But then it's easier to topple when the load it is bearing isn't equally distributed

Not if your table is a triangle

And yet triangular tables are a fairly poor shape for restaurants etc.

Clearly, graceless barbarians and children cannot be afforded the luxury of a sturdy table, then.

Better solution: create a startup to use computer vision to scan the ground and find the optimal rotation for your table. Raise millions in investor capital. Exit before they figure out your company can't make a profit.

Ultimate solution: use a tatami mat.

You'll need to incorporate AI somehow to boost media interest, investment and moxie.

Me: Alexa, unwobble my table Alexa: "Scanning ground..."

> Three points define a plane; it's guaranteed not to wobble.

This gets repeated a lot. I think if you stop to consider the common case of non-planar ground, you will see that this mathematical factoid isn't actually super-relevant.

(I will concede that it's not trivial to add a fourth leg and make it co-planar to the other three. But this often isn't the cause of wobble.)

It's more relevant that three legs have three degrees of freedom (ignoring rotating or translating the table), and thus can each sit at an independently chosen height.

(It is conceptually satisfying that once you throw rotation in, the added degree of freedom permits four legs to meet the ground!)

Do you carry a spare table when you go to restaurants?

I deal with analogous situations, on a larger scale, all the time. The solution most designers choose is to make the legs adjustable (like via screws) so you get the strong broad support of multiple legs while gaining the ability to deal with imperfections.

Only if they are non-collinear

Hence tri-pods