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How is the "perpetual calendar" composed?

  • How is the "perpetual calendar" composed?

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    A "perpetual calendar" usually means tables( or devices based on them), with which you can quickly establish which day of the week falls on one or another calendar date. At one time, this task was solved on the basis of the above calendar cycles. It consists of two dimensions."Horizontally" it is necessary to establish correspondence of days of the week to the numbers of months during a certain calendar year."Vertically" it is necessary to find changes in this distribution in the transition from year to year, from century to century.

    Construction of the "eternal calendar" is carried out in two ways: with the help of e-mail( according to the Western European tradition - calendar) letters and by using monthly coefficients.

    With the help of a yulette. It has already been noted that seven literal( calendar) letters are, as it were, "forever" painted in a cyclic sequence according to the numbers of calendar months. Therefore, if only the day of the week is found for at least one calendar date of the given year, that is, if at least one letter of contact is compared with the day of the week, then, according to Table, the change of the days of the week for everythingof the year.

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    For the Julian calendar, the change takes place during the 28-year solar cycle is shown in Table.7( respectively, Western European Sunday letters - in the table), and their significance for each specific year of Constantinople and our era - in Table. It was not difficult to compose the first. In considering the second, it should be recalled that in the 100 Julian years, there are 36,525 days or 5,217 weeks and 6 days. Therefore, in each subsequent century, say March 1, and in general all the numbers of the month, one day is earlier than in the corresponding year of the previous century. In turn, the 700 Julian years are 255,675 days or 36,525 weeks or 25 full 28-year cycles. It follows that the distribution of the voucher according to the dates of the Julian calendar every 700 years is completely repeated. Having painted the same inside the same century, it is not difficult to compile the same table for all the others: with an increase in the number of centuries per unit, it is necessary to move one line to the left in the line of the letters of letters, also carrying out a cyclic transition from the 7th row to the top of the table.to the 1 st, bottom.

    After the table.was compiled( and this happened many hundreds of years ago), it remained to make the final step-to combine with it other tables. More precisely, proceeding from odn. Table. It was necessary to take the distribution of the days of the week according to the numbers of the months corresponding to one or another party, and add it to the other tables. Of course, several generations of computers worked on the compilation of such an eternal calendar, but the result, as we see, turned out to be quite good. In addition, restless inventors discovered that instead of the letters of letters, you can use the same days of the week, and this made the table even more compact. The table is equally used to determine the day of the week by the dates of the Gregorian calendar. Therefore, it is appropriate to recall here that 400 years of this calendar contain 146,097 days, that is, exactly 20,871 days. As a result, the cycle is delivered, and therefore the schedule of the days of the week by the number of months in this calendar is repeated after 400 years. In this period of time, each of the three centuries contains 5217 weeks and 5 days, in the fourth - 5,217 weeks and 6 days. And this means that after a century that ended in a leap year( 1600, 2000), and two subsequent ones in the line of letters of letters, there is a shift to two positions back. And only due to the inclusion of the 366th day at the end of February of the next leap-year-old centenary( and the change takes place on March 1), the return journey for this secular year is carried out one position to the left.

    By the way, because of this "behavior", on January 1, 1 year of the new century, the Gregorian calendar falls on only one of the four days of the week: on Monday( 1601, 2001), Saturday( 1701, 2101), Thursday( 1801, 2201) and Tuesday( 1501, 1901).

    Based on monthly coefficients. We have already described the basic principles of constructing an "eternal calendar" with the help of monthly coefficients, which are the sum of the solar epakt for the corresponding year and the regulars-the shift established at the beginning of each month of the days of the week accumulating from month to month throughout the year. Once again, we recall that the decision of the International Bureau of Standards( Resolution No. 2014) is considered the first day of the week to be Monday, so the days have a corresponding numerical designation: Mon - 1, W - 2, Wed - 3, Thu - 4, Fri - 5,6, Sun - 7.

    As already mentioned, the beginnings of both Byzantine and Western European solar 28-year cycles are shifted relative to the epoch n.e. This, of course, does not create difficulties in calculating the monthly coefficients of the "eternal calendar", but it is much more customary to keep accounts for years through the centuries, especially since formulas can easily be copied in a form fully suitable for counting years beginning from 1 year.e.

    First of all, since the insertion of the 366th day is made at the beginning of the 4th, 8th, etc., the formula for calculating the shift of days of the week from year to year will be written in the same form. However, instead of the year number in the 28-year Q cycle, the ordinal number of the year n should be used.e. R. Excluding multipliers multiples of 7 from this number, it is not difficult to get the following expression instead:

    Here, T is the ordinal number of the year in the current century, and C is the number of complete past centuries. If E takes a negative value, it must be replaced by the addition to module 7( for example, instead of -5, take + 2, etc.).

    It is obvious that for each specific year the monthly coefficients K have a very definite value. In other words, the sum of ES + RS remains constant regardless of the choice of the beginning of the years account. But if the reference point is shifted in comparison with the traditional one, for example, the Byzantine one, then the values ​​of the regulars, the shifts from month to month of the days of the week, falling on the 1st day, should also be recounted. It is not difficult to see that when the years are counted in and.e.these shifts( denoted by Mi, i = 1, 2,. .. 12), can be written in the form of the

    label. January 4( 3)

    April

    3

    July 3

    October

    4

    February 0( 6)

    May

    5

    August 6

    November

    0

    March 2

    June

    1

    September 2

    December

    2

    The corresponding values ​​for the leap year are indicated in brackets.