The three-legged table discussion thread

[Star Worms]

Following on from http://forum.team17.co.uk/showpost.php?p=545909&postcount=85 ... :p

I've whacked up a diagram to show what I mean. On the right it's a birds' eye view of the tables. The dot shows the centre of gravity. When the table is tipped, the centre of gravity becomes more vertical to the legs of the chair. When it passes the legs, the table will tip. With a 4 legged chair you have to tip it further than with a 3 legged chair to make it fall over.

[AndrewTaylor]

What if the table is triangular?
Or the legs are arranged differently?
Or the ground is uneven?

You can't just make a statement like "three legged tables are less stable than four legged ones" unless you qualify it properly.

[bonz]

What if the table is triangular?
Or the legs are arranged differently?
Or the ground is uneven?

You can't just make a statement like "three legged tables are less stable than four legged ones" unless you qualify it properly.
Of course, a crooked 4-legged table standing on a field would be less stable than a 3-legged one with with the legs forming an equilateral triangle in a room with a perfectly horizontal floor.
To reasonably compare 2 such tables, the conditions would have to be the same.

An arrangement where (any number of) legs have the same distance from the center of mass and the maximum possible distance between each other will always be the most stable.

The shape of the table is irrelevant as long as the material is homogenous. (In a thought experiment, you could reduce the table to a single point where all the mass resides, which is supported by a number of massless legs.)

The only variable should be the number of legs actually.

[Star Worms]

The only variable should be the number of legs actually.Quoted for emphasis.

To compare something properly you change 1 variable. There's no use comparing a 3 legged with legs 1 metre apart to a 4 legged table with legs 20cm apart.

[Vader]

If you're tipping the tables over two legs then a crucial factor in the likelihood of them tipping is the counterweight.

Assuming all attributes of the tables are identical bar the number of legs and their arrangement (4 = square, 3 = equilateral triangle), the four legged table has +1 Table Leg to it's Counterweight attribute, making it harder to tip.

In terms of which is more likely to tip when simply standing still on a flat surface, they are virtually identical.

[M3ntal]

I'm assuming this is a continuation from a discussion elsewhere. Could someone please post the link to the thread / log of chat / relavent information for those of us who have no clue why Star Worms appears to have both started and ended the discussion in his first post ;).

[SupSuper]

The four-legged table seems just as likely to tip from wherever you push it, while the three-legged table seems less likely to tip (than the four-legged table) if pushed from one of the triangle's sides, but more likely from one of the triangle's corners.

Also, the discussion came from here: http://forum.team17.co.uk/showpost.php?p=545909&postcount=85

[bonz]

The four-legged table seems just as likely to tip from wherever you push it, while the three-legged table seems less likely to tip (than the four-legged table) if pushed from one of the triangle's sides, but more likely from one of the triangle's corners.
No, it's still harder to tilt the 4-legged table from the corner than from the sides, but definitely easier than tilting the 3-legged table from the corner.
This gets easier the more legs you add to your table, ultimately equalling when you have reached your circular table with "infinite" legs: a cone tilts equally in all directions.

Speaking of cone, you can reduce the issue of tilting to pyramids and cones actually: tetrahedron -> 4-sided pyramid -> ... -> cone.

[Paul.Power]

But three-legged tables don't wobble as much, do they? Perhaps most tips are caused by initial wobbling than anything else.

[FutureWorm]

The way I see it, a pentagon would be the best of both worlds. Although pentagonal tables are rather uncommon.

[MrBunsy]

A pentagon would be worse though, the advantage the 3 legged table has is that all legs are on the ground however uneven, but a pentagon would stuggle at least as much as a 4 legged one, although it may be slightly more stable.

[bonz]

the advantage the 3 legged table has is that all legs are on the ground however uneven
Well, only if you don't care that everything on the table falls down. Even tripods for cameras are adjustable. So this isn't really an argument either.

A table with 3 legs, if placed on uneven ground with one leg, will tilt, while a 4-legged table with one leg on the same uneven spot doesn't necessarily have to tilt.
(Like a car can drive on 3 wheels, while a 3-wheeler can't drive on two.)

[AndrewTaylor]

Quoted for emphasis.

To compare something properly you change 1 variable. There's no use comparing a 3 legged with legs 1 metre apart to a 4 legged table with legs 20cm apart.

Yes, but the point is that there isn't just one variable. To compare two tables on one surface only and conclude that three legs are worse than four is like doing a drag race between two cars and concluding one is better because it finished sooner. It might have bad brakes, or no handling, and you'd never know.

On uneven ground, three legs are better. If the table has a huge lead counterweight in the centre then it doesn't matter how many legs it has because it isn't tipping anywhere. If there are three people eating at a table then three legs are better because they'll be less in the way.

This isn't a simple question of one thing being better than another; they both have uses. You'll never need to fold a beermat and put it under a three-legged table. This is scientific fact.

If you what to exhaustively test the effects of changing just one variable, you have to test that variable in all reasonable conditions.

Well, only if you don't care that everything on the table falls down. Even tripods for cameras are adjustable. So this isn't really an argument either.
Of course it is. People who use tripods wioth their cameras want the image to be dead level. When do you ever care if a table is a few degrees off? That's what head is for.

[bonz]

If there are three people eating at a table then three legs are better because they'll be less in the way.
You can say the same for every other number of legs.
Besides, 3 people can also sit on a 4-legged (and more) table without them being in the way.
(This of course has an upper limit when there are so many legs that you can put your feet under the table at all.)
You'll never need to fold a beermat and put it under a three-legged table. This is scientific fact.
Hehe.
I bet the teamsters have long experience in that area.
Of course it is. People who use tripods wioth their cameras want the image to be dead level. When do you ever care if a table is a few degrees off? That's what head is for.
Ehrm, in laboratory conditions a horizontal table is often required.
Highly sensitive scales and highspeed centriguges need to be exactly levelled (most of them have a built-in water-level for that purpose) and I found that adjusting one that has 3 "legs" is much more complicated than one with 4 "legs".

[Paul.Power]

You'll never need to fold a beermat and put it under a three-legged table. This is scientific fact.Mathematical fact, indeed.

[SupSuper]

Mathematical fact, indeed.Geometrical fact, even.

[Xinos]

I have conducted a highly advanced computer simulation in order to test weather or not a three legged table is more stable than a four legged table. Find out which is better!

Can you handle the truth? (http://planet-eggplant.com/uploader/table.avi)

[bloopy]

You'll never need to fold a beermat and put it under a three-legged table. This is scientific fact.

Badly worded. What if the floor is sloping and you need the table to be a flat surface?

[Paul.Power]

Badly worded. What if the floor is sloping and you need the table to be a flat surface?Cover it in Velcro.

[bloopy]

Or cut the legs a bit. Or fix the floor. Or modify gravity.

[AndrewTaylor]

Badly worded. What if the floor is sloping and you need the table to be a flat surface?

If you're doing something that precise then you shouldn't use a beermat.

[SupSuper]

I wish schools used three-legged tables. All the desks seem to wobble like crazy.

[Xinos]

I wish schools used three-legged tables. All the desks seem to wobble like crazy.

Replace the tables because they are too lazy to replace the missing pads that sits at the bottum of the table legs to prevent scratches on the floor? Or simply tighten some screws? :p

[AndrewTaylor]

Replace the tables because they are too lazy to replace the missing pads that sits at the bottum of the table legs to prevent scratches on the floor? Or simply tighten some screws? :p

Often the floor is at fault. That costs a lot more to fix.