Mathematician reveals hidden 5.7m-year cycle behind the date of Easter

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Mathematician reveals hidden 5.7m-year cycle behind the date of Easter

Dr Stephen Woodcock loves Easter, but not because he's a big chocolate egg fan (although he is).

Dr Woodcock is a mathematician. Mathematicians love cracking open chaos to find the pattern within.

And Easter has one of the most interesting patterns of all.

Easter has no fixed date. It slides across the calendar, propelled by two huge cycles: the cycle of the moon, and the cycle of the calendar.

Together, they create a third cycle, which Dr Woodcock terms the "Easter cycle".  If you lived for 5.7 million years, you would see it through just once.


Mathematicians refer to repeating patterns of numbers as cycles. Easter Sunday falls on April 1 this year, April 21 next year, and April 12 in 2020; in 5.7 million years, that pattern will repeat itself.

“If they’d just written down what day they crucified the bloke on, it all would have been easier wouldn’t it?” says Dr Woodcock, who lectures at the University of Technology Sydney.

Easter Sunday falls between March 22 and April 25 – that's any one of 35 days.

Easter Sunday is always on the Sunday after the first full moon after the March equinox, when day and night are of equal length.

This year, the equinox was March 21. The first full moon after the equinox arrives a few minutes before midnight Saturday March 31, making April 1 Easter Sunday. If the first full moon arrived after midnight, Easter Sunday would be the following week.

The full moon rises every 29.53 days. Because it does not quite align to our calendar, every year full moons rise on different dates according to a cycle that repeats every 19 years.

If we were to fast forward 19 years, the full moon would arrive on exactly the same day.

If you want to make your head hurt even more, Easter does not even use the astronomical full moon – it uses the ecclesiastical or paschal full moon, which the Christian Church calculates using an ancient, arcane and slightly innaccurate equation.

This can mean the paschal full moon disagrees with the astronomical full moon, further complicating the date of Easter.

The second cycle, the calendar cycle, takes a full 400 years to repeat. In 400 years, April 1 will again be a Sunday.

Why? Notice your birthday is on a different day of the week every year - that's because there are 52 weeks in a year plus one extra day. That pushes the calendar forward every year.

When you add in leap years (add two days to the year's length ... unless the year is divisible by 100 ... Unless it's also divisible by 400), the calendar slowly rotates through a 400 year cycle.

Combine the cycle of the full moon and that of the calendar and you get Dr Woodcock's 5.7 million year Easter cycle.

"It’s mind-bendingly long,” says Dr Woodcock.

“Throw in some other periodic adjustments to account for the quirks of both our calendars and astronomical movements and the end result is a pattern of Easter dates which only fully repeats itself after exactly 5.7 million years".

It gets even weirder. Despite the cycle lasting 5.7 million years, you will never see Easter Sunday falling in the same week two years in a row.

And for each day Easter Sunday falls on, there are only eight possible days (out of 35) it can fall on the next year.

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