Several people emailed me that Sept 16, 2025 is  (In America) 9-16-25 which is NOT a Pythagorean triple (the triple is (3,4,5)) but is the integer sides of a right triangle. 9-16-25 is the only such triple that is also a date. So this type of day only happens every 100 years. The next one will be Sept 16, 2125.

Since that is SO rare, lets look at Pythagorean triples.

1) Pythagorean triples that work as dates, that are in the future

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 25, 2025 was recent and I missed it!) 

August 15, 2117 is 8-15-17 

I think that's it- recall that we need the first number to be in \(\{1,\ldots,12\}\) and the second number 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: see here.) 

2) How come nobody emailed me on (say) March 4, 2005? 3-4-5 is a P-triple but its also just three numbers in a row. I wonder why nobody emailed me on May 12, 2013 since 5-12-13 is a really cool P-triple. Oh well. 

3) What other days are of math interest using Month AND Day AND Year? So pi-day does not count.

Here are a few.

a) Square days:

Sept 27, 2025  is 9-27-2025 and \(9272025=3045^2\). 

Bonus: if you write it as 27-09-2025 then note \(27092025=5205^2\).

Feb 2, 2084 is 2-02-2084 and \(2022084=1422^2\).

c) All the same digit. We give a few examples: 

Jan 1, 1 (so the year 1- which I hear was a good year for wine)  1-1-1. 

Jan 1, 2011 is 1-1-11 (Should that count?) 

November 1, 2011 is 11-1-11

November 11, 2011 is 11-11-11

d) Palindrome days (same-digit-days are a subset)

March 11, 2030 is 03-11-30 might be the next one.

e) I was hoping that Feb 2, 2022 (2-2-22) would be a Tuesday (Twosday) but alas, it was not.