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12/5/13 — Happy Right Triangle Day!

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

5-12-13 Triangle blue

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

5^2 + 12^2 = 13^2

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

5-12-13 plus 9-12-15 Triangle blue

to make the 13-14-15 triangle!

13-14-15 triangle blue

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!  If you’re in New York City, you might want to join the Museum of Math as they pythagorize the Flatiron Building!

One Comment

  1. Simon Gregg says:

    Thanks for notifying us all about this important triangle occasion. I went back to my happy triangle day blog post http://seekecho.blogspot.fr/2013/05/happy-right-triangle-day-12513.html and realised I still have work to do!

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