Friday, December 25, 2009

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
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.


  1. I'm using these calculations a lot when making CAD drawings of my constructions. And (as stupid as this may sound) I have used the angle so much that I was somehow thinking the angle in this post wasn't right. I recalculated it and it turns out you flipped two numbers after the comma :-) No worries though :-)
    143.1031 > 143.1301. Not a big thing, but in CAD drawings this shows up.

    Also, the 6,8,10 triangle (7 and 9 and 11 in LEGO beams) is one I use frequently.

  2. Yep, you're right, I flipped them. I'll fix that. Fortunately, only two people in the world that I know of even know about that angle when it comes to Lego. ;)

  3. Before I knew about the connection to Pythagoras I used this chart:
    Can be very useful sometimes!

  4. This is a great post, I was also wondering why those angles, I will share this with my community. Even the comments are of value, Thanks for the Inside Lego bitmap Laurens :)

  5. It's nice to see that I wasn't the only one in the dark.

  6. In the first picture you show 3 different lift arms, but they aren't all at the same angle. (I checked with mine). what are the angles of the others?

  7. I am not exactly sure what you are talking about. I just took those three beams and ran three pins thru them to check and I could connect all three and they are all the same angle. The other angled beam with two bends has two 45 degree bends. Is that what you are talking about?