Is there a fallacy in the Gregorian Calendar?

Question

Which is more accurate in describing a years length, considering the year being not a leap year....365 days, or 52 weeks. I was thinking, let's say someone makes $25 an hour, works 8 hrs. a day and 5 days a week Mon-Fri. To figure out the individuals yearly income, which of the following ways is most correct?

25 d*8hrs.*5days*52weeks or 25d*8hrs*5days*4weeks*12months?

If some months don't have four full weeks, then how can there consistently be 52 weeks in a year?

Where and why did the concept of leap year originate? And does anyone know a brief history of how Western culture came to officially using the Gregorian Calendar as a measure of our days?

Answer 1

No fallacy.  The Gregorian calendar is the most accurate one devised to date.  All calendar's accumulate errors because the rotation of the earth and the length of a year are not in perfect synch.

A year is 365.2424 days long

or 52 weeks and 1.2424 days long

52 weeks is a 'round number'.  365/7 = 52 and one day remainder.  for leap year it is 52 and 2 days remainder.

The Romans figured out a year was not 365 days, but seemed to be 365.25 days.  Since we can't tell the earth to only do a quarter turn at the end of the year and we want to start each new year on a whole day, we just call a year 365 days and every 4 years add a day to account for the accumulated 'error'.  That was the Julian calendar devised in Roman times and used until 1582 (and until 1752 in England and North America)

We use the Gregoran Calender becasue it is the most accurate devised to date.  It does not get off by more than a day for 10,000 years.  The Julian Calendar had a leap year every 4 years.  Since a a year is not quite 365.25, (Its 365.2424) days Every time we add a leap year we get a little off.  After 100 years, we are off a whole day.  In 1542 they figured we were off more than a week.  So with better math and better insturments they recalculated the solar year and found the error.  (365.2424 instead of 365.25).  To get back in synch they just had to skip the accumulated days (in 1582 October 4 was followed by Oct 15).

To keep the corrected calendar accurate they had to change the rules for leap year.  Today leap year is:

Every year dvisible by 4 but not years divisible by 100 unless they are also divisible by 400.

So 1896 was a leap year, 1900 was not a leap year, 1904 was a leap year.

1996 was a leap year, 2000 was a leap year (divisible by 400), and 2004 was a leap year.

2096 will be, 2100 will not be, 2104 will be.

With this scheme the Calendar runs about 10,000 years before its off a whole day.

Answer 2

So many questions.

First, even if all months had a full four weeks, that wouldn't still get you to 52 weeks, since 12 * 4 is only 48.

The year is calculated to represent a rotation around the sun.  It is more like 365.25 days a year, but no one really has a quarter-day, so we add a day in every four years.

If you are salaried you will make the same amount.  If you are hourly, you'll probably pick up an extra day every four years.

The Gregorian Calendar came into use, if I recall correctly, in the  late 1500s (I may be off).  It was an effort to (1) honor a ruler at the time and (2) better adjust to the agrarian (farming) requirements.  Calendars originally were pretty lame for the winter months.  Their use was mainly to coordinate planting and market days.  We later tried to standardize it, and it's been a juggling act ever since.

I once wrote some date-calculation software and in researching it was surprised to find out the shift, particular when calendars changed, and apparently there's an 18 year or something period where people were running on both calendars.

Oh, and to make it more fun, we toss in a "leap second" every once in a while.

Some months have nearly 5 weeks, many more are less, but trust me, it all works out to 52 weeks (with the occasional leap day).