Happy Easter & Happy Passover!

Happy Easter & Happy Passover!

Good Friday, April 15, 2022 / Erev Pesach, Yom Shishi, 14 Nisan, 5782.

By happy coincidence, this day is important for both Easter and Passover: Good Friday today, and the first Passover Seder tonight, after sundown.

But how do we know when it’s Easter or when it’s Passover? 

Since this blog post is being hosted by the British Society for the History of Mathematics website, let’s hear what a historic British authority on Christian Calendrics had to say:

“To the most excellent and illustrious lord, King Nechtan [King of the Picts], from Abbot Ceolfrid [of Wearmouth and Jarrow] – Greetings in our Lord.

“In response to your devout enquiries… I am most willing… to explain the Catholic observance of Easter.

“After the sacrifice of Christ our Passover, the Lord’s Day [Sunday]  (which the ancients called the first day [<<Yom rishon>>, in Hebrew] after the Sabbath) was made holy for us by the joy of his resurrection and … the Apostles established this day for the Easter feast…. [A]ccording to the Law, the first month of the year [in that period, April in the Christian calendar and Nisan in the Jewish] and its fourteenth day and the evening of that day should be awaited. And if by chance that day fell on the Sabbath [i.e. Saturday] … all churches throughout the world, who constitute the one Catholic church, should prepare bread and wine as a sacrament of the Body and Blood… in the solemn celebration of Easter.

“Therefore if it could be … that a Sunday should always fall on the fifteenth day of the first month, that is, on the fifteenth appearance of the moon, we should be able always to celebrate our Easter at the very same time as the ancient people of God, as we do by the same faith, although by a different kind of sacrament. But because the days of the week do not keep pace with the phases of the moon, the apostolic tradition… decreed that, when the first month came round of the evening of its fourteenth day, they should wait further for the Sunday, from the fifteenth to the twenty-first day of that month. And on whatever of these days Sunday should occur, Easter should be celebrated on that day, because this falls within the seven days of unleavened bread, or at any rate occupies some of these days. For even if only one of them is included, that is the seventh day… no one can accuse us of not keeping the Easter Day, … in the third week of the first month as the Law decrees.” (Bede 1968, pp. 315-319).

Well, that’s Bede’s explanation (in English translation from the original Latin) of the date of Easter, from about 1300 years ago. So how do we figure out when it’s Passover (Pesach)?

Pesach starts on the 15th of Nisan every year, and lasts for seven more days, that is until the 22th of Nisan at the end of the [Jewish] day. Or for this Jewish year: from Erev Shabbat, 15 Nisan, until Havdalah, Yom rishon, 23 Nisan, 5782.

In the Civil Calendar that means, for 2022/5782 from 7:43 pm on Friday, April 15, until 7:52 pm, on Saturday, April 23. That’s Toronto time. For London, England, and for Jerusalem, Israel, the times are respectively, 7:39 pm & 7:51 pm and 6:27 pm & 6:33 pm. All times are local Daylight Savings Time. (Again, we render homage to Sandford Fleming.)

An interesting note is that Pesach 5782 ends on St. George’s Day 2022. By the way, our previous major Jewish holiday (<<Yom tov>> = lit. “Day good”), Purim, 14/15 Adar II, 5782, coincided with St. Patrick’s Day, March 17, 2022. Both St. Patrick’s Day and Purim celebrations encourage significant happy consumption of alcoholic drinks.

Nisan? What’s that?

“Nisan” is the one of the twelve names for the months in the Jewish (Hebrew) Calendar.

To help to explain the Jewish calendar and its use today, luckily, I have the work of retired University of Ottawa mathematics professor (and fellow member of CSHPM), Edward L. Cohen to rely on. Since at least the mid-1990s he’s been working on calendrics, covering a wide range over time and space of the world’s calendars. Not only has he been studying the Jewish calendar, but also the Gregorian, Islamic, Mayan, and French Revolutionary calendars, to name just a few.

We’re in the Jewish year 5782. Rosh Ha-Shonah (literally “The Head of the Year” in Hebrew) is the holiday that marked the Jewish New Year. By our traditional understanding, Rosh Ha-Shonah 5782, marked exactly 5781 years since the moment of Creation, on Yom Shlishi (Third Day), the 1st of Tishrei, 5782 :: Monday/Tuesday, September 6/7, 2021. 

5782 is a leap year; that means it has thirteen instead of twelve months. In order they are (days in the month): Tishrei (30) Cheshvan (29) Kislev (30) Tevet (29) Shevat (30) Adar I (30) Adar II (29) Nisan (30) Iyar (29) Sivan (30) Tammuz (29) Av (30) Elul (29). For a total of 384 days, making it a regular leap year.

