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I have a related question about the 400 rule. I recently (last night) got in to a bit of a discussion about leap years and said that only those centuries which are divisible by 400 are leap years (Leap Centuries) but those not divisible are not leap years. But I added: That year zero (Year X(ex) was not a leap year because zero is not divisible by 400. I was immediately asked what I meant by year zero (X). I said, I meant “the year when Christ (Χριστός) was born”. The year preceding 1 AD. I knew when asking that some of my friends have said that year zero doesn't exist. So that was partly why I had been considering it. Then yesterday I was discussing when leap years occur and how some are and some aren't according to the 400 year rule. So the years 2400AD, 2000AD, 1600AD, 1200AD, 800AD, 400AD will be or were leap years and 400BC and 800BC would have been if the rule existed during those times. Logically year Zero between 400AD and 400BC would follow that general mathematical sequence and so at first I thought that therefore obviously the year of the birth of Christ (Χριστός) would have been a leap year. (I also was aware some people say he was born 2BC, but that did not come in to it, because it was a question of mathematics, Leap years and the leap year rule (hypothetical, if he had been)). So I was at first happy to believe the year of his birth (Year zero) was in deed a leap year. About thirty minutes later I was applying the 400 rule when suddenly I realised that zero (naught) is not divisible by 400. So there fore it is an exception to the 400 rule. So 12BC, 8BC, 4BC, 4AD, 8AD and 12AD were leap years but year Zero was not as Zero was not divisible by 400. But then my friend (Amazing mathematical Abilities (Teaches mathematics) said that Zero was divisible by 400. He briefly and swiftly explained an example ( something about vectors) an explanation which was too brief and swift for me who by then was experiencing difficulties with what he had just said. So he seemed to contradict my basic understanding that nothing divided by anything is nothing.
I respect his abilities at maths as I know they are far greater than mine in many ways. But I was still interested to know if I was wrong or my basic education was wrong and so therefore fore he was right. I started a bit of research and found some sites would side with 0/x=0 where as some of the other more advanced sites seemed to make different statements about various branches of mathematics which all seemed above my abilities as I have not the time for an in-depth study of those higher aspects. I became more focused on the concept of 0/x=0 or undefined, pertaining to the impossibility of the concept and so mathematicians had left it undefined as a suitable definition. That seemed to suit my purpose of the mathematics. It left me still with the basic concept that zero divided by any number equals zero. So my friend could also be right as it is right for some maths and for other maths 0/x=0 is considered correct. But he was really saying that for the purpose of leap years, “year-zero” would be a leap year contrary to my mathematical belief that zero is not divisible by 400.
So I am still uncertain which way to decide. So I decided to ask others for their views. I realise some may say there is no year zero so the question is unrealistic. I would accept that as a realistic and valid answer as I am also yet undecided if there was a year zero or not for the purpose of some calculations. But for other situations I am sure there is a year zero. Or there is a year before the birth of Christ. (Well maybe there is, (Just depends how far a person wants to go or something).
So that is the question pertaining to leap years and the rule of dividing by 400. Is year zero (which I call year “X” some times) divisible by 400? Was that millennial year a leap year like the year 2000AD and 2000BC (but not 1000AD or 1000BC)? So sequentially leap years were: -20BC, -16BC, -12BC, -8BC, -4BC, 0?, +4AD, +8BAD, +12AC. +16AD, +20AD...ETC. ETC.? (AD could be replaced by CE (Christian Era or Common Era))? Thank you.
Mike,
By definition: divisible means an integer is capable of being divided by another integer without a fractional remainder.
or you can think of it as being able to divide a number into equal "whole" parts with no remainder.
The number "zero" can be divided by "any number" into equal parts of "zero". The only exclusion is you cannot divide zero by itself. That is undefined.
So the answer to "zero" divided by 400 is "zero" with no remainder and therefore "zero" is divisible by 400.
ASP
There was no year 0. The year before 1 was year -1.
I apologize in advance for any ambiguity.
"With this rule, 97 leap days are added every 400 years, which means the average length of year in the Gregorian calendar is 365.2425 days."
If the rule off 400 is applied to centuries, would that not leave 96 leap years in a 400 year period instead of 97?
e.g. 100/4 = 25
However, since 100 isn't divisible by 400 creating a whole number, wouldn't we say 24 leap days happen over a 100 year span?
e.g. 24 x 4 Centuries = 96 Leap Days over a 400 year period?
02/13/2024 good going love it happier, happier ,,,,birthday to you all and everyone else and God,, loves us all, that use it Right ,,,.
I think I see where you have miss calculated.
So if we use the divisible by 400 rule we have one century in 4 being a leap year where as the other three are not. So the year 1600 would have been a leap year and 1700, 1800, and 1900 were not.
So there are 25 leap years in every century which starts with a leap year (EG 1600, 2000, 2400)and only 24 leap years in the century's which are not divisible by 400. So 3 times 24 + (1 Times 25) equals 97. I think you just forgot to add the leap year for the century beginning with a leap year. so you went for, “times 25” instead of “3 times 25 plus 1 times 24”.
In twenty centuries such as between the years 2000 and 4000 there would be only 5 Centuries which begin on a Leap year.
Hold on what u mean by something divisible by 400?
My cousin is 15 but really 3years old
Hi, who came up with the idea of Leap Year, and that it should be in February and no other month like July? I understand that there are different days in each months are, 31, 28/29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 days/month. Instead of a leap year, the days in August could be 31, then the series goes on......
August has have 31 days for many many leap and common years
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