The message
from quisquiliae contains these words:

Sitting on a stool the weight is centred so 3 legs will provide
stability on an uneven surface. But using a stool for standing on is
another matter. Step on the stool with just one leg and you can place
your weight in the centre, then step up with the second foot, that foot
will have to go nearer the edge, transferring any weight to that foot
will tend to either distribute the load on to one leg or on the edge of
the segment of stool that lies between two legs. Either is unstable.

If the weight is on both feet the stool will be stable provided the
centre of gravity of the person standing on it is within (as in
vertically above) the area bounded by a line drawn round the outside
edges of the stool legs. That applies whether the stool has 3 or 4 legs.

For a three legged stool to be stable for _standing on_ the triangle
over the legs needs to be large enough to accomodate two feet well
within its boundary. If not either it will tilt with the weight of one
foot (if that is off centre) or do so when the weight distribution
changes to accomodate two feet.

Not so. You can stand on a 3 legged stool much smaller than that. It is
easy enough to shuffle around without actually lifting the feet off the
seat but for the stool not to turn over when the stander lifts one foot
the marginal condition is for the centre of the foot (ie the point
directly below the bodys centre of gravity) to be on the outer boundary
referred to above.

Four legs will better accomodate the shifting load during step-on step-off.

Only if the all four legs are firmly in touch with the ground otherwise
the undamped shake during the single leg step up could easily magnify
out of control.

--
Roger