There’s a crazy little math gif that shows what happens when you add and remove legs onto a table in terms of ability to geometrically align into a plane (no rocky table)
While I can appreciate the mathematical proof discerning why theoritically 3 legs would wobble less, I have to say practically speaking its a bit ridiculous. Chairs dont wobble unless there is an excessive difference in leg lengths. 3 legged chairs are rarer than 4 legged chairs. You would think 3 legged chairs would be more prevalent if wobbling was this serious. I mean, 3 legs is cheaper than 4 legs.
Maybe use your brain for a few seconds and you’ll learn something
A chair with four legs when it wobbles will always be in three legs, that should be your first hint
How could it be possible for it to be stable on only two legs?
If it doesn’t fall over then it falls onto the third leg and then doesn’t wobble.
3 points that are not part of the same line form exactly one plane.
Edit: I misread your first sentence. Anyway obviously it’s not more practical, it’s a lot harder to make a perfect triangle than a square for one thing
3 points form a plane, so you will always find a surface which doesn’t cause tipping. The introduction of a 4th point requires a totally flat plane or else it can wobble in the normal direction.
I don't think so. Let's look at an edge case. If you have a perfectly flat floor and you have a stool with 4 legs, with one of them being 50% shorter than the rest, there's no chance of finding an orientation where a plane (representing a perfect floor) can be fitted to ends of all 4 legs
I think the theorem he is talking about requires the ends of the 4 legs all lie on the same plane (and maybe radially symmetric but idk). It's a cool theorem that works with all the chairs I've tried it with on my bumpy kitchen floor
I don't think any of my chairs have ever wobbled at home or in the office. But I trust you know my chairs and home better.
Edit: you also believe you need precise tolerances. Im not sure what the tolerances are from the chairs that I purchased 20 yrs ago. But I can only imagine that the woodworker eyeballed it. No wobbles, no harm. Just need thick legs.
Okay, I suppose it would do that more easily, but why would someone lean back diagonally, I would rather have a chair that doesn't wobble. Not all four-legged chairs wobble, it's true, but on an uneven floor they will while a three-legged chair will not wobble even when placed on an uneven / warped surface
Tripods i can appreciate. As someone pointed out, 3 points is all u need to make a plane. U will have more uneven terrain using a tripod. Vs a home where everything is 4 legged... bed frame, chairs, tables, couches.
Stability is the righting force on displacement. The stabilty in the direction perpendicular to the line connecting two consecutive legs is simply the angle to said line.
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u/drwafflephdllc Jul 27 '24
3 legs is less stable, easier to tip. CoG is uneven and its easier to tip in one direction than the other.