Re: Date and time on Cindu: yearly update

To be a little more specific:

If year N is leap, then either N+6 or N+7 is leap.

If N+6 is leap, then either N+12 or N+13 is leap.

But if N+7 is leap, the next leap year after that has to be N+13, not N+12.

Either way, N+19 is leap and the same pattern repeats.

That means a way to figure out if a year is leap directly, without
having to count to it from a known leap year, is to divide the year
number by 19 and look at the remainder.

Take 700, 706, and 713, which we know to be leap.  700 / 19 is 36 with
a remainder of 16.
706 / 19 is 37 with a remainder of 3. And 713 / 19 is 37 with a remainder of 10.

So any year whose New Count year number leaves a remainder of 3, 10,
or 16 when divided by 19 is leap.  For instance, years 3, 10, and 16
were the first three leap years of the New Count.

You can imagine a big clock with numbers that run 1-19 instead of
1-12, with a "year hand", and little stars by 3, 10, and 16.  Whenever
the year hand is pointing at a star, the year is leap.

Now, calculating remainders is something that computers are good at,
but they rarely offer an easy way to do it to the non-programmer.  In
your typical calculator (physical or virtual), if you divide 700 by
19, you'll get something like"36.842105", which isn't that helpful for
our purposes  To figure out the remainder in that case, you can just
subtract the part before the decimal and then multiply back by 19,
rounding to the nearest whole number to make up for loss of precision
in the calculator:
 700 / 19 = 36.842105 - 36 = .842105 * 19 = 16.000001 => 16.


On 5/19/08, Mark J. Reed <markjreed@...> wrote:
> Ok, sorry, I'm being confusing again.
>
> You have some year that is leap.  Call it year number N.  Now,
> depending on the particular year, the next leap year might be either
> N+6 or N+7.  And the one after that could be either N+12 or N+13.
>
> But no matter what N is, the *third* leap year after it will always be
> N+19.  Pick any leap year N and year N+19 is also a leap year.  That's
> what I meant when I said there was a 19-year cycle.
>
> More later - must take kids to school.
>
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Mark J. Reed <markjreed@...>

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