Wednesday, January 7, 2015

A Golden Day

Yesterday, January 6, was "Golden Ratio" day, in the same way that March 14 is "Pi Day." On those days, the numerical expression of the date matches a particular mathematical constant. Pi, the ratio of a circle's circumference to its diameter, is about 3.14. Extend it out a few digits, and you get a particularly nice matchup this year, since the year also matches the ratio. In fact, at 9:26:53 AM we'll match it out quite a ways: 3.141592653. It won't happen again until 2115.

The golden ratio, a number designating a particular geometric proportion found to be particularly pleasing aesthetically and recurring in many natural phenomena, is about 1.6. That makes January 6 "Golden Ratio Day." The multi-digit congruence we'll see on Pi Day this year will happen for the golden ratio in three years, although we can't carry it out to the second as we can with pi. Since the value of the golden ratio is 1.618033988, we'd have to have a minute with 88 seconds in it to do so. But at 3:39 in the morning of January 6, 2018, we can take it out to the minute. Or we could say that the "0" represents a time after midnight, but unless we're using military time notation we usually don't write it like that - and we'd have to figure out how to squeeze 98 seconds into a minute instead, and that still won't work.

"E day," which will match the calendar to Euler's constant, will be February 7. Euler's constant is the base of the natural logarithm of a number. Its yearly match will also be in 2018, but we can only go out to the hour with it as the date-corresponding value is 2.71828182, and we'd have to find an hour with 81 minutes in it. While the average political speech can seem to drag on forever, it still does so at the old-fashioned rate of 60 minutes per hour, rather than through some quirk of relativity.

By far the most fun of these mathematical dates would probably be February 5 and April 6. These would be written 2.5 (in shorthand, "α") and 4.6 (in shorthand, "δ"), the approximate values of two numbers called "Feigenbaum constants." At that, though, my explanation must stop, as figuring out what the heck a Feigenbaum constant is used for is beyond any math I can pretend to know.

But it will sure be fun to watch people's faces when I wish them "Happy Feigenbaum Day!" on February 5 and then again on April 6.

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