Have you ever noticed that Easter always takes place on a different day? The date of Easter is extremely important, since, after that, other dates are defined, such as Carnival and Corpus Christi. But who decides this date? How can we find out the correct date each year? And what does Mathematics have to do with it? One of the ways to discover the date of Easter is an interesting mathematical curiosity.
the day of Easter varies with the year and the phase of the moon. But a very wise mathematician, Carl Friedrich Gauss (1777 – 1855), found a way to find the exact date of Easter in any year that falls within the range 1900-2099. Through simple mathematical calculations, we can determine which day Easter will be in any year!
Think of any year between 1900 and 2099. Let's call this year The. We will do some divisions, and each rest of Division will be identified by the following letters:
x → the rest of the division of The for 19
y → the rest of the division of The per 4
z → the rest of the division of The per 7
k → the rest of the division of (19.x + 25) per 30
w → the rest of the division of (2.y + 4.z + 6.k + 5) per 7
Easter Sunday of the year The it will be on the day (k + w + 22) of March or on the day (k + w – 9) of April.
Let's calculate what day Easter will be 2020? In that case, a = 2020, we will then identify what the value of x:
The x is the remainder of the 2020 division by 19
Let's also calculate the value of y:
The y is the remainder of the division of 2020 by 4
Now we want to find the value of z:
The z is the remainder of the 2020 division by 7
We need to solve the numeric expression19.x + 25 to find the value of k:
The k is the remainder of the division of 139 by 30
Finally, we need to resolve the expression 2.y + 4.z + 6.k + 5 to find the value of w:
The w is the remainder of the division of 135 by 7
Okay, now that we've found the values for k and w, we'll do two more calculations. First let's see if it's possible for Easter 2020 to take place in March:
k + w + 22 = 19 + 2 + 22 = 43
As there is no “March 43” day, Easter 2020 will not be in March. Let's check which day in April it will take place:
k + w – 9 = 19 + 2 – 9 = 12
Therefore, Easter Sunday in April 2020 will take place on April 12th.
Introduce this mathematical curiosity to your friends, choose a year and challenge them to find out what day Easter will be that year!
By Amanda Gonçalves
Graduated in Mathematics
