please empty your brain below
But, I'm not understanding number 16: how leap years are more likely to fall on Monday, Wednesday and Friday and least likely to fall on Tuesday and Thursday?
I'm thinking it must be to do with multiples of 7s and 4s with some missed out for the centuries, from when it started in 45BC?
Blue Witch, if you look at the links I just did it also shows why the 29th falls more on some days of the week than others.
However if the pattern did repeat (e.g February 29th 1612 occurred on the same day of the week as February 29th 2012 - which I can't be bothered to work out) it is probably true that some days are more likely than others.
Of course it may just be similar to the lottery argument. Just because one number has come up more frequently in the past it doesn't mean it will do so in the future.
In any case occasionally, once in every few thousand years, a leap day may be added or cancelled to get everything in sync again in which case ultimately no day of the week will prevail as being more common.
Or as my biology teacher put it, all fertile women are pregnant for two weeks in every month whether they conceive or not!
Anyway, great post DG. :-)
The thing is, it's not exactly a quarter of a day every year - a year is 365.242 days, which means that 24.2 days need to be added (on average) each century.
If the years divisible by 100 were all leap years, then 25 days would be added per century, which is almost one day too many. And if the '00 years were all not leap years then 24 days per century are added.
So, the rule that's used is that years divisible by 100 are not leap years, unless they're also divisible by 400 (i.e. 2000 was a leap year, but 1900 wasn't and 2100 won't be), so over a 400-year period there are 97 leap years, or an average of 0.2425 days per year.
(The difference of 0.0005 days per year is less than the difference between the different ways of measuring a year - even such simple things as weather you measure from one summer solstice to the next or from one winter solstice to the next don't give the same answer.)
Interestingly, the Wikipedia link in No. 24 that Barry suggests says, "The Gregorian calendar repeats itself every 400 years, which is exactly 20,871 weeks including 97 leap days. Over this period, February 29 falls on Sunday, Tuesday, and Thursday 13 times each; 14 times each on Friday and Saturday; and 15 times each on Monday and Wednesday."
Which is slightly different again to DG's statement at No. 16. "The most likely days of the week for February 29th to fall are Monday, Wednesday and Friday. The least likely are Tuesday and Thursday."
Someting's not quite right somewhere, and I still haven't found an answer I can understand (but, I think that it *is* quite different to the lottery PofP because you've got fixed parameters - I still think 4s and 7s - here: what falls when is not a chance effect as with lottery balls)
On a side note by baker has his birthday today. ;-D
dg writes: From everything I've seen online, UK leaplings have to wait for March 1st for their legal birthday in non-leap years. But I'd like to see that in black and white somewhere.
What I was trying to say was that a lot of people think if something has happened more often in the past it will happen more often in the future. Clearly this is not always true and the lottery is a classic example of this. Of course there are bound to be some balls that have appeared more frequently than others but it doesn't mean they will do so in the future. Nor is the converse argument that they will appear less frequently to even things out true either.
But you are correct. A lottery is a chance event and so is different to leap years which I now know has a fixed underlying pattern.
Your first line from Wikipedia is the critical one "The Gregorian calendar repeats itself every 400 years, which is exactly 20,871 weeks including 97 leap days"
Its a bit, but not quite, like the person who arrives at a random time at a railway station. The fast trains leave at 25 and 55 minutes past the hour and the slow ones on the hour and half hour. Despite arriving at random times the underlying pattern of events means they will catch the fast train five times out of six.
http://en.wikipedia.org/wiki/Leap_second
A positive leap second will be introduced at the end of June 2012.
The sequence of dates of the UTC second markers will be:
2012 June 30, 23h 59m 59s
2012 June 30, 23h 59m 60s
2012 July 1, 0h 0m 0s
So we get a two leaps in 2012!
http://www.bbc.co.uk/news/science-environment-16625614
Incidentally, is it just chance that the leap years are those divisble by 4? The AD system of counting was devised six centuries after the Romans set the four year leap year pattern. (Dionysius Exiguus, c525AD,
12 - there is some doubt about how long Frederic had to go to reach his 21st birthday. Beacause 1900 was not a leap year, it would in fact be 67 years in the future unless he was born in the first 16 years of the 19th century, or in the 20th. He himslef calculates it will be in 1940, placing the action in 1873 or 1877 (depending on whether he knows about 1900), but this is inconsistent with the Major General making a reference to G&S's earlier operetta "That infernal nonsense Pinafore", which did not come out until 1878.
One also wonders why the M-J's daughters thought it a good idea to go for a swim on the Cornish coast at the end of February?
16 - the reason for the imbalance is because 400 years happens to be a whole number of weeks, and thus the calendar repeats every 400 years, not every 2800, and not every permutation is cycled through. For example Leap Year Day in a century year is always a Tuesday! In the same way, if there were 364 days in a year, your birthday would always fall on the same day of the week, instead of stepping through a 4x7(x400)cycle. dates.
I read once that the 13th of the month falls on Fridays more often than any other day of the week.
28. What actually happened (I think) was that Sweden decided in 1700 to convert from Julian to Gregorian, and so had 28 days in February that year. However, they did not omit the other ten days needed to realign with the Gregorian calendar. (Apprently the intention had been to have no leap years between 1700 and 1740, but in the event 1704 and 1708 were leap years (presumably someone either forgot or changed their mind))
In 1712 it was decided instead to revert to the Julian calendar, and so February 1712 had an extra day (30th) to compensate for the one omitted in 1700.
Sweden eventually converted in 1753.
http://www.bbc.co.uk/news/magazine-17203353
Yes, sorry, the original information I posted was wrong (warning: never trust the internet). But I've independently checked this Wikipedia claim...
"The Gregorian calendar repeats itself every 400 years, which is exactly 20,871 weeks including 97 leap days. Over this period, February 29 falls on Sunday, Tuesday, and Thursday 13 times each; 14 times each on Friday and Saturday; and 15 times each on Monday and Wednesday."
...and that's absolutely correct.
http://www.bbc.co.uk/news/uk-england-bristol-17220978
TridentScan | Privacy Policy