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Why the years 100, 200 and 300 are not leap years? 400th year is a leap year |
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| Example question: After 1*365 + 1/4 days earth completes 1 round After 2*365 + 2/4 days earth completes next round After 3*365 + 3/4 days earth completes next round After 4*365 + 4/4 which is 1 day earth completes next round Hence 4th year is a leap year Hence 8th year is a leap year .. Hence 96th year is a leap year Hence 97th year is not a leap year Hence 98th year is not a leap year Hence 99th year is not a leap year But why 100th year is not a leap year? |
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| 1 year is equal to | 365 + 97/400 days | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 365 + 0.2425 days | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4 year is equal to | 4*365 + 4*(97/400) days | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4*365 + 4*0.2425 days | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 4*365 + 0.97 days and not 4*365 + 1 day which is 4*365 + 1 day - 0.03 day Hence for each leap year 0.03 day is added extra. |
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| Assume that I am making new calander format to have 100 leap year. So 100 years have 25 leap years. |
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| For 100 years(due to 25 leap years) 0.03 * 25 day are added extra 0.75 day added extra during first 100 years. |
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| Assume that I am making new calander format to have 200 as leap year. So from 101 to 200 years have 25 leap years. |
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| From 101 to 200 (due to 25 leap years) 0.03 * 25 days are added extra 0.75 day added extra during next 100 years (from 101 to 200). 0.75 + 0.75 days added extra from 01 to 200 years 1.50 days added extra from 01 to 200 years |
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| Assume that I am making new calander format to have 300 as leap year. So from 201 to 300 years have 25 leap years. |
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| From 201 to 300 (due to 25 leap years) 0.03 * 25 days are added extra 0.75 day added extra during next 100 years (from 201 to 300). 0.75 + 0.75 + 0.75 days added extra from 01 to 300 years 2.25 days added extra from 01 to 300 years |
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| Assume I am following same current calenter format for the year 400 to be leap year. So from 301 to 400 years have 25 leap years. |
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| From 301 to 400 (due to 25 leap years) 0.03 * 25 days are added extra 0.75 day added extra during next 100 years (from 301 to 400). Hence 0.75 + 0.75 + 0.75 + 0.75 days added extra from 01 to 400 years Hence 3 days added extra after 400 years |
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| This is the reason making 100, 200, 300 as not a leap year, for reducing that 3 days. However this description based on assumption given above Assume I am following... |
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| Let us re calculate without assumption. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| From 01 to 100 years 24 leap years are there ( from 01 to 96 years) For these leap years, 0.03 days were added extra for 24 times. So 24*0.03 were added extra. Hence 0.72 days were added extra. However for years 97,98,99 and 100, need to add 0.97 days. So (0.97 - 0.72) day needs to be added during the year 100. which is (0.25) day needs to be added during the year 100. |
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| Like the same, 0.25 day needs to be added during the year 200 for leap years from 101 to 200. Since old addition 0.25 was not done during 100, adding that for the year 200. So 0.50 day needs to be added during the year 200. |
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| Like the same, 0.25 day needs to be added during the year 300 for leap years from 201 to 300. Since old addition 0.50 was not done during 200, adding that for the year 300. So 0.75 day needs to be added during the year 300. |
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| For years from 301 to 396, 24 leap years are there. So, 24*0.03 days were added extra. which is 0.72 days were added extra. Hence deducting 0.72 from 0.75 deducting from 0.75 since 0.75 was not added for the year 300. That is equal to 0.75 - 0.72 which is equal to 0.03 This 0.03 day needs to be added during the year 400. |
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| For following years need to add 0.2425 days 97 0.2425 98 0.2425 99 0.2425 400 0.2425 and 0.03 Here adding 0.03 due to exception for the years from 01 to 396 |
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| Based on that, for the year 400, need to add the following: 0.2425 + 0.2425 + 0.2425 + 0.2425 + 0.03 This is equal to 1 day. Hence making 400 as a leap year. That's why we celebrated year 2000 as a leap year. |
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| Hence next round off of leap year exception will be following year: 2400 |
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| All Gregorian calendar description here are based on the assumption => | 1 year is equal to 365 days + 97/400 days 1 year is equal to 365 days + 0.2425 days 1 year is equal to 365 days + 0.2425*24 hours 1 year is equal to 365 days + 5.82 hours 1 year is equal to 365 days + 5 hours and 0.82 hours 1 year is equal to 365 days + 5 hours and 0.82*60 minutes 1 year is equal to 365 days + 5 hours and 49.2 minutes 1 year is equal to 365 days + 5 hours and 49 minutes and 0.2 minutes 1 year is equal to 365 days + 5 hours and 49 minutes and 0.2*60 seconds 1 year is equal to 365 days + 5 hours and 49 minutes and 12 seconds 1 year is equal to 365 days + 5 hours 49 minutes 12 seconds. |
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Also nano seconds taken by earth(if any) to complete one rotation around the sun are not taken into consideration. Hence I feel this inclusion might be required during the year 2400. Used the word might since written taken by earth(if any). |
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All existing operating systems can be advanced to include the exceptions for handling time exceptions: 1. from birth and even after death, 2. shared market date/timings 3. fixed deposit 4. mutual fund... 5. national savings certificate 6. all types of insurance 7. all types of loans Selected Programming Languages which is referring programming languages of all operating systems(AIX/HP-UX/Linux(all Linux or UNIX oriented operating system)/SunOS/Windows) Operating system names displayed here are sorted names.
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