manesiro
04-July-2006, 02:22 PM
Surplus Three Days in 2000 Years
We know that Earth takes 365 days 5 hours 48 minutes and 46 seconds in its one revolution round the Sun. Thus one Solar Year consists 365.2422 days. In 10000 years, there will be 3652422 days and in 2000 years there must be 730484.40 days.
Historically, we know that
1. In Julian calendar, every 4th year was a leap year having 366 days. Thus total numbers of days in each century were 36525.
2. In year 1582, 10 days were deleted from the month of October.
3. Year 1600 was a leap year having 366 days.
4. Years 1700,1800 and 1900 were having 365 days each.
5. Year 2000 was a leap year.
Calculating days from first day of first century to 31-12-1500
== 36525*15
=547875
The numbers of days from 1-1-1501 to 31-12-1600 were 36515.
The numbers of days from 1-1-1601 to 31-12-1700 were 36524.
The numbers of days from 1-1-1701 to 31-12-1800 were 36524
The numbers of days from 1-1-1801 to 31-12-1900 were 36524
The numbers of days from 1-1-1901 to 31-12-2000 were 36525
Total numbers of days from 1-1-01 to 31-12-2000 are 730487
Finding week-day of any date
We know 1st January 2001 fell on Monday. If we divide 730487 by 7, we get 2 as remainder. Thus weekday of 1st month of 1st year of 1st Century (1-1-01) was Saturday.
There were 25 leap years of 366 days in each Century from 1st to 16th. All these centuries from 1st to 15th consisted of 36525 days. The 16th century consisted of 36515 days. There were 24 leap years in 17th, 18th and 19th Centuries. These centuries consisted of 36524 days. Again, 25 leap years in 20th Century as year 2000 was leap year and thus 20th century had 36525 days.
The days will shift by 6 days if previous century consists 36525 days and will shift 5 days if previous century consists of 36524 days as we can see by dividing total number of days of previous century by 7.
Thus
1-1-01 Saturday
1-1-101 Friday
1-1-201 Thursday
1-1-301 Wednesday
1-1-401 Tuesday
1-1-501 Monday
1-1-601 Sunday
1-1-701 Saturday
1-1-801 Friday
1-1-901 Thursday
1-1-1001 Wednesday
1-1-1101 Tuesday
1-1-1201 Monday
1-1-1301 Sunday
1-1-1401 Saturday
1-1-1501 Friday
As we know 16th century was of 36515 days, so the days will shift 3 days and
1-1-1601 Monday
17th, 18th and 19th centuries were of 36524 days and so the days will shift by 5 days and
1-1-1701 Saturday
1-1-1801 Thursday
1-1-1901 Tuesday
The 20th century was of 36525 days; the days will shift again 6 days
1-1-2001 Monday
After finding the day of first day of each century, we can find the day of 1st of any year in that century. (The 16th century has special features and will be described later)
We will take number of years and add to it number of leap years and then divide it by 7 , thus we will know the shift of days from the day of 1st day of that century.
As we know that 1-1-1901 was on Tuesday.
We can know day of 1-1-1991 by adding 22 leap years to 90 years and dividing this figure of 112 by 7.We get 0 as remainder. Thus 1-1-1991 will fall on same day-Tuesday.
After finding day of 1st January of any year, we can find the day of 1st of other months.
1st February +3
1st March +3 if non-leap year
+4 if leap year
1st April +3 to 1st March
1st May +2 to 1st April
1st June +3 to 1st May
1st July +2 to 1st June
1st August +3 to 1st July
1st September +3 to 1st August
1st October +2 to 1st September
1st November +3 to 1st October
1st December +2 to 1st November
The day of 1st of any month is also the day of 8th, 15th, 22nd and 29th of that month. Thus we can find day of any date of any month of any year of any century.
Special case of 16th Century
We know day of 1-1-1501 was Friday.
We can find day of 1-1-1582 by adding 20 leap years to 81 years and dividing by 7 thus we get 3. Thus day of 1-1-1582 will be Monday.
1-2-1582 Thursday
1-3-1582 Thursday
1-4-1582 Sunday
1-5-1582 Tuesday
1-6-1582 Friday
1-7-1582 Sunday
1-8-1582 Wednesday
1-9-1582 Saturday
1-10-1582 Monday
1-11-1582 Monday (because October 1582 had 21 days and so there will be no shift from day of 1st October)
1-12-1582 Wednesday
1-1-1583 Saturday
As number of days in 1582 were 255 (10 days deleted from month of October)
1-1-1584 Sunday
1-1-1585 Tuesday because 1584 was leap year
1-1-1586 Wednesday
1-1-1587 Thursday
1-1-1588 Friday
1-1-1589 Sunday because 1588 was leap year
1-1-1590 Monday
1-1-1591 Tuesday
1-1-1592 Wednesday
1-1-1593 Friday because 1592 was leap year
1-1-1594 Saturday
1-1-1595 Sunday
1-1-1596 Monday
1-1-1597 Wednesday because 1596 was leap year
1-1-1598 Thursday
1-1-1599 Friday
1-1-1600 Saturday
1-1-1601 Monday because 1600 was a leap year
From here, we join the mainstream as described above.
