More Maths for Leap Year

February just had its last 29th day for the next 4 years. As you already know, 2016 is a leap year, that means that it has one more extra day in February making it 366 days long. I thought that it would be a good idea to share with you some maths behind all this concept of leap year. So here are a couple of interesting facts:

  • the Earth revolves around the Sun in 365 days 6 hours 9 minutes and 18 seconds; so you can observe that basically a year on Earth is not exactly 365 days. tropical-year-illustration
  • the tropical (or solar ) year is the one that interests us the most because this is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth.  Basically it is the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. The seasonal cycle does not remain exactly synchronized with the position of the Earth in its orbit around the Sun. On the 1st January 1901 (time 00:00) it was recorded to be 365 days 5 hours 48 minutes and 45 seconds. This values decreases by 0.53 seconds per century.
  • there is an incredibly beautiful history behind the concept of calendar and I totally advice you to try and find out more about it. Let me know in comment box bellow if you would like to see future posts on the history of calendars and the mathematics behind it.
  • at the moment we are using the Gregorian Calendar, which was created by the astronomer Luigi Lilio Ghiraldi and approved by Pope Gregory XIII. The project was approved on 24th February 1582. In that year they decided to skip some days so that the calendar could work properly and the year would be closer to the actual Earth year. So in 1582 after 4th October came 15th October so that the year was as closer as possible to the tropical year.
  • the Gregorian year is not equal to the tropical year, but 26 seconds long. Even if we have the leap year there will still be an extra day every approx 3 323 year, so it was decided that the years 4000, 8000 etc to not be leap years. This will make the error to be smaller: one day every 20 000 years.

How can we find out is a year is a leap year? 

In this second part of the post I thought about explaining the mathematical method we use to find out is a year is a leap year. The algorithm is not that hard to understand and quite interesting.

Firstly, if a year is not divisible by 4 then it is just a common year (365 days). Therefore we are mostly interested in the year which are divisible by 4, but we cannot take all these years because that will make a considerable error for the future. So, if the year is not divisible by 100 then it is a leap year. Also if the year is divisible by 400 it is a leap year.

There are many explanations, so let us take an example to understand what happens:

year = 2000 , 2000 is divisible by 400 so it is a leap year;

year = 1900, 1900 is divisible by 4, but it is divisible by 100 so it is a common year;

year = 2200, 2200 is divisible by 400 so it is a leap year;


Hope this helps you understand more about why we need the concept of leap year and some of the mathematics behind it.

Have a great day. You can find me on Facebook,  Tumblr,  Google+,  Twitter,  Instagram  and  WeHeartIt. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy! ~LThMath



One thought on “More Maths for Leap Year

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  1. And Gregorian Calendar caused problems in the orthodox christians…!
    A part of them didn’t like the idea of the new calendar, because it was suggested by catholics…!
    So they still use (in religion’s matters, not in everyday use) the old calendar.
    They are called “old-calendar-people ” (παλιοημερολογίτες in greek)…
    In church services they are 13 days back…!
    e.g. they have Christmas, in January’s 7th…!

    Liked by 1 person

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