Happy Pythagorean Triple Day!

Thursday is Pythagorean Triple Day, one of the rarest math holidays.

The numbers of Thursday’s date: 7/24/25 or 24/7/25, fit the pattern of the Pythagorean Theorem: 7 squared + 24 squared = 25 squared.

Any three numbers that fit the a² + b² = c² pattern form a Pythagorean Triple.

Celebrate with Pythagorean Math Puzzles

The wonderful Don Steward collected a variety of math puzzles and investigations suitable for math journaling. His family and heirs have kept the website going, and it’s a great place to browse for ideas.

Here are a few activities you might enjoy with your kids, arranged roughly in order of difficulty:

• Introduction to Pythagoras

• Pythagorean Art (Choose your favorite design, cut it out of construction paper, and explain how it demonstrates the Pythagorean Theorem.)

• Grid Triangles and Pythagoras

• 3D Pythagoras

• Ancient Chinese Maths in Right-Angled Triangles

The first activity requires no knowledge of the Pythagorean Theorem to start with, but it gives students a chance to search for patterns.

The second activity can focus on art or high school geometry, depending on how rigorously your student explains the proof diagram. (Do all the angles and sides really fit together as shown? How do you know?)

The rest of the puzzles involve applying the Pythagorean Theorem to a variety of situations.

For Older Students

If your students have learned to work with matrices, they may like to create some Barning trees, as explained on Pat Ballew’s blog:

• Pythagoras and Matrices

What if You Missed the Holiday?

Well, the Pythagorean Theorem is always true, no matter what day it is. And these math investigations are evergreen, so you can do them anytime.

But if you want to wait, there’s Pythagorean Theorem Day on September 16 (9/16/25) and another Pythagorean Triple Day coming next year.

• Can you figure out when is the next Pythagorean Triple Day?

Unfortunately, unless I’m counting wrong, it looks like those may be our last Pythagorean holidays this century. Isn’t it a good thing we don’t actually need a holiday to play around with math?

Have fun exploring number relationships with your kids!