Thus we can find the day of any date of any month of any year of any century.
We know that Earth takes 365 days 5 hours 48 minutes and 46 seconds in its one revolution round the Sun. Thus one Solar Year consists 365.2422 days. In 10000 years, there will be 3652422 days and in 2000 years there must be 730484.40 days.
Historically, we know that
1. In Julian calendar, every 4th year was a leap year having 366 days. Thus total numbers of days in each century were 36525.
2. In year 1582, 10 days were deleted from the month of October.
3. Year 1600 was a leap year having 366 days.
4. Years 1700,1800 and 1900 were having 365 days each.
5. Year 2000 was a leap year.
Calculating days from first day of first century to 31-12-1500
== 36525*15
=547875
The numbers of days from 1-1-1501 to 31-12-1600 were 36515.
The numbers of days from 1-1-1601 to 31-12-1700 were 36524.
The numbers of days from 1-1-1701 to 31-12-1800 were 36524
The numbers of days from 1-1-1801 to 31-12-1900 were 36524
The numbers of days from 1-1-1901 to 31-12-2000 were 36525
Total numbers of days from 1-1-01 to 31-12-2000 are 730487
Finding week-day of any date
We know 1st January 2001 fell on Monday. If we divide 730487 by 7, we get 2 as remainder. Thus weekday of 1st month of 1st year of 1st Century (1-1-01) was Saturday.
There were 25 leap years of 366 days in each Century from 1st to 16th. All these centuries from 1st to 15th consisted of 36525 days. The 16th century consisted of 36515 days. There were 24 leap years in 17th, 18th and 19th Centuries. These centuries consisted of 36524 days. Again, 25 leap years in 20th Century as year 2000 was leap year and thus 20th century had 36525 days.
The days will shift by 6 days if previous century consists 36525 days and will shift 5 days if previous century consists of 36524 days as we can see by dividing total number of days of previous century by 7.
Thus
1-1-01 Saturday
1-1-101 Friday
1-1-201 Thursday
1-1-301 Wednesday
1-1-401 Tuesday
1-1-501 Monday
1-1-601 Sunday
1-1-701 Saturday
1-1-801 Friday
1-1-901 Thursday
1-1-1001 Wednesday
1-1-1101 Tuesday
1-1-1201 Monday
1-1-1301 Sunday
1-1-1401 Saturday
1-1-1501 Friday
As we know 16th century was of 36515 days, so the days will shift 3 days and
1-1-1601 Monday
17th, 18th and 19th centuries were of 36524 days and so the days will shift by 5 days and
1-1-1701 Saturday
1-1-1801 Thursday
1-1-1901 Tuesday
The 20th century was of 36525 days; the days will shift again 6 days
1-1-2001 Monday
After finding the day of first day of each century, we can find the day of 1st of any year in that century. (The 16th century has special features and will be described later)
We will take number of years and add to it number of leap years and then divide it by 7 , thus we will know the shift of days from the day of 1st day of that century.
As we know that 1-1-1901 was on Tuesday.
We can know day of 1-1-1991 by adding 22 leap years to 90 years and dividing this figure of 112 by 7.We get 0 as remainder. Thus 1-1-1991 will fall on same day-Tuesday.
After finding day of 1st January of any year, we can find the day of 1st of other months.
1st February +3
1st March +3 if non-leap year
+4 if leap year
1st April +3 to 1st March
1st May +2 to 1st April
1st June +3 to 1st May
1st July +2 to 1st June
1st August +3 to 1st July
1st September +3 to 1st August
1st October +2 to 1st September
1st November +3 to 1st October
1st December +2 to 1st November
The day of 1st of any month is also the day of 8th, 15th, 22nd and 29th of that month. Thus we can find day of any date of any month of any year of any century.
Special case of 16th Century
We know day of 1-1-1501 was Friday.
We can find day of 1-1-1582 by adding 20 leap years to 81 years and dividing by 7 thus we get 3. Thus day of 1-1-1582 will be Monday.
1-2-1582 Thursday
1-3-1582 Thursday
1-4-1582 Sunday
1-5-1582 Tuesday
1-6-1582 Friday
1-7-1582 Sunday
1-8-1582 Wednesday
1-9-1582 Saturday
1-10-1582 Monday
1-11-1582 Monday (because October 1582 had 21 days and so there will be no shift from day of 1st October)
1-12-1582 Wednesday
1-1-1583 Saturday
As number of days in 1582 were 255 (10 days deleted from month of October)
1-1-1584 Sunday
1-1-1585 Tuesday because 1584 was leap year
1-1-1586 Wednesday
1-1-1587 Thursday
1-1-1588 Friday
1-1-1589 Sunday because 1588 was leap year
1-1-1590 Monday
1-1-1591 Tuesday
1-1-1592 Wednesday
1-1-1593 Friday because 1592 was leap year
1-1-1594 Saturday
1-1-1595 Sunday
1-1-1596 Monday
1-1-1597 Wednesday because 1596 was leap year
1-1-1598 Thursday
1-1-1599 Friday
1-1-1600 Saturday
1-1-1601 Monday because 1600 was a leap year
From here, we join the mainstream as described above.
Thus we can find the day of any date of any month of any year of any century.