# A math challenge

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• posted on June 23, 2010, 9:50 pm

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I think the two triangles have to be the most ingenious response so far. You could save a couple of legs by building a regular rectangular table, cutting it diagonally to include three legs on one side of the cut, and hinging it along the cut. You wouldn't have a continuous surface but you wouldn't necessarily have that with the two triangular tables, either.
A mathematically precise solution would fit my personal idea of elegance, even if I was the only one to appreciate it. The adjustable-leg solutions, ranging from matchbooks to macpherson struts, are neat but not really elegant.
Legs in two adjacent corners and the third halfway along the opposite side are not the best solution. Better would be to bring the legs away from the corners and closer to the third leg - if I had a sketch pad, you'd see immediately why.
Oddly enough, you don't gain anything from making the table long and narrow. Draw lines between the legs and imagine them as the axes of rotation. Push down on the unsupported corners and you'll see that there's just as much mass counterbalancing the force with a rectangular table as with a square one.
The length of the legs do make a difference. I think the higher the table, the more it will resist tipping from a vertical force applied ouside the support triangle. However, I'd like my table to be at a standard height.
I agree that you can be too finicky with the design but if I go to the trouble of building this thing I'd like it to be an interesting solution to what has to be a very common problem.
I also like solving puzzles and, so far, this one has been beyond me. Nemo
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• posted on June 24, 2010, 11:28 pm
On Jun 23, 5:50 pm, snipped-for-privacy@nusquam.rete wrote:

That word, elegant, I do not think it means what you think it means.
Getting unnecessarily complicated is not elegant, simple nor admirable.

Most people will thank you for that.
From your leg length description it sounds like you might have chosen the wrong moment arm as the important one.

Yes, and which has very common solutions. There's an old Chinese curse, "May you live in interesting times." You are proposing an interesting solution for your table. Making an adjustable leg that nobody can tell is an adjustable leg qualifies as elegant and interesting...to you, and that's the only one that will really be interested. No?
R
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• posted on June 25, 2010, 12:09 am

Ron, when your ass is as big as mine, bending over to adjust a table leg each time the table's moved is far from elegant!
I've sketched some approximate solutions and the three-legged table looks like it could be surprisingly stable. I was hoping that someone would rise to the mathematical challenge of optimizing the placement of the legs - more as an interesting puzzle than as a practical problem since there's a certain amount of leeway in the actual placement before stability is seriously affected. The answer would involve simultaneous equations - easy enough - and, probably, some fairly elementary calculus (an oxymoron if ever there was one!).
N
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• posted on June 25, 2010, 8:25 am
On Jun 24, 8:09 pm, snipped-for-privacy@example.com wrote:
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How often do you have to adjust a table leg? Certainly not every time you move it.
R
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• posted on June 23, 2010, 8:47 pm
snipped-for-privacy@nusquam.rete wrote in

Not nearly so glamorous, but why don't you just use some lege levelers.
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• posted on June 23, 2010, 9:42 pm
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I suggest about 18 inches into the ground.
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There are no stupid questions, but there are lots of stupid answers.

Larry Wasserman - Baltimore Maryland - lwasserm(a)sdf. lonestar. org
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• posted on June 23, 2010, 10:33 pm
snipped-for-privacy@nusquam.rete wrote:

Go with three regular legs on each of three corners.
On the fourth corner, an adjustable leg - perhaps salvaged from a camera tripod.
Personally, I use folded napkins...
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• posted on June 23, 2010, 10:52 pm
Make it a 4 leged table, with one of the legs with an adjustable / telescoping foot. For an example see http://www.leevalley.com/en/garden/page.aspx?pY776&cat=2,42194 (I got mine for father's day)
However, the table may not end up level, but it will be stable.
Another solution would be standard threaded feet such as http://www.leevalley.com/en/hardware/page.aspx?p@040&cat=3,40993,41283
Why were the stones not set level ? I can understand each stone being a unique shape - that is a feature of flagstones

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• posted on June 24, 2010, 4:12 am
On 23 Jun 2010 06:40:40 GMT, snipped-for-privacy@nusquam.rete wrote the following:

Screw the math. Use adjustable (threaded) feet and tee-nuts. http://fwd4.me/UDX nylon 1/4" are just peachy, wot?
Once you get the level set, put dots of fingernail polish where the legs go so your wife doesn't get upset when she moves the table and finds it uneven again. Demand that she heeds the finnernail polish. <bseg>
-- Peace of mind is that mental condition in which you have accepted the worst. -- Lin Yutang
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• posted on June 26, 2010, 2:23 am
<Nemo....> wrote in message

The flagged patio is a complication as is the rectangular table. If, for example, the patio was an undulating surface with no sudden changes of height a round table with four equal legs will have stability in two places in one revolution. Perhaps in the case of the flagstones if the table legs were spaced so that two ajacent legs would fit on the same stone then the other two legs will find one position that is stable so long as the other two are still on the same stone. Am I making sense? It would be easy to experiment with, just find chairs of different sizes and try it! But all this means a round table.....;>(( phil (_not_ a genius) kangas
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• posted on June 29, 2010, 1:31 am
snipped-for-privacy@nusquam.rete wrote:

Go for 4 legs with adjustable feet. (if the table just has to be stable and not necessarily level, you just need 2 adjustable feet -- or one if you also get to turn the table)
Bob
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• posted on June 29, 2010, 2:58 am

Actually, only one.

Actually, only one whether or not you get to turn the table.
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Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

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• posted on June 29, 2010, 3:10 am

That's not right. If the terrain that the table sits on is varied enough, then two adjustable feet are needed to keep the table surface horizontal enough to stop things from sliding off it.
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• posted on June 29, 2010, 4:08 am
Only one would be required if you rotate it.
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• posted on June 29, 2010, 4:21 am
Sorry. Only one adjustable leg would be required for a three legged table to keep it level anywhere. This would not apply for a four legged table.
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• posted on June 29, 2010, 4:26 am
Sorry again. My sleep patterns are all over the shop I just cannot get the group out of my head! WHY DO YOU NOT LOVE ME! ME ME ME ME ME ME ME ME!!!!
What you need is a single leg table with a gyro mounted. This way even on a moving bus the table will balance!
Now I just happen to have such a table kept safe in my butt. Collapsible and folds in no more space than a medium sized gerbil there is one for everyone! Share anyone?
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• posted on June 29, 2010, 1:23 pm

That requires a continuous (more accurately differentiable) surface. E.g.m consider a tripod with 2' spacing between feet, placed on a surface consisting of four 1.25' square blocks, with the taller ones 1", 2" and 3" above the lowest one. You can't fit two of the legs on the same block, so the two fixed legs will not be the same height--tilted table.
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• posted on June 29, 2010, 1:30 pm
True enough.
My scenario only works for a planar surface tipped at any angle. The three legged chair can always be turned so two are horizontal to each other and the adjustable compensate for the slope.
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• posted on June 29, 2010, 11:30 pm
On Tue, 29 Jun 2010 09:23:12 -0400, alexy wrote:

I have the answer, not the one the OP wanted but an answer none the less.
Build a tripod with a center pipe mounted on a ball joint to fit the table top to, the lower end of the pipe will have a 2 cubic foot container filled with mercury(close as possible to floor) weighing about 1700 pounds, table will be stable on any footing and top will be level
basilisk
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• posted on June 29, 2010, 4:09 am

Just one will do. The three other legs, by themselves will form a tripod and will find a place to stand, then all you do is lower the fourth. What you end up with in terms of level, well that's another matter entirely.