
How to Stabilize a Wobbly Table (2007) - crazyoscarchang
https://www.maa.org/external_archive/devlin/devlin_02_07.html
======
kaasmonster
Numberphile made a video on this: [https://m.youtube.com/watch?v=OuF-
WB7mD6k](https://m.youtube.com/watch?v=OuF-WB7mD6k)

However, I tried doing this many times, but it was hardly ever successful.

~~~
ranie93
most likely due to the caveats I assume:

"Two caveats. This only works for a table with equal legs, where the wobble is
caused by an uneven floor. If the table has uneven legs, you probably need the
folded napkin. Also, the floor can be bumpy but has to be free of steps"

Spherical cows rearing their ugly heads once again

~~~
thfuran
How does that work? I guess the sphere just expands?

~~~
zentiggr
Old physics joke about using approximations to model a farming problem...
"Start with a spherical cow in vacuum, ..."

~~~
twic
thfuran's comment extends the joke by inquiring how a cow might raise its head
while being a perfect sphere.

~~~
zentiggr
Gotcha - 'rearing their ugly heads'... I should slow down and think the thread
through every now and then lol

------
bvanderveen
Best solution: replace it with a table with 3 points of contact with the
ground. Three points define a plane; it's guaranteed not to wobble.

~~~
asdfman123
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.

~~~
twic
Ultimate solution: use a tatami mat.

------
mauvehaus
Possibly dumb question: Will this work for tables where there is no point of
rotation that the equal-length legs are equidistant from? I.e. there's no
point of rotational symmetry as far as the legs are concerned.

It seems that the argument is predicated on the idea that after rotating the
table 90 degrees, there's a leg in the same location on the ground as there
was before rotating the table 90 degrees.

The linked paper [0] goes so far as to cover the case of rectangular tables,
but it's quite common to have trapezoidal arrangements of legs, on e.g. a
demilune table. Chairs also often have their 4 legs arranged in a trapezoid.

If the linked paper addresses this, it's in mathematical language beyond my
reading comprehension :-/

[0] [https://arxiv.org/abs/math/0511490](https://arxiv.org/abs/math/0511490)

~~~
michaelt
There'll be a point of rotation the legs are equidistant from for any
_symmetrical_ trapezoidal arrangement of legs - it just might not be under the
table. After all, a demilune table is a circular segment!

Of course, as most demilune tables are put against walls, rotating them _into
the wall_ is probably a better idea in theory than in practice.

~~~
mauvehaus
"Of course, as most demilune tables are put against walls, rotating them into
the wall is probably a better idea in theory than in practice."

Depending on how the wall and floor are framed, there might not even be a
well-defined "floor" if you try. Or the floor may not have a smooth curve.

Also: is there a word or phrase for the situation of getting 2 informative
answers to a question and being _even more confused_ than when you asked?
Because I'm there thanks to you and dzdt.

------
istjohn
By far the most interesting part to me was this aside:

>> But getting it to work proved much harder than some other equally cute,
real-world applications of the IVT [Intermediate Value Theorem], such as the
fact that at any moment in time, there is always at least one location on the
earth's surface where the temperature is exactly the same as at the location
diametrically opposite on the other side of the globe.

~~~
yesenadam
How to find one (two): The temperature at the spot (B) on the other side of
the world from you (A) is either the same (Finished) or different. If
different, head towards B, (any direction is fine!) and at some point before
you get there and the A vs B temperatures are swapped, the two will be the
same. Since the direction you go doesn't matter, evidently there's a path
"around the world" where this true, not just a point! (Ok, just a point if
they're initially the same.)

------
KirinDave
I suspect this is a local thing these folks experienced. I've never eaten at a
place with a floor so uneven it makes tables wobble, but I've been to places
where the endcap for the legs had fallen off pretty often.

~~~
KineticLensman
> a place with a floor so uneven it makes tables wobble

Many outdoor paved patios have exactly this property, especially as the slabs
settle over time

~~~
KirinDave
Slabs?

~~~
KineticLensman
Paving slabs - UK term for the individual 'stones', typically large squares or
rectangles.