A regular non-leap year has 354 days, a difference of 30 days, the length of the leap month Adar I. There are also defective years of 353 and 383 days respectively and excessive years, 355 and 385 days.

So, Rosh Ha-Shonah must be the first of Tishrei. That is the first day of Rosh Ha-Shonah. Since Canada is in the Diaspora, not in Eretz Israel (the Land of Israel), Rosh ha-Shonah is a two-day holiday.

So, when was Rosh Ha-Shonah for 5781, our previous year? When will it be in 5783? That’s easy: 1 Tishrei and 2 Tishrei, of course. But if we want to determine the date of Rosh Ha-Shona in the modified Gregorian Calendar that we use in Canada as our civil calendar, here’s what we have to do.

The Jewish calendar is based on the Moon and regulated by the Sun. The time from one New Moon to the next was known to be 29 days, 2 hours, 44 minutes, 3 1/3 seconds (a molad in Hebrew, pl. moladot).

Thus, every month has either 29 or 30 days, as exemplified above by 5782. Except, for Cheshvan and Kislev which can have either 29 or 30 days, all the months have the same length as they do for 5782.

In combination with the length of the solar year, the Jewish Calendar has a Metonic cycle of 19 years in which the lunar and solar calendars eventually match up again. The seven leap years with the extra month are in italics:

1, 2, 3, 4 ,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

Cohen has provided a table for us, running from 1883/5644 to 2110/5871, and from Metonic Cycle 298 to 309. Note that the Gregorian year is that of the Jewish year’s Rosh Ha-Shonah. Thus, we have 2020/5781 and 2021/5782 on the list.

In this table 2021/5782 is listed as S07-T, K. this means that the first day Rosh Ha-Shonah is September 7, 2021, and it’s on a Tuesday. “K” is the type of year.  “K” is one of the seven types of leap year, in this case with the first day of Rosh Ha-Shonah on a Tuesday and the first Day of Pesach (Passover) on Shabbat (Saturday). A “K” year is also a regular leap year of 384 days.

For 2021/5781 and 2022/5782 we have listings of S19-S, B and S26-M, E, respectively. So here we have Rosh ha-Shonah starting on September 19 (a Saturday) and September 26 (a Monday). “B” and “E” are both types of ordinary (non-leap ) years, with “B” defective (353 days) and “E” excessive 355 days.

Cohen also shows how he generates this table, but that’s another story.

There were many more Jewish holidays for us to commemorate throughout the month of Tishrei, 5782, (September 6 – October 6, 2021), such as:

Yom Kippur – The Day of Atonement: 10 Tishrei, 5782 (September 16-17, 2021),

Sukkot – Fall Harvest Festival: 15-20 Tishrei, 5782 (September 20-26, 2021),

Simchat Torah – Anniversary of Receiving the Torah at Mount Sinai: 23 Tishrei, 5782 (September 28-29, 2021).

But these are many more stories.



Bede (1968), revised translation edition by R. E. Latham, translated by Leo Sherley-Price, 1955, first composed in Latin, 731 CE., A History of the English Church and People in Penguin Classics. Penguin Books, Harmondsworth, England and Markham, Ontario, Canada. 364 pp., incl.9 pp. Notes, 3 pp. Genealogy of the English Kings, 12 pp. Index.

Edward L. Cohen:
(1994) “The Hebrew Calendar Simplified” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 7: 50-57
(1996) “Gregorian Dates for the Jewish New Year” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 9: 79-90
(2000) “Adoption and Reform of the Gregorian Calendar” Math Horizons 7(3): 5- 11
(2001) “The French Republican Calendar” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 14: 32-40
(2002) “The Mayan Calendars” Proceedings of the Canadian Society for the History and Philosophy of Mathematics, 15: 36-57
(2003a) “Calendars of the Dead-Sea-Scroll Sect” Cubo Matemática Educacional, 5(2): 1-16
(2003b) “The Islamic Calendar” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 16: 116-130
(2005) “The Iranian Calendar” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 18: 64-74
(2006) “Ancient Egyptian Calendars” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 19: 64-79
(2007) “Important Indian Calendars” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 20: 83-93
(2008) “Chinese and Japanese Calendars” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 21: 53-72
(2010) “The Roman Calendars” Proceedings of the Canadian Society for the History and Philosophy of Mathematics 23: 72-84


Other BSHM Time related blog posts

May 21, 2021, “Time Zones I: ‘Half an Hour Later in Newfoundland’ ”.

February 20, 2022. “Time Zones II: Sir Sandford Fleming and Standard Time”.

March 30, 2022, “Time Zones III: Sir Sandford Fleming at Home. My Home, That Is!”

CSTHA Calendrics Blog Posts:

March 5, 2021, Mi’kmaw Calendar

Sept. 3, 2021, “Jewish Calendar in Canada”