Mathedu - Reengineering Mathematics

Mathedu Reengineering Mathematics

The Blog of Mathedu Academy

A content for the curious of the mathematics in the real world… and beyond, including video tutorials.

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Why is there a February 29, 2020, and not in 2021 or 2019?

Well, the day length is exactly the time by which the earth makes a turnaround on itself. And the year is exactly the time by which the earth makes a complete revolution around the sun.
Thus, the number of days of the year must be the ratio of the year length on the day length say, in seconds.
The problem is that there is no reason for that ratio to be an integer.

And in fact, it is not: the closest integer to that ratio is 365.
That is why we say that a year is 365 days long, for instance in the expression "365 days on 365" to say every single day of an entire year.

But the ratio is
not exactly 365. It is closer to 365 and 1/4.
So, it was decided to add an extra day every 4 years.
The years where that extra day is added are the "leap years". These leap years have 366 days.
For convenience reasons, the day that is added is at the end of the shorter month in the year, February: February has 29 days on the leap years, and 28 days the other years.
And for convenience reasons as well, it was decided to fix leap years for the years that are numbered a multiple of 4 in our Gregorian Calendar.
That is why the 29th of February did not exist in 2019, but will exist in 2020.

But the leap years are not
every years being a multiple of 4 in the Calendar.
This is because the ratio is not exactly 365 and 1/4
: it is closer to 365 + 1/4 - 1/100.
So it was decided to skip the leap years that are a multiple of 100 (such years are also a multiple of 4 because 100 is a multiple of 4: 100 = 4 x 25.).
That is why the 29th of February did not exist in the exact secularly years, such as 1900.

But it existed in 2000. Why? Because it was a multiple of 2000, and the ratio is in fact closer to 365 + 1/4 - 1/100 + 1/2000.
This the beginning of a series development into rational approximations.

We could continue like that, but it is not worthwhile before a long period of time, of the order of magnitude of 10,000 years!

So we stop here for our period of time. With that rule, it is possible to forecast a calendar at least until the year 10,000 and, by that time, many things may have changed, including the calendar!