Table of Contents
Calendar
Calendar Mathematics Formulas and Concepts
Odd Days
Odd days are the number of days more than the complete weeks in a given period.
Leap Year
A leap year has 366 days (52 weeks and 2 days).
\[
\text{Leap Year} = \left\{
\begin{array}{ll}
\text{Divisible by 4} & \text{and not by 100} \\
\text{or} & \text{Divisible by 400}
\end{array}
\right.
\]
Ordinary Year
An ordinary year has 365 days (52 weeks and 1 day).
Counting Odd Days
- 1 ordinary year = 1 odd day
- 1 leap year = 2 odd days
Number of Odd Days in Given Days
\[
\text{Odd Days} = \text{Total Days} \mod 7
\]
Finding the Day of the Week
To find the day of the week for any given date:
- Calculate the number of odd days up to that date.
- Use the reference day (e.g., 1st January 1900 was a Monday).
Day Codes
Each day of the week is associated with a code:
- Sunday: 0
- Monday: 1
- Tuesday: 2
- Wednesday: 3
- Thursday: 4
- Friday: 5
- Saturday: 6
Month Codes
Each month has a specific code:
- January: 0 (6 in a leap year)
- February: 3 (2 in a leap year)
- March: 3
- April: 6
- May: 1
- June: 4
- July: 6
- August: 2
- September: 5
- October: 0
- November: 3
- December: 5