20070321, 20:31  #12 
Jun 2005
101110100_{2} Posts 

20070321, 21:18  #13 
"Lucan"
Dec 2006
England
1933_{16} Posts 
That the floor is continuous (no steps) is one of my assumptions.

20070323, 11:58  #14 
Nov 2003
2^{6}×113 Posts 

20070323, 13:27  #15 
Jun 2003
The Texas Hill Country
2×541 Posts 
Bob,
I think that he means that "the floor is continuous" is one of the "two simple assumptions" that he used in his answer. "However, with two simple assumptions, you can rectify the problem by rotating the table through an angle <90 degrees. How come? and what are the assumptions?" Last fiddled with by Wacky on 20070323 at 13:28 
20070323, 13:32  #16 
Jun 2003
The Texas Hill Country
2·541 Posts 
I suspect that "The feet of the table are coplanar" is sufficient, but not necessary, to serve as the other assumption.

20070323, 14:41  #17 
"Lucan"
Dec 2006
England
6,451 Posts 
This was my other assumption (feet at corners of a square).
It is most definitely necessary though. David 
20070323, 15:21  #18  
Nov 2003
2^{6}×113 Posts 
Quote:
I can also replace "height is a u.r.v." with "height is a continuous function", but the function will be nowhere differentiable. The height will be a lacunary function. All that is required is that within a circle of radius epsilon of each point, the height of the floor varies sufficiently. "sufficiently" depends on how far the 4 feet of the table depart from a plane. If the feet are coplanar, then I believe that the height varying by k * epsilon for any k > 1 in the neighborhood of the point on which the 4th leg will sit is sufficient to let one apply the Ham Sandwich Theorem. However, while continuous, the floor will not be *smooth* 

20070323, 16:06  #19  
"Lucan"
Dec 2006
England
1933_{16} Posts 
Quote:
Wacky, did you get necessary and sufficient the wrong way round? Last fiddled with by davieddy on 20070323 at 16:07 

20070323, 16:27  #20  
Jun 2003
The Texas Hill Country
43A_{16} Posts 
Quote:
If my assertion is correct, then coplanar feet is sufficient. However, if would not be necessary. 

20070323, 16:43  #21 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
Uneven floor !
All that 'higher maths' when all one has to do is place a wedge under the leg that's off the floor. Plain common sense! Mally 
20070323, 17:16  #22 
"Lucan"
Dec 2006
England
6,451 Posts 
To be fair, I think it is only RDS who has introduced the higher maths.
I suppose your solution (if they provided a sufficiency of paper napkins) would be at least as practical as rotating the table a bit. I was in a restaurant whe I first had this insight. David 
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