Beautiful, Simple, Exact, Crazy by Apoorva Khare

Author:Apoorva Khare
Language: eng
Format: epub
Publisher: Yale University Press
Published: 2015-04-04T04:00:00+00:00

Therefore, March 12 will be the next day after Wednesday, which is a Thursday.

If the next year is a leap year, then there are 366 days between March 12 this year and the next. Then we have

In this case, March 12 the next year will be a Friday.

In general, the day of the week of any given date moves one day ahead if the year in between is common, and two days ahead if the year in between is a leap year.

We can reformulate the last conclusion as follows: the day of the week of a given date moves one day forward each year, and one additional day forward each leap year.

Let us recall the rule that defines a leap year. It has three parts:

All years divisible by 4 are leap years,

Except those divisible by 100,

But including those divisible by 400.

For example, years 1968 and 2004 were leap years; and so was the year 2000, because it is divisible by 400. But the year 1900 was not a leap year, because 1900 is divisible by 100 but not by 400.

Now we can use the rule derived in Example 12.14 to find the day of the week of any date in the past, or of a particular event that happened some time ago, or will happen in the future.

Example 12.15. Margaret was born on September 3, 1986, and in 2013 her birthday fell on a Tuesday. On what day of the week was Margaret born?

Solution: The leap years between 1986 and 2013 are: 1988, 1992, 1996, 2000, 2004, 2008, 2012. Therefore, there are 7 leap years and 2013−1986 = 27 total years. We have to subtract 1 for each year, and 1 more for each leap year from the day of the week of Margaret’s birthday in 2013. We compute

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