5/12/13 — Happy Right Triangle Day! Published by on

Happy Right Triangle Day! Today we celebrate a favorite geometric object: the 5-12-13 right triangle.

Of course, the sides of this triangle satisfy the Pythagorean Theorem

but one reason I like this particular right triangle so much is the role it plays in another favorite triangle. The 5-12-13 triangle fits together perfectly with the 9-12-15 right triangle

to make the 13-14-15 triangle!

The 13-14-15 triangle is special in its own right: it is a Heronian triangle, a triangle with rational side lengths and rational area. In fact, this triangle has integer side lengths and integer area, making it especially interesting!

Happy Right Triangle Day! Be sure to marvel at some perpendicularity today.