Jun 17, 2011 - 5 Doomsday method. Python code for doomsday of year y (does it work? why?) s = floor(y / 100) x = y % 100. # % is modulo in python if odd(x):.
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The Doomsday rule
Outline 1 Introduction 2 The Gregorian calendar 2.1 Leap years in the Gregorian calendar 3 Doomsday 4 Doomsday formula 5 Doomsday method 5.1 Applications
Judicaël Courant
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6 Conclusion
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The Doomsday rule
1 Introduction What days of the week are: • January the first of 2011? • June the 6, 1944 • July the 14, 1789 • May 1st, 2012?
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The Doomsday rule
If you do not know the answer, could you compute it? Could you devise an efficient algorithm to calculate the day of the week of any given date (say from year 1 to 9999) in the Gregorian calendar? Goal: being able to calculate it mentally in a few seconds
Judicaël Courant
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The Doomsday rule
2 The Gregorian calendar • The calendar we use today • Introduced by Pope Gregory XIII on 1582 • Similar to the previous Julian calendar; main difference: leap years
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The Doomsday rule
2.1 Leap years in the Gregorian calendar Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year.
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3 Doomsday Day of the week of “march 0” (last day of february) Doomsday for 2011: Monday, for 2012: Wednesday. Doomsdays every year: • 4/4, 6/6, 8/8 and 10/10 • 5/9 and 9/5; 11/7 and 7/11 • Normal years: january 3 and february 0 • Leap years, january 4 and february 1 Judicaël Courant
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The Doomsday rule
Applications: In 2011, what is the day of the week of • December, 25? • October, 17? • July, 14? • November, 11?
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4 Doomsday formula Number the day of the week from 0 to 6, starting with Sunday. Then the Doomsday of year y is
2+y+
y y y − + 4 100 400
mod 7
Why? Not very easy to compute mentally.
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5 Doomsday method Python code for doomsday of year y (does it work? why?) s = floor(y / 100) x = y % 100 if odd(x): x = x + 11 x = x / 2 if odd(x): x = x + 11 x = x + 2 * (s mod 4) return ((2 - x) % 7) Judicaël Courant
# % is modulo in python
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The Doomsday rule
5.1 Applications What days of the week are: • January the first of 2011? • June the 6, 1944 • July the 14, 1789 • May 1st, 2012?
Judicaël Courant
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The Doomsday rule
6 Conclusion • Doomsday rule is easy • Practice, practice, practice • Next challenge: convert calendar dates to ISO week dates (see Wikipedia, ISO_8601)
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