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Easter Date Calculator (Computus Algorithm)

Computus Algorithm:

\[ \begin{align*} a &= year \mod 19 \\ b &= \left\lfloor\frac{year}{100}\right\rfloor \\ c &= year \mod 100 \\ d &= \left\lfloor\frac{b}{4}\right\rfloor \\ e &= b \mod 4 \\ f &= \left\lfloor\frac{b + 8}{25}\right\rfloor \\ g &= \left\lfloor\frac{b - f + 1}{3}\right\rfloor \\ h &= (19a + b - d - g + 15) \mod 30 \\ i &= \left\lfloor\frac{c}{4}\right\rfloor \\ k &= c \mod 4 \\ l &= (32 + 2e + 2i - h - k) \mod 7 \\ m &= \left\lfloor\frac{a + 11h + 22l}{451}\right\rfloor \\ month &= \left\lfloor\frac{h + l - 7m + 114}{31}\right\rfloor \\ day &= ((h + l - 7m + 114) \mod 31) + 1 \\ \end{align*} \]

(Gregorian calendar)

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1. What is the Computus Algorithm?

The Computus algorithm is a mathematical calculation to determine the date of Easter Sunday in the Gregorian calendar. It was established by the First Council of Nicaea in 325 CE and refined over centuries to account for calendar reforms.

2. How Does the Calculator Work?

The calculator uses the Computus algorithm which involves these steps:

\[ \begin{align*} a &= year \mod 19 \\ b &= \left\lfloor\frac{year}{100}\right\rfloor \\ c &= year \mod 100 \\ d &= \left\lfloor\frac{b}{4}\right\rfloor \\ e &= b \mod 4 \\ f &= \left\lfloor\frac{b + 8}{25}\right\rfloor \\ g &= \left\lfloor\frac{b - f + 1}{3}\right\rfloor \\ h &= (19a + b - d - g + 15) \mod 30 \\ i &= \left\lfloor\frac{c}{4}\right\rfloor \\ k &= c \mod 4 \\ l &= (32 + 2e + 2i - h - k) \mod 7 \\ m &= \left\lfloor\frac{a + 11h + 22l}{451}\right\rfloor \\ month &= \left\lfloor\frac{h + l - 7m + 114}{31}\right\rfloor \\ day &= ((h + l - 7m + 114) \mod 31) + 1 \\ \end{align*} \]

Explanation: The algorithm calculates Easter as the first Sunday after the first full moon occurring on or after the vernal equinox (fixed at March 21 for calculation purposes).

3. Historical Background

Details: The current algorithm was established by the Gregorian calendar reform in 1582. It's based on the 19-year Metonic cycle of the moon and corrections to maintain alignment with astronomical events.

4. Using the Calculator

Tips: Enter any year between 1583 (when the Gregorian calendar was adopted) and 9999. The calculator will determine the date of Easter Sunday for that year.

5. Frequently Asked Questions (FAQ)

Q1: Why does Easter's date change every year?
A: Easter is based on lunar cycles (full moon) and the solar year (spring equinox), which don't align perfectly with our calendar.

Q2: What's the earliest possible Easter date?
A: March 22 (occurred in 1818 and will occur again in 2285).

Q3: What's the latest possible Easter date?
A: April 25 (occurred in 1943 and will occur again in 2038).

Q4: Does this work for Orthodox Easter?
A: No, Orthodox churches use the Julian calendar for Easter calculations, resulting in different dates.

Q5: How accurate is this algorithm?
A: It's perfectly accurate for the Gregorian calendar system, matching ecclesiastical definitions exactly.

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