[HELP] Pythagoras not applicable to Technic?

[Cumulonimbus]

I have the following question that I can't seem to answer, so I will try my luck here:

Most here will be familiar with the Pythagorean theorem (a^2 + b^2 = c^2) and the resulting Pythagorean triples like 3:4:5. These describe ratios between the lengths of the edges of a triangle so that one corner is perpendicular (which is very useful in bracing structures).

But I can't wrap my head around the fact that this doesn't seem to apply to the Technic building system. The theorem should be independent of the unit of length, whether it is inches, meters or studs.

So why isn't it possible then to construct the following, where the lower holes of the yellow and the green liftarm align:

Assuming that TLG hasn't found a way to break physics, what am I missing?

Edited November 28, 2014 by Cumulonimbus

[Josephiah]

You need to count the space from one hole to the next, not just the number of holes. So a 345 triangle would be a 456 in terms of Lego beam lengths. Does that help?

[andythenorth]

I think it's because an idealised 3:4:5 triangle relies on corners being at the exact endpoint of the line (I'm not great at maths, but I think strictly it also relies on an unmeasurably thin line).

The Lego liftarms are not connecting at the end point, but rather some distance along (maybe about 10% from end on a a short liftarm like a 3L).

Try taking a sheet of paper and drawing lines along the center-line of each beam, and you'll see how the distance between the connection points isn't 3:4:5 (I haven't done this, interested what ratio it actually is).

I wondered if the gaps between the stud holes might also affect the strict 3:4:5, but I couldn't see how, they looked like a constant factor to me.

Edited November 28, 2014 by andythenorth

[Josephiah]

Another way to think about it is that the "corners" of the triangle are actually the central axes of the holes/pegs at the corners.

[hrontos]

The point you are missing is that in case of technic and pins you have to calculate distance from the middle of the pin hole. So L beam with 4 holes is 1 hole "shorter". Use 6, 5 and 4.

[Josephiah]

What you have effectively tried to create in your picture above is a 234 triangle, which obviously won't work.

(Is there a way to edit existing posts in this, rather than keeping adding more when I think of another comment? :) )

[Cumulonimbus]

Yes, I understand. I was too focussed on the holes. Thanks for clearing that up, I will sleep well tonight.

[mzoli]

Check the Technic Design school guide: link

Edited November 28, 2014 by mzoli

[aeh5040]

So - the laws of geometry live to fight another day...

Incidentally, there are numerous examples of Pythagorean triangles in official models. E.g. a yellow 6-8-10 triangle features prominently on the side of the 42009:

And 3-4-5's form a vital part of the 9398 chassis:

I'm not aware of any 5-12-13 triangles in official sets, but I'd be happy to be proved wrong on that...

Blakbird???

Edited November 29, 2014 by aeh5040

[miguev]

  On 11/28/2014 at 9:36 PM, Josephiah said:

You need to count the space from one hole to the next, not just the number of holes. So a 345 triangle would be a 456 in terms of Lego beam lengths. Does that help?

Nailed it. This is actually used in the Hot Rod (42022) set, using thin 6L liftarms.

[Zerobricks]

And of course the 4x6 bent liftarm is designed for this exact purpose. And the #3 and #5 connectors.

[Jeroen Ottens]

  On 11/29/2014 at 8:08 PM, Zblj said:

And of course the 4x6 bent liftarm is designed for this exact purpose. And the #3 and #5 connectors.

You're right about the liftarms, but wrong about the connectors. They have the wrong angle. The angles for the 3/4/5 triangle are ~53, 90 and ~47 degrees. #3 is 22.5 and #5 is 57.5 degrees, close, but not close enough.

[Zerobricks]

Nope connectors do work, check the code pilot's bed. Its just that they are used for the different orientation.

Edited November 29, 2014 by Zblj

[Jeroen Ottens]

  On 11/29/2014 at 8:20 PM, Zblj said:

Nope connectors do work, check the code pilot's bed. Its just that they are used for the different orientation.

The cod pilot's bed is not a 3/4/5 triangle. That is a 1.91 / 4.6 / 5 triangle. Or in the model it is slightly stressed 2/4.5/5 triangle.

[DrJB]

I thought answers to the OP were finalized long ago ... interesting the 'life' this thread has traken on :)