Angled Beams

Have you ever wondered why these beams are at an angle of 143°? More precisely, 143.1301°.

It’s a good question, and I wondered for a long time as well. Then I discovered why, and it's actually pretty simple. It’s because of the Pythagorean Theorem. You know,

I discovered it while I was building a long truss, much like this one.

If you look closely at this simple truss and count not the holes but the hole spaces. The hole spaces are the length between the holes. For example, if you have a nine hole beam, there are eight spaces, a fifteen hole beam, there are fourteen holes spaces, etc. When you count them up, you'll find you have a common 3-4-5 right triangle.

Remember that the Pythagorean Theorem only works for right triangles, so the formula works out to be

3^2 + 4^2 = 5^2

or

9 + 16 = 25

I know that once I figured this out, life got much better and I began to use these oddball beams a whole lot more often.  The 3-4-5 right triangle is very useful in engineering and especially useful in building with Lego. I have used it several times, and I hope to share some constructions with you soon.