Definition:Calendar/Gregorian
Definition
The Gregorian calendar is the calendar which was introduced by Pope Gregory XIII in $1582 \, \text{CE}$.
Over the course of the next few centuries it was gradually adopted by the various subcultures of Western civilization.
It was derived as a refinement of the Julian calendar to correct for the discrepancy between the Julian calendar and the tropical year.
The years themselves are assigned the same numbers as their Julian counterparts.
An evolving modern convention is to refer to $\text{A.D.}$ and $\text{B.C.}$ as $\text{CE}$ and $\text{BCE}$, for common era and before common era respectively.
Like the Julian calendar, it divides the year into either $365$ days or $366$ days, according to the year number.
The months, similarly, are kept the same as for the Julian calendar.
The only difference is in the determination of which years are classified as leap years.
Let $y$ be the year number.
Then $y$ is a leap year if and only if
- $y$ is divisible by $400$
or:
Thus, for example:
Gregorian or Civil Year
A Gregorian year, also known as the civil year, is the length of a year as defined using the Gregorian calendar.
- $1$ Gregorian year $= \begin{cases} 366 \, \text {days} & : 400 \divides y \\
365 \, \text {days} & : 400 \nmid y \text { and } 100 \divides y \\ 366 \, \text {days} & : 100 \nmid y \text { and } 4 \divides y \\ 365 \, \text {days} & : 4 \nmid y \end{cases}$
where:
- $y$ denotes the number of the year
- $4 \divides y$ denotes that $y$ is divisible by $4$
- $4 \nmid y$ denotes that $y$ is not divisible by $4$.
Also see
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $365 \cdotp 2422$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $365 \cdotp 24219 \, 878$