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Four-legged stool


Best Answer plasmid, 17 June 2014 - 03:35 PM

Spoiler for

Edit: This assumes that the legs of the stool form a square. Determining whether it applies if the legs are in any other orientation is left as an exercise for the reader. Go to the full post


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10 replies to this topic

#1 bonanova

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Posted 01 June 2014 - 06:42 AM

Since three points determine a plane, or for some such reason, we all know that a milking stool with three legs will always sit firmly without rocking on an uneven surface (barn floors included, especially.) Moreover, the stool can be placed anywhere on that surface. In other words, the center of the stool can be positioned (without rocking) above any point on the floor.

 

Is the same true for a four-legged stool?

 

You may assume the floor satisfies reasonable conditions of smoothness (no cracks or holes, etc.)


Edited by bonanova, 03 June 2014 - 08:11 PM.
Reworded for clarity.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 bonanova

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Posted 06 June 2014 - 04:58 PM

No math required. ;)


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#3 m00li

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Posted 06 June 2014 - 11:20 PM

a 3 legged stool with vertically straight legs of heights 10 meter,1 meter and 1/2 meter will be very unstable. do u mean to say all three legs are equal? if so, then i do not understand the question


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#4 bonanova

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Posted 06 June 2014 - 11:54 PM

I totally agree that stools with legs like that would be problematical.

Happily very few stools are made that way.

The set-up part of the question is intended to call to mind the generally well known

property of three-legged stools (long ago milking stools were made with three

legs for this very reason) that they do not rock, even if placed on uneven (e.g. barn) floors.

 

The question is the sentence with the question mark at the end of it. To elaborate:

Can a four-legged stool (also) be positioned (arbitrarily) over a mildly uneven surface in such a way that it is steady - i.e. will not rock? Equivalently, can a 4-legged card table (with nominally equal legs) be made to rest steady, without rocking, when positioned arbitrarily over a mildly uneven floor?

 

The question is not meant to be tricky or out of the box, only to inspire some analytical thinking.

Feel free to reply if something is still not clear.


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#5 TimeSpaceLightForce

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Posted 07 June 2014 - 05:44 PM

Spoiler for


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#6 bonanova

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Posted 07 June 2014 - 07:05 PM

Spoiler for

 

That is an equivalent question. Nice.

Along with the requirement that the center of the square can be arbitrarily positioned.


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#7 bonanova

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Posted 17 June 2014 - 04:23 AM

Is there a proof for either question?
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#8 DeGe

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Posted 17 June 2014 - 09:44 AM

Spoiler for 3 pts vs 4 pts

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#9 Rainman

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Posted 17 June 2014 - 11:57 AM

Spoiler for


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#10 plasmid

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Posted 17 June 2014 - 03:35 PM   Best Answer

Spoiler for

Edit: This assumes that the legs of the stool form a square. Determining whether it applies if the legs are in any other orientation is left as an exercise for the reader.

Edited by plasmid, 17 June 2014 - 03:57 PM.

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