I’m on vacation right now or I’d write something much
more thorough longer, but I wanted to point out a really interesting puzzle about triangles posed by Ben Vitale on twitter yesterday:
Since I never know if the link’s from twitter will be preserved in the embedding, here’s a direct link to his blog:
He gives a couple of examples and challenges the reader to find some more. One of his examples solutions is the triangle with sides , , and which has an area of 21.
Following the hint on Ben’s blog, I played around a little bit and found that the triangle with side lengths of , , and has an area of 3. Here’s my work, where you’ll see the Fibonacci numbers hiding in the middle of the page!
I really like this problem, and as I mentioned to Ben via Twitter last night if we weren’t on vacation I’d be working through this problem straight away with my kids. This problem shows a beautiful connection between geometry and arithmetic, and the Fibonacci numbers come up in my example from a neat connection to continued fractions. What a wonderful problem. Thanks Ben!