2022 was a hard year for the world, and for many of the various communities I’m in. But there was still lots of joy in it as well – and as a math geek, I of course found some in the elegant numbers that cropped up throughout the year.
Numerically, at least, the days of 2022 held up no matter how upside-down they were at times. And they really added up towards the end.
February 2, 2022 brought us the magical palindrome-ambigram-Groundhog Day: written as 2/2/22, the date read the same forwards and backwards, as well as under 180° rotation. This was the last time that would happen on Groundhog Day until next century, so Punxsutawney Phil was kind enough to record a commemorative message for my students:
https://twitter.com/skominers/status/1488859752016789510.
Give it a listen – Phil was very enthusiastic!
And there were more palindrome-ambigram days: We had another one on 2/20/2022, as well as on “Twosday,” 2/22/22 (what were you doing that day at 22:22?). In the European date convention, we also had them in January, May, August, and November – 22/1/22, 22/5/22, 22/8/22, and 22/11/22. (That last one also compounded beautiful with a particular time in the evening to yield the mega palindrome-ambigram 22:11 22/11/22.)
Meanwhile, owing to a different form of symmetry, 5/5/22 was an perfect day for reflection. (Can you figure out why?)
Plus 8/22/22 was also a rare “adding up day:” 8 = 2+2+2+2. Veterans Day (11/11/22) was another one, in a different additive format (11+11 = 22).
Surprisingly, Thanksgiving’s date (in the form 1124) and the year (2022) were separated by just one step in back-and-forth base 9/base 10 conversion:
1124 (in base 10) is written as 1478 in base 9; 1478 (in base 10) is written as 2022 in base 9.
And the year itself had a few rather special numerical properties, too. For example:
2022 was the first year (AD/CE) such that it (2022 = 2 × 3 × 337), the next year (2023 = 7 × 17^2), the year after that (2024 = 2^3 × 11 × 23), and the year after that (2025 = 3^4 × 5^2) have maximal exponents in their prime factorizations respectively equal to 1, 2, 3, and 4. (The next such year is 11149.)
2022 was only the second year (AD/CE) whose Roman numeral representation, MMXXII, is made up of three double-letter pairs. The first such year was CCXXII = 222, and this only happens twice more under the base symbol set (MMCCII = 2202 and MMCCXX = 2220). (hat tip: 2600)
If you take the 2022nd prime (17581) and add or subtract 2022, you get another prime – 19603 and 15559, respectively. (1776, 1848, and 1920 had this property; we’ll see it next in 2304.)
Moreover, 2022 is a substring of its base-3 representation. (This last happened in 1121, and next occurs in 12101.)
Plus 2022 is the number of subsets of {1,...,32} whose harmonic mean is an integer. ({1,...,30} and {1,...,31} respectively give 2020 and 2021 subsets – but {1,...,33} gives 3933!)
And finally, 2022 was a particularly good year to have overlap with Rosh Hashanah 5783 because 2022 + 5783 = 7805 is the largest number of pieces one can obtain by slicing a bagel with 35 cuts. (If that's not predictive of a sweet new year, I don't know what is!)
So happy New Year!
Farewell to 2022, and welcome to 2023, which is shaping up to be pretty numerically exciting as well. Indeed, it’s the first year since 1 AD/CE that is equal to the sum of its digits times the square of the sum of its digits squared (try saying that 2023 times fast!):
2023 = (2 + 0 + 2 + 3) × (2^2 + 0^2 + 2^2 + 3^2)^2
There are only a few more such years ever – the next is 2400, followed by 52215, 615627, 938600, and 1648656.
And 1/1/23 is the only Fibonacci New Year's Day this century (when the date on 1/1 lines up with the first four elements of the Fibonacci Sequence – 1, 1, 2, and 3). You should make a wish at 5:08.
QED.