Monday, March 17, 2014

Mathematical Holidays

So, last Friday (3/14) marked another Pi Day. Next year will be even more exciting, because we'll cover pi to an extra two decimal places: 3/14/15... I suppose at 9:26:53 a.m., all the mathematicians will shoot their guns in the air.

I think I wrote last year how people in countries that write dates as Day/Month instead of Month/Day don't get to have Pi Day, because there's no 14th month. I've always been partial to writing the month first, because it makes more sense from a place-value perspective. Day/Month/Year makes sense, and so would Year/Month/Day, but Month/Day/Year? It's all out of whack. I like the military style: 14 MAR 2014. No mistaking that.

However, the base-ten representation of pi is no more fundamental than its representation in any other base. The only other bases that make any sense are base seven (7 days in a week) or base 12 (12 months in a year). You could do base 30, but not all months have 30 days.

In base 7, pi = 3.066... Rounding this to two places, you get 3.10 (not 3.07 - there is no digit 7 in base 7!) So Pi Day could be the 10th day of the 3rd month or the 3rd day of the 10th month. In base 10, that translates to the 7th day of the 3rd month or the 3rd day of the 7th month, so March 7 or July 3 depending on how you write your dates.

In base 12, pi = 3.185... Rounding this to two places, you get 3.19. The 19th month in base 12 is the 17th month in base 10, but there is no 17th month, so the only date that makes sense is the 19th day of the 3rd month in base 12. But 19 in base 12 is 17 in base 10, so that would make Pi Day March 17th. That won't work because people are too drunk on green beer to care about pi on March 17.

Arguably, the base of natural logarithms (e) is even more important than pi, for reasons I won't bore you with. But the decimal expansion of e is 2.718..., which doesn't give a good date. Maybe the 271st day of the the year, which would be September 28 in a non-leap year. September 28 is the 272nd day of the year in a leap year, which is OK because e really rounds to 2.72. It's 2.501... in base 7 is and in base 12 it's 2.875... Can't make any dates from those.

I've always been partial to the Euler-Mascheroni constant, gamma = 0.5772... That's totally unworkable as a decimal date.  I also like the Golden Ratio, 1.618... Because it's a ratio, it's logical (for the purpose of this silly post, I guess) to use it to divide the year. In a non-leap year, August 14 divides the year into 226 days that have passed and 139 that remain, and 226/139 is as close as you get to the Golden Ratio with a whole number of days. I'd trade Labor Day for a Golden Ratio Day on August 14. You'd get a day off before the kids have gone back to school, and it would eliminate that annoying short week the first week of school.

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