Calendars may seem like an unlikely place to find mathematics, but it is in them. 2020 happens to be a leap year, which means that the upcoming month of February will include a Saturday the 29th. Making sense of why this is and how calendars can change from one year to the next is what this application of math is meant to accomplish. Two useful concepts to keep in mind are the Doomsday rule and the Leap Year formula.
The Doomsday rule takes advantage of every year having a certain number of days that can be easily remembered called Doomsdays. The simplest are (4/4) April 4th, (6/6) June 6th, (8/8) August 8th, (10/10) October 10th, and (12/12) December 12th which occur on the same day of the week in any given year. However, other months have doomsdays that may require more creative ways to remember them. Along with such mnemonic tricks, addition and division are used. Once mastery of the algorithm is achieved, for instance, it may be possible to determine from the top of one’s head what day of the week one’s birthday is to be on in any particular future year or had been on in any past year.
The Leap Year formula, admittedly, is much easier to remember and uses only division. It goes as follows: check if a year’s number is evenly divisible by four; if so, also check if the number isn’t evenly divisible by one hundred; if so, check if the number is evenly divisible by four hundred. If these characteristics are met, then the year is a leap year. However, due to how the Earth revolves around the Sun, this may not mean that there will be a leap year every four years.
Although not related to the math, it’s interesting how the leap year has been around since 45 BC and was invented by astronomer Sosigenes and politician Julius Caesar, whereas the Doomsday rule has been around since 1973 and was invented by mathematician John Conway. The current usage of leap days was adopted in 1582 from a proposal by chronologist Aloysius Lilius that was modified by mathematician Christopher Clavius.
