On 9/16/25, celebrate a date of mathematical beauty

"First, "all three of the entries in that date are perfect squares and what I mean by that is 9 is equal to 32, 16 is equal to 42, and 25 is equal to 52," says Colin Adams, a mathematician at Williams College who was first tipped off about today's special qualities during a meeting with his former student, Jake Malarkey. Next, those perfect squares come from consecutive numbers three, four, and five. But perhaps most special of all is that three, four, and five are an example of what's called a Pythagorean triple."

""And what that means," explains Adams, "is that if I take the sum of the squares of the first two numbers, 32 + 42, which is 9 + 16 is equal to 25, which is 52, so 32 + 42 = 52." This is the Pythagorean Theorem: a2 + b2 = c2. "And that in fact is the most famous theorem in all of mathematics," says Adams. It's a theorem that means something geometrically, too. Any Pythagorean triple including 3, 4, and 5 also gives the lengths of the three sides of a right triangle."

"There are no other dates this century that meet all these conditions, so most of us will experience it just once in our lifetime. (Fun bonus: It turns out the full year, 2025, is also a perfect square: 45 times 45.) A suggested name for the day is Pythagorean Triple Square Day, and a suggested celebration is cutting a rectangular cake along the diagonal to yield two right triangles."

The date 9/16/25 features three entries that are perfect squares: 9 = 3^2, 16 = 4^2, and 25 = 5^2. Those squares come from consecutive integers 3, 4, and 5, which form a Pythagorean triple because 3^2 + 4^2 = 5^2, illustrating the Pythagorean Theorem a2 + b2 = c2. Any Pythagorean triple provides the side lengths of a right triangle, with the squares of the two shorter sides summing to the square of the hypotenuse. No other date this century meets all these criteria, and the year 2025 is itself a perfect square (45^2). A playful celebration idea is cutting a rectangular cake along its diagonal to make two right triangles.

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