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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi all,

*Last edited by gAr (2011-07-06 23:32:20)*

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi gAr;

Have you heard of Zeller's congruence? Yours is similar in some ways.

Would like to move this over to "Formulas." I do not think we have one in there.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Thanks for telling about that, I didn't know such a formula existed.

Okay, you may move it to "formulas".

I still can't explain the strange behaviour of my formula during leap years!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi gAr;

What anomalous behaviour? Do you have an example?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

The behaviour which I mentioned in the postscript of post #1.

For leap years, subtraction is required only for the first 2 months, then it's alright!

E.g,

2004/01/13 - 3

2004/02/13 - 6

2004/03/13 - 6

May require a small correction, but unable find that.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

I can not explain that either. Have you found any mistakes that the method makes?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Not able to find any!

When posting, I believed everything was fine.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

In leap years February makes its contribution of one extra day - the 29th of Feb.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

That should affect months after february, not before.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

hi gAr

Is this your own formula and you want to verify that it works?

OR

a formula that you have found and you want to know why it works?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi Bob,

It's my own formula which I derived today, not perfect yet.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

OK. I'm impressed!

But why not yet perfect?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Thank you!

I think it's because the sequence I'm considering adds the extra day of the leap year to the next year, and not to the months after february of the leap year.

It may require some rearrangement of months, like moving out the first two months to the previous year, and moving in the two months of the next year, hmmm let me check that way!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi gAr;

In Zeller's the year starts on Mar 1. That is a clue as to why you add to your first two. They are really the last two monts of the year!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Yes, I'm thinking of that, we posted at the same time!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

Yes, he has Jan and Feb as the last 2 months of the previous year.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

Hi gAr,

If we consider 2 cases, the years 400 and the year 2000. then y would be the same for both cases. But that would be a contradiction right?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

You are not thinking in terms of mods. The days of the week could be the same for groups of years. There is no contradiction.

Modular equations can have an infinite number of solutions because as far as mod 7 is concerned { ...,-5,2,9,16,...} are all the same.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi 123ronnie321,

According to the rule to find leap year, the same set of calendars repeat every 400 years.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

I am sorry. You are right!

Is there something wrong with this website -

http://www.calendarhome.com/cgi-bin/tyc … ppresshol=

http://www.calendarhome.com/cgi-bin/tyc … ppresshol=

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Thanks for telling, I guess it was not followed those days.

I'll look at some history.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

The method you are using may not apply for those two dates. 400 AD is the Julian calendar and 2000 AD is the Gregorian. In 1752 they changed from the Julian to the Gregorian. About 12 days were lost. That might be the discrepancy.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Yes, thanks.

Would there be any further correction, say after 10000's of years.

I checked for 6666A.D, it works fine for that year.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

I do not think so. Except that every 3000 years or so there is a loss of a day using the Gregorian calendar.

This is what I am using you will see a similarity with yours.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay.

I'll continue with the formula then. Let past 1600 be whatever it was!

Sakamoto's algorithm works great, very similar to mine!

I'll stop the duplication of work.

Thank you.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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