360º view of the Perpetual Calendar













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Doomsday Timeline

by the doomsayers The Doomsday Algorithm was first introduced in 1973. Over the years, it has undergone many refinements and improvements. The ultimate goal is to make the algorithm easy to calculate mentally in addition to being easy to remember. Here is a timeline of important modifications to the Doomsday algorithm. Please email spectralfft at yahoo.com for corrections/suggestions to this timeline 1882: Christian Zeller devised the Zeller's congruence algorithm for determining the day of the week for any calendar date. This algorithm is not suitable for mental calculation but works well in computer software. 1887: Lewis Carroll published a perpetual calendar algorithm in the journal Nature with the title "To Find the Day of the Week for Any Given Date". Carroll's algorithm can be performed mentally. Lewis Carroll, himself, can calculate the day of the week in about 20 seconds. 1967: Martin Gardner published "Tricks of Lightning Calculators...
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Methods for Accelerating Conway's Doomsday Algorithm

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updated arXiv version of this document: http://arxiv.org/abs/1006.3913 and part 2 http://arxiv.org/abs/1010.0765 Abstract We propose a simplification of a key component in the Doomsday Algorithm for calculating the day-of-the-week of any given date. In particular, we propose to replace the calculation of the required term: floor(x/12) + x mod 12 + floor((x mod 12)/4) with 2 y + 3(y mod 2) + z + leap where x is an input two-digit year; y is the tens digit of x; z is the ones digit of x; leap is the number of leap years in the y decade less than or equal to x excluding the start of the decade; We argue that this simplification makes the algorithm simpler and easier to calculate mentally. Introduction The Doomsday rule is an algorithm for calculating the day of the week for any given calendar date. It was invented by John Horton Conway in 1982. It was designed to be simple enough that, with practice, one can do the calculation in his head without paper or penc...
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