It happens that 9272025 = 3045^2, while if you write your dates in British style, 27092025 = 5205^2. I wonder if this phenomenon ever repeats. Unfortunately, the ISO (and Quebec) date notation 20250927 is not a square.
I wrote a program to test all dates between 1 AD and 9999 AD. There are only 34 that work. However a lot of them work only because the month number and day number are equal. I think those don’t really count. If you omit those, there are only seven (or arguably five because two are paired: 1/3/225 = 3/1/225 and 4/12/900 =12/4/900). The last one before today was over a thousand years ago, on 4 December 900. The next one after today will be almost a thousand years from today, on 22 April 3025. So today is indeed a very special day.
Here’s the full list (asterisks mark the ones with equal day and month):
* 01/01/25 * 04/04/100 01/03/225 03/01/225 * 09/09/225 * 07/07/281 04/12/900 12/04/900 * 03/03/1081 * 06/06/1444 09/27/2025 * 01/01/2036 * 02/02/2084 * 08/08/2649 04/22/3025 * 05/05/3504 * 01/01/4049 * 04/04/4121 * 12/12/4324 * 03/03/4564 * 02/02/4929 * 11/11/5556 * 07/07/5600 01/15/5625 * 10/10/6041 * 01/01/6064 * 09/09/6256 * 06/06/6369 * 02/02/7776 * 05/05/8001 * 03/03/8049 * 01/01/8081 * 04/04/8144 * 08/08/8336
ETA: Oh, and none of them have a square ISO date.
That will be my 1063rd birthday! And is also 1000 years beyond my current age.
Excellent work!
This works only if you always use 4 digit years. For example, 010125 is not a square, although 01010025 is.
Note that most–though not all of the years are also square. This is true of all the non-starred examples, that is those with day not the same as month. For example, 2025 = 45^2; 3025 = 55^2. One day a waiter at a Chinese restaurant, inferring from our conversation that we were a groups of mathematicians, taught us a rule for squaring a 2 digit number ending in a 5. If the number is n5 then multiply n*(n+1) and append 25. Actually, this works even if n is not a single digit.
Yes, I was using 4-digit years. It seemed best to use a consistent format for all dates. If you don’t use 4-digit years, these are the matches before 1000 AD. (The matches after 1000 AD are of course the same as I listed upthread.)
* 02/02/5 * 07/07/56 * 01/01/124 * 08/08/201 * 12/12/201 10/30/225 * 07/07/281 * 04/04/496 * 02/02/500 * 05/05/521 * 03/03/601 * 01/01/761 * 06/06/841
Notice that the unstarred one is still in a square year. This method allows you to get past year 9999, although I don’t advise it.
Note that now all the unstarred ones are in years divisible by 25. Strange.