Several people emailed me that September 16, 2025---written as 9-16-25 in the US---represents the integer side lengths of a right triangle.
9-16-25 is the only such triple that is also a valid date. This kind of mathematical alignment only happens once every 100 years. The next occurrence will be September 16, 2125.
Since this is such a rare event, let's explore some more math-themed dates.
1) Pythagorean Triples That Work as Future Dates
Note that 9-16-25 is not a Pythagorean triple; however, 3-4-5 is.
Here are some future dates that are both Pythagorean triples and valid calendar dates:
March 4, 2105 is 3-4-5
May 12, 2113 is 5-12-13
June 8, 2110 is 6-8-10
July 24, 2125 is 7-24-25 (Darn---July 24, 2025 was recent and I missed it!)
August 15, 2117 is 8-15-17
I think that's it. Recall that we need the month to be in \(\{1,\ldots,12\}\) and the day to be in \(\{1,\ldots,31\}\) with some exceptions:
Thirty days has September, April, June, and November
All the rest have thirty-one,
Excepting February, fun!
And that has twenty-eight days clear
And twenty-nine in a Leap Year
There are 24 versions of this poem at a website which is here.
2) Why Didn't Anyone Email Me About Earlier Dates?
I wonder why nobody emailed me on, say, March 4, 2005 (3-4-5). That's a Pythagorean triple, but maybe it just looked like three consecutive numbers. Oh well.
And what about May 12, 2013 (5-12-13)? That's a really cool Pythagorean triple. Oh well.
3) Other Math-Related Dates Using Month, Day, and Year.
So dates like Pi Day don't count---we want the full date to be interesting mathematically. Side note---I looked up how Pi Day is referred to and its Pi Day, not \(\pi\) day. Probably because not all typesetting systems can easily produce \(\pi\).
Every year divisible by 4 is a leap year.
That is the end of my post. A bonus for my readers: a mini meta post. Long time reader and fellow SUNY Stony brook math major David Marcus (he was class of 1979, I was class of 1980) has been proofreading some of my posts before I post them. Lance suggested I used chatty instead. Instead of using chatty instead, I used chatty and then used David. David still found mistakes. I give an example here by pointing to all three versions:
Given the typical number of mistakes, I'm surprised to hear that there is any proofreading at all...
ReplyDeleteThanks for the heads up. AFTER David M proofread it I made some changes----more than usual after my final proofread---whi ch indroduced errors. So the errors not being found are NOT chatty's fault and NOT David's fault.
DeleteUpon reading your comment I ran it through ChatGPT and found some errors, that I corrected. I am curious if there are any left- I suspect yes but I am curious- and I am also curious if Chatty caught the errors you found. So please read and leave a comment with the errors you found.
Any relation that David Marcus has to Professor Michael Barry Marcus who has been NY based?
DeleteOctober 24th, 2026 will be a (multiple of a) pythagorean date! I think it's the last one for this century.
ReplyDeleteI look forward to that day!
DeleteWow, these numbers are so profound.
ReplyDeleteThey remind me of the Great Tetrakis 1+2+3+4=10
12:34 on the tenth happens every month shortly after half past noon.
The Gregorian calendar repeats itself every 400 years (obviously excluding century numbers). So if you are looking for a pattern, and you don't find it in a 400 year period, it will never happen.
ReplyDeleteThere are 365 * 400 + 100 - 4 + 1 == 146097 days in a 400 year period. And this makes for exactly 20871 weeks. Hence the repeat after 400 years.
Thanks! now I don't have to dig deeper. I saw that there was a 5-5-5-6 progression in the cycle but had not gone further yet. (hadn't even summed those leaps to get 21 yet. I must be getting old that I was like pattern loops, pattern makes sense, pattern must continue). Of course the current leap day system will be off by about a day in 3333 years so maybe the pattern will br preen evntually
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