14. Counting Days with Calendars
Thirty days hath September,
April, June and November;
February has twenty eight alone
All the rest have thirty-one
Except in Leap Year, that's the time
When February's Days are twenty-nine
Between the last minute of December 31st, and the first minute of
February 1st, January provides 31 calendar days.
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Full Calendar Days from start of
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first of
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Dec
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31
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Nov
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30
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Oct
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31
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Sept
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30
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Aug
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31
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July
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31
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June
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30
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May
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31
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Apr
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30
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Mar
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31
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Feb
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28
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Jan
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31
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59
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90
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to start of
first of
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Jan
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Feb
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Mar
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Apr
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May
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June
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July
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Aug
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Sept
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Oct
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Nov
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Dec
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Jan
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In the table cell common in Jan row and Feb column, we put 31 as that is
the number of full days between any time on January 1st, and the same
time of day on February 1st. Likewise, in non-leap years there are
28 full days from a time of day in Feb 1st to the same time of day in
March 1st. We are just going to form the table for non-leap
years. There are similar meanings for all other subdiagonal
entries.
In non-leap years, The number of full days from to the start of Jan
1st to the start of
- Feb 1st is 31
- March 1st is 28 more or 59 as February has 28 days outside of leap
years.
- April 1 is 31 more or 90 as March has 31 days
- May 1st is 30 more or 120 as April has 30 days
- June 1st is 31 more or 151 as May has 31 days
and so on. That gives the entries in the January row of the table:
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Full Calendar Days from start of
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first of
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Dec
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31
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Nov
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30
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Oct
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31
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Sept
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30
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Aug
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31
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July
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31
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June
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30
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May
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31
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Apr
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30
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Mar
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31
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Feb
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28
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Jan
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31
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59
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90
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120
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151
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181
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212
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243
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273
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303
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334
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365
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to start of
first of
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Feb
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Mar
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Apr
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May
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June
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July
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Aug
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Sept
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Oct
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Nov
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Dec
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Jan
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From the table entry in the Jan row and May column, the four months
between Jan 1st and May 1st, that is all of January, February, March
and April, has 120 days.
The rest of the table is filled in a similar manner.
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Full Calendar Days from start of
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first of
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Dec
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31
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Nov
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30
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61
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Oct
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31
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61
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92
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Sept
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30
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61
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91
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122
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Aug
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31
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61
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92
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122
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153
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July
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31
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62
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92
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123
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153
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184
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June
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30
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61
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92
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122
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153
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183
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214
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May
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31
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61
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92
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123
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153
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184
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214
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245
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Apr
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30
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61
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91
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122
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153
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183
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214
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244
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275
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Mar
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31
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61
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92
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122
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153
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184
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214
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245
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275
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306
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Feb
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28
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59
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89
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120
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150
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181
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212
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242
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273
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303
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334
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Jan
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31
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59
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90
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120
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151
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181
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212
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243
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273
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303
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334
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365
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to start of
first of
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Feb
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Mar
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Apr
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May
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June
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July
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Aug
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Sept
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Oct
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Nov
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Dec
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Jan
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Table Use
- Number of days from start (or any time) of May 1st to the start (or
the same time) of Dec 1st is 214.
- The days from start (or any time) of Feb 1st to the start (or
the same time) of Oct 1st are 273 in number in a nonleap year. But
in the leap year, the count would be 273+1 = 274 due to the presence of
an extra day February 29.
- Number of Days from Oct 1st (start) to January 1st (start) is 92
- Number of Days Jan 1st (start) to Aug 1st (start) is 212 in a
non-leap year and 212+1 = 213 in a leap year.
- The number of days from the start of Oct 1st of one year to the
start of Aug 1st in the next year is Number of Days from Oct 1st
(start) to January 1st start plus number of days from January 1st start
to Aug 1st in the next year. That would be 92+ 212 = 304 if the next year
does not have a Feb 29, and 304+1 = 304 if it does.
- The number of days from the start of April 1st to end of August 31st
or the start of Sept 1st is 153. Therefore the number of days from
the start of April 1st to the start of Sept 18th (end of the 17th)
would be 153 + 17 = 170.
- Number of days from Feb 1st (start) in one year to Feb
1st (start) in three years time would be 3 × 365 = 1075 if none of
the years covered is a leap year, and 1075+ 1 = 1076, if any one is a
leap year.
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Secondary
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Algebra
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Calculus Starter Lessons
Calculus Lessons Elsewhere:
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They cover basic topics in ways likely to complement your
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