The Last Pythagorean Theorem Day of the Century

Oct 24, 2026 · @MrPurdyMath

Today is October 24, 2026, written 10/24/26. Those three numbers are the side lengths of a right triangle, which makes today a Pythagorean Theorem Day.

Soak it in, because it's the last one we'll get this century. The next one isn't until March 4, 2105.

I love dates like this because they turn a calendar into a math prompt. Nobody has to be convinced that the date matters. It's right there at the top of every worksheet, every agenda slide and every phone lock screen. All we have to do is ask students to look at it differently.

Check the math

The Pythagorean Theorem says that in a right triangle, the squares of the two legs add up to the square of the hypotenuse. A date qualifies when month² + day² = year².

10^2 + 24^2 = 26^2

100 + 576 = 676

Picture a right triangle with a short leg of 10, a long leg of 24 and a slanted side of 26. Today's date is that triangle.

This is a great moment to slow down with students. Before anyone reaches for a calculator, ask: how could you tell whether 676 is a perfect square without one? (It ends in 6, so its square root ends in 4 or 6. 25² is 625, so try 26.)

Why this is the last one until 2105

This century has had just 12 Pythagorean Theorem Days, and 10/24/26 is the final one. Here's the full list, using month/day/year:

Date	Triangle (month, day, year)	Check
10/24/26	10, 24, 26	100 + 576 = 676
7/24/25	7, 24, 25	49 + 576 = 625
12/16/20	12, 16, 20	144 + 256 = 400
8/15/17	8, 15, 17	64 + 225 = 289
9/12/15 and 12/9/15	9, 12, 15	81 + 144 = 225
5/12/13 and 12/5/13	5, 12, 13	25 + 144 = 169
6/8/10 and 8/6/10	6, 8, 10	36 + 64 = 100
3/4/05 and 4/3/05	3, 4, 5	9 + 16 = 25

So why the 79-year wait? The calendar puts a ceiling on the legs. The month can't be more than 12 and the day can't be more than 31, so the biggest possible hypotenuse is √(12² + 31²) = √1105, about 33.2.

That leaves the years 27 through 33 as the only candidates after today. None of them has a right triangle whose legs fit on a calendar. For example, 29 needs legs of 20 and 21, and there's no 20th month. Once 2033 passes, the years are simply too big. The pattern only starts again when the two-digit year resets to 05, in 2105.

The triangle hiding inside today

Today's triangle is really a smaller one, doubled. Divide 10, 24 and 26 by 2 and you get 5, 12 and 13, the second-most-famous Pythagorean triple after 3-4-5.

That splits the dates into two families:

• Primitive triples have no common factor, so they can't shrink: 3-4-5, 5-12-13, 8-15-17 and 7-24-25.

• Scaled triples are a smaller triangle stretched by a whole number. Every one of them traces back to just two primitives: 6-8-10 (3-4-5 × 2), 9-12-15 (3-4-5 × 3), 12-16-20 (3-4-5 × 4) and today's 10-24-26 (5-12-13 × 2).

This is similarity hiding in plain sight. Scaled triangles have the same angles and the same shape, just a different size. Students who notice that 3-4-5 shows up three times on the list have discovered something real about how right triangles work.

Bring it to your classroom

You don't need a full lesson for this. Each of these fits into a warm-up or the last ten minutes of class.

1. Notice and wonder. Write 10/24/26 on the board with no context and ask, "What's special about today?" Let students get there on their own.

2. Prove it without a calculator. Have students show that 676 is a perfect square using estimation and the last digit.

3. Predict the next one. Give them the past dates and ask when the next Pythagorean Theorem Day will be. The 2105 answer always gets a reaction, and the √(12² + 31²) argument is a great piece of reasoning to share.

4. Sort the triples. Ask which dates are scaled copies of a smaller triangle. This connects the Pythagorean Theorem to similarity and scale factor.

5. Change the format. Does the date still work written day/month/year, the way much of the world writes it? (Yes: 24/10/26 is the same triangle with the legs swapped.) What about year-first?

6. Graph it. Plot every month/day pair on a coordinate grid. Each Pythagorean date is a point with whole-number coordinates sitting exactly on a circle x² + y² = r², where r is the year. It's a nice bridge to the distance formula and the equation of a circle.

One last look

Most of us won't see another Pythagorean Theorem Day, so today is worth a pause. Take a second to look at the date, square a few numbers and enjoy a little math that's hiding in plain sight.

If you try any of these with your students, I'd love to hear how it goes. Find me at @MrPurdyMath and tell me what they noticed.