*** Friday, the 13th ***
Today, it’s *not* Friday, the 13th - a day usually associated with bad luck. I will not look into the superstition, but instead into a little known fact:
The 13th of every month falls more often on a Friday than on every other day of the week.
Sounds strange, doesn't it?
So, let’s have a look into the #math, shall we?
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** The Basics **
Our calendar is called the “Gregorian” after Pope Gregor XIII, who introduced it in the year 1582, at least for the Catholic World.
Others joined the party later (e.g. England - surprise!)
It works like this: a normal year has 365 days, with February having 28 days every 4th year is a leap year, with 366 days and February having 29.
Every century (100 years) ends with a normal year instead of a leap year. We call these centuries short centuries.
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Every 4th century (long century) ends with a leap year, instead of a normal year.
That’s it. Thus, we call a cycle of 400 years a "full cycle“.
The first thing to observe is:
* Every consecutive full cycle starts on the same weekday! *
This is easy to see. We only have to prove that the number of days in a full cycle is a multiple of 7:
We could just count the days and look whether the number is divisible by 7, but we're doing it the fancy way (skip that part, if you like):
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In the image is the Math.
The next thing to look at, is on which weekdays fall the 13th of each month, depending on the day the year begins.
In order to make things easier, we’ll let our years start in March (like the Romans did). By doing so, we don’t have to distinguish between leap years and normal years, because the leap day is always the last day of the year.
We also don’t need to bother with long and short centuries, as only the very last century is a long one.
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Now, we need to check how often the 13th of March falls on which weekday in a century. A quick look into the calendar shows us:
The 13th of March 2000 (the beginning of a new full cycle) was a Monday, the weekday 0.
We remember that after a normal year, the next one starts with the following day and after a leap year with the day after.
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When we write down the weekdays of the 13ths of March of a century, we can look for weekdays which might appear more often than others, and we learn that, when the first 13th in a year is a Monday (0), we have an extra year starting on a Tuesday (1) and one on a Thursday (3).
Now, it’s time to remember that the very last year of the century isn’t a leap year (we only look at short centuries), so the 13th of March 2100 falls on a Saturday (5), not on a Sunday.
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2200 on [5+5] = [7+3] = 3, Thursday
2300 on 1, Tuesday
** Harvest Time! **
Now we know which type of years occur more often than others:
2000s 0: 1,3
2100s 5: 6,1
2200s 3: 4,6
2300s 1: 2,4
In total: 1,1,2,3,4,4,6,6
Remember the Excess function, we defined before (toot 5)? We can now sum up the extra weekdays:
** Conclusion **
We see that the day 4 (Friday) appears more often than all other weekdays during a full cycle of 400 years.
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Does this have anything to do with bad luck?
Probably not, but now you know:
If you ever felt that Friday the 13th comes all the time:
There’s some truth to it!
** Addendum **
In Spanish-speaking countries and Greece, the day of bad luck is Tuesday, not Friday, the 13th.
8/8 (end)
@mina OK, either the whole 13th babble is bullshit and it is the 14th in reality, or the whole math was wrong and today is the 13th. In any case so much stuff went south today, that I'm sure today is the unlucky day. Therefore, I decided to stay home for the rest of this Friday.
PEOPLE BEWARE!