Did you know that October 24th, 2026, is a very special day for us math lovers? Writing the date as 10/24/26, the date creates the following Pythagorean triple:

10² + 24² = 26²

Making it a Pythagorean Theorem Day! In fact, it is the very last one of the century (the next being in 2105). Over the years, our Maple community has been exploring some incredibly interesting ways of visualizing, proving, and applying one of math's most famous theorems!

To celebrate this great day, I thought we could revisit some of our coolest posts on the topic.

Exploring Pythagorean Triples

Since we are celebrating a pythagorean triple day, the Maple Learn post on Generating Pythagorean Triples is a great way to explore the theorem. Any three positive integers that satisfy the pythagorean formula are considered one of these triples (the most popular being 3, 4, and 5). The generation of these values can be looked at from both a geometric and algebraic perspective!

How many ways can one theorem be proved?

One of the coolest things about the Pythagorean Theorem is that we are still discovering new ways to prove it! Traditionally, a geometric method was used to prove the theorem, as can be seen in this Maple Learn post. But in only 2023 two high school students, Calcea Johnson and Ne'Kiya Jackson, presented a new trigonometric proof for the Pythagorean Theorem. 

This was incredible since most trigonometric proofs are based upon the theorem itself, so being able to prove it without these was very impressive! You can explore their approach in Johnson and Jackson's Proof of the Pythagorean Theorem, or read more about it in the MaplePrimes post New Proof of the Pythagorean Theorem.

This even inspired some mathematical artwork in Maplesoft's art competition, Paige Stone created an embroidery piece Infinite Similar Triangles based on the Johnson-Jackson triangle construction. What a fun reminder that math is just as creative as it is logical!

Applications Beyond Right Triangles

The Pythagorean Theorem is mostly thought of as a right triangle problem, but it is so much more than that!

Consider the Staircase Paradox. If you keep decreasing the size of steps to a staircase, the shape begins to look like a straight diagonal, but the length does not approach the length of that diagonal! The Pythagorean Theorem helped us uncover the surprising behavior behind these limits. 

Another interesting application is in Finding the Shortest Path Between Two Points, where the theorem can be applied to arc length calculations. This theorem can show up in some unexpected places! Below is an example of some curves the Pythagorean theorem can be used to calculate!

Happy Pythaorean Theorem Day!

From geometry, to algebraic and trigonometric proofs, mathematical art or simply a good paradox, the Pythagorean Theorem can be explored endlessly. Do you have a favorite proof, application, or derivation from the Pythagorean Theorem? Try to appreciate it a little more on this day, since we won't have another for a while!