic progression, ceiling function, congruence modulo, floor function, and Bahre Hasabe are fundamental concepts necessary for this development. Utilizing these concepts, the study successfully developed mathematical algorithms for the perpetual Ethiopian calendar and analogous calendars.

Keywords: Arithmetic progression; Bahre Hasabe; Ceiling function; Congruence modulo; Ethiopian calendar; Fasting dates; Floor function; Holidays

References

  1. Abebe, M. (2019). History of Ethiopian calendar. Ethiopia: Dessie Press.

  2. Fekadu, N. (2018). History of Ethiopian and Gregorian Calendar. Ethiopia: Bahir Dar Press.

  3. Temesgen, K. (2020). Comparison of Ethiopian and Gregorian Calendar. Ethiopia: Addis Ababa Press.

  4. Chalie, A. (2017). Contributions of Ethiopian Orthodox Church for Perpetual Ethiopian Calendar. Ethiopia: Debre Markos Press.

  5. Manaye, B. N. (2016). The use of Bahre Hasabe for the development of digital Ethiopian. Ethiopia: Gondar Press.

  6. Zenebe, N. (2021). Perpetual Ethiopian and European Calendar and Organizer System for an Android Based Smart Phones. Ethiopia: AAU – ETD.

  7. Proofwiki. (2018). Definition: Congruence (number theory). Retrieved on November 11, 2018, from https://proofwiki.org/wiki/.

  8. Cleveland, T. (2018). Number Theory. Scientific e-Resources. Retrieved from http://books.google.ie/books?id=o-PEDwAAQBAJ$&$printsec=frontcover$&$dq=number+theory$&$hl=$&$cd=5$&$source=gbs$\textunderscore$api

  9. Nagell, T. (2021). Introduction to Number Theory. American Mathematical Society. Retrieved from http://books.google.ie/books?id=Znc5EAAAQBAJ$&$printsec=frontcover$&$dq=number+theory$&$hl=$&$cd=3$&$source=gbs$\textunderscore$api

  10. Fine, B., Gaglione, A., Moldenhauer, A., Rosenberger, G., & Spellman, D. (2017). Algebra and Number Theory. Walter de Gruyter GmbH \(\&\) Co KG. Retrieved from http://books.google.ie/books?id=7-Y3DwAAQBAJ$&$printsec=frontcover$&$dq=number+theory$&$hl=$&$cd=1$&$source=gbs$\textunderscore$api

  11. Jongsma, C. (2020). Introduction to Discrete Mathematics via Logic and Proof. Springer. Retrieved from http://books.google.ie/books?id=1NUKzgEACAAJ$&$dq=discrete+mathematics$&$hl

  12. Levin, O. (2018). Discrete Mathematics. Createspace Independent Publishing Platform. Retrieved from http://books.google.ie/books?id=BWhCugEACAAJ$&$dq=discrete+mathematics$&$hl=$&$cd=1$&$source=gbs$\textunderscore$api

  13. Shah, D., Sahni, M., Sahni, R., León-Castro, E., & Olazabal-Lugo, M. (2022). Series of Floor and Ceiling Function—Part I: Partial Summations. Mathematics, 10(7), 1178. https://doi.org/10.3390/math10071178.

  14. Yadav, D. (2020). Multi-Dimensional Arithmetic Progression. Retrieved from http://books.google.ie/books?id=ImVuzQEACAAJ$&$dq=arithematic+progression$&$hl=$&$cd=1$&$source=gbs$\textunderscore$api

  15. Tesifa, G. (2020). Abushaher (yekene mekuteria). Ethiopia: Aksum Publishing House.

  16. Cai, L. (2022). Arithmetic Progression & Geometric Progression (A-level H2 Math). AcesMath! Retrieved from http://books.google.ie/books?id=HX9sEAAAQBAJ&printsec=frontcover&dq=Arithmetic+progression&hl=&cd=4&source=gbs_api