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Mentally Calculate The Day Of Any Date With The Doomsday Rule
Calculate A Date's Weekday With The Doomsday Rule
If the article above had you puzzled, this video should clear up any questions.
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Key Facts In This Video

Simply typing a date into the website WolframAlpha can tell you which day of the week it falls/fell on. 00:08

The doomsday rule states that certain days of the year will always fall on the same day. 00:50
The Origin Of The Modern Calendar
Without it, we wouldn't have the doomsday rule.
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Key Facts In This Video

The ancient Egyptians used Sirius to predict the annual flooding of the Nile, allowing them to become one of the first civilizations to use a solar calendar rather than a lunar one. 00:34

Julius Caesar started the more precise Julian Calendar in 45 B.C. 02:07

The Mayan calendar consists of 18 months of 20 days each, with five extra days at the end of the year. 05:20
The Easiest Way To Calculate Pi
Mental arithmetic it ain't, but this is still a brilliant way to calculate pi to a large number of digits.