As a Software Engineer I ran in to a task where I needed to calculate all the Faroese holidays, which included Easter. After googling and researching the topic from head to toe, I have to say it has been quite interesting.

Easter does not have a fixed date like Christmas or New Year’s Eve. Instead, it’s determined by a set of calculations based on the cycles of the moon. This complexity has made it a topic of intrigue for centuries, and many algorithms have been developed to predict its date.

In this post, we’ll delve into the intricacies of calculating Easter, using both the magic of mathematics and practical C# code.

The Mathematics Behind Easter

The date of Easter is determined by the Paschal Full Moon. Traditionally, Easter Sunday falls on the first Sunday following the first full moon that occurs on or after the vernal equinox. The vernal equinox is fixed on March 21 for the purpose of determining the date of Easter, regardless of the astronomical equinox date.

To compute the date of the Paschal Full Moon, Christians have historically used a method known as the “Computus.” Here is a simplified version of the Computus:

Golden Number: This represents the position of the year within the 19-year Metonic cycle of the moon. It is computed as:

\[ \text{Golden Number} = (\text{Year} \mod 19) + 1 \]

Century: Simply the century of the given year:

\[ \text{Century} = \left\lceil \frac{\text{Year}}{100} \right\rceil \]

Using the Century, various correction factors are introduced:

\begin{align*} a &= \text{Year} \mod 19 \\ b &= \left\lfloor \frac{\text{Year}}{100} \right\rfloor \\ c &= \text{Year} \mod 100 \\ d &= \left\lfloor \frac{b}{4} \right\rfloor \\ e &= b \mod 4 \\ \end{align*}

More corrections:

\begin{align*} f &= \left\lfloor \frac{b + 8}{25} \right\rfloor \\ g &= \left\lfloor \frac{b – f + 1}{3} \right\rfloor \\ h &= (19a + b – d – g + 15) \mod 30 \\ \end{align*}

Yet more corrections:

\begin{align*} i &= c \mod 4 \\ k &= \left\lfloor \frac{c}{4} \right\rfloor \\ l &= (32 + 2e + 2i – h – k) \mod 7 \\ \end{align*}

The month and day of the Paschal Full Moon:

\begin{align*} m &= \left\lfloor \frac{a + 11h + 22l}{451} \right\rfloor \\ \text{Month} &= \left\lfloor \frac{h + l – 7m + 114}{31} \right\rfloor \\ \text{Day} &= ((h + l – 7m + 114) \mod 31) + 1 \\ \end{align*}

Now, let’s translate this into C#!

C# Code to Calculate Easter

public static DateTime CalculateEaster(int year)
{
    int a = year % 19;
    int b = year / 100;
    int c = year % 100;
    int d = b / 4;
    int e = b % 4;
    int f = (b + 8) / 25;
    int g = (b - f + 1) / 3;
    int h = (19 * a + b - d - g + 15) % 30;
    int i = c % 4;
    int k = c / 4;
    int l = (32 + 2 * e + 2 * i - h - k) % 7;
    int m = (a + 11 * h + 22 * l) / 451;
    int month = (h + l - 7 * m + 114) / 31;
    int day = ((h + l - 7 * m + 114) % 31) + 1;

    return new DateTime(year, month, day);
}

This function takes in a year as an argument and returns the date of Easter for that year as a DateTime object.

Wrapping Up

The calculation of Easter is a fascinating blend of astronomy, mathematics, and tradition. While the Computus may seem complex, it’s a testament to the lengths early Christians went to ensure the accurate celebration of their most important holiday. With the power of modern programming languages, we can easily compute the date for any given year.

Whether you’re a developer looking to incorporate Easter calculations into software or just a curious mind. This is an interesting bit of trivia to ponder on.

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