Math Is Fun Forum

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Perpetual calendar

Hi all,

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

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"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

Hi gAr;

What anomalous behaviour? Do you have an example?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

Not able to find any!
When posting, I believed everything was fine.

---

"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."

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Perpetual calendar

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

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

That should affect months after february, not before.

---

"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."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,618

Re: Perpetual calendar

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

Hi Bob,

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

---

"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."

Bob

Administrator

Registered: 2010-06-20

Posts: 10,618

Re: Perpetual calendar

OK.  I'm impressed!   

But why not yet perfect? 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

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!

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

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!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

Hi bobbym,

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

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

Hi;

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

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Perpetual calendar

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?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

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.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

Hi 123ronnie321,

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

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"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."

123ronnie321

Member

Registered: 2010-09-28

Posts: 128

Re: Perpetual calendar

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=

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

Hi,

Thanks for telling, I guess it was not followed those days.
I'll look at some history.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

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.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

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.

---

"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."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Perpetual calendar

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.

http://en.wikipedia.org/wiki/Calculatin … f_the_week

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Perpetual calendar

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.

---

"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."