surface gauge - why flat base?

Very cool. I like your logic much better than mine. :)

Even without the constraint of the rotation, it's (now) easy to see that if you keep three legs on a wavy floor and move it around randomly, you will always be able to find a spot where the the forth leg would hit the floor making all 4 touch at that point. The rotation idea is simple proof that there there must always be at least one location where that was true (assuming the chair legs were correctly aligned on a plane).

You're correct, John...My language was sloppy. I should have said that D could then be made to touch the floor and A would then be off it.

But, the real point is that before you get to 90 degrees of rotation you'll reach a point where all four legs will be touching the wavy floor.

It's worked OK for me every time I've tried it.

Jeff

My curious mind got to wondering when I first got involved with this whole silly musing about four legged stools and wavy floors.

Looks like it was over 12 years ago, and this link provides a grandios explanation of why what I said really does work:

Jeff (Who can't recall any other US holidays referred to by their dates instead of their given names. He doesn't think that the shipment of mayonaise on the Titantic is a US holiday yet.)

There is of course a "flaw" in this proof (pun intended)...it assumes that the available floor space is big enough for all 4 legs of a stool to be on it at the same time. You'd have a hard time proving it in my workshop

Regards, Tony

I did that, although I was making a small aluminium sanding block (I'm now sure my sanding block needed to quite THAT flat, but it was, as you say, fun).

BugBear

I don't quite follow this. I thought the important feature was that the scriber should be at a consistent height - and it will be even if you rotate it.

Russell

Here's an easier way to visualize it.

Stool with legs A, B, C, D all the same length, sitting on a wavy surface. Surface is only mildly wavy with no steps or discontinuities.

Stool is unstable - it rocks on legs diagonally opposite. Let's say they are A and C. It appears that legs A and C are too long. Rotate the stool 90 degrees, so that legs B and D are where A and C were, and since they are all the same length B and D will now be solid and A and C will appear too short. They went in that 90 degree rotation from too long to too short. At one place at least in that rotation they were just right.

John Martin

But not necessarily at the same time.

Henry

If it's a continuous floor surface with no steps, there's guaranteed to be at least one spot where they will all touch the floor at the same time.

Before the A or C leg can lift off the floor in the rotation, the B and D legs must first both touch the floor. It's at that point in the rotation where the B and D legs first touch the floor that they will all be touching the floor at the same time.

It's the same reason you can't draw a graph of two lines - one tiled up, and the other tilted down, that you can't get from the point on the x axis where the line A is above B, to the point where line A is below B, without going through the point where the lines intersect. It's at that point where both lines are the "same height" on the graph.

That's what is to be proved.

And that does it nicely! So I was wrong.

Henry

would swing in if the 3

Think of it this way:

A three footed gauge will generate error if ANY of the feet are imperfect.

A flat-bottomed gauge has more that three points. It has hundreds. If one of those has an error, it will not affect the gauge.

Doesn't work for me with a pub table, all that happens is I get the "what's he up to now?" look from the landlord. So back to the tried and tested folded beer mat that the bloody cleaners throw away each night. Grrrrrr!

Regards,

David P.

So do the landlord a favour and install leveling feet on your table - different table every visit, the people will really wonder what's up with you. Gerry :-)} London, Canada

So you have a non standard wavy floor. It's what I believe the mathematicians would call 'ill conditioned' Get the landlord to replace it with a better one.

Henry

Any continuous-surface-floor (no jumps, steps, holes) would be ok, if the ends of the legs are coplanar. Most likely one of the pub table legs is shorter than the others, by about the thickness of a folded beer mat.

-jiw

Because someone took the leveling foot home for their own use. Gerry :-)} London, Canada