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ELI5 Yahaaa

Three feet always land

Why Does a Chair Wobble When a Stool Never Does?

Three feet always sit flat on any floor at once. A fourth foot has to get lucky.

Three legs Steady on any floorFour legs Steady only if thefloor suits it
Nothing is wrong with the wobbling chair. It has one leg too many.
  1. Step 1 of 5

    Any three feet can always be laid flat.

    Three feet, placedanywhereExactly one flatsurface fitsSo a stool cannotrock
    This is not good design. It is geometry, and it cannot be got wrong.

    Take three points anywhere and there is exactly one flat surface passing through all three. That is why a three-legged stool cannot rock: whatever the floor is doing, all three feet reach it.

  2. Step 2 of 5

    A fourth foot arrives too late.

    Four feet, onefloor The fourth lands ahair short

    The first three feet settle onto the floor and use up all the freedom. The fourth is stuck with whatever height that decision leaves it, and the floor rarely agrees.

  3. Step 3 of 5

    No floor is actually flat.

    A wobble you can hearunder amillimetreA floor's ordinary unevennessseveralmillimetresacross a room
    The chair is not badly made. The gap is smaller than the floor's own error.

    Boards cup, tiles sit proud, carpet compresses unevenly and concrete cures with a slope. A gap of half a millimetre under one foot is enough to rock a chair you can hear across a room.

  4. Step 4 of 5

    This is why cameras stand on three legs.

    A tripod Three feet, nothingto adjustA four-legged stand One foot always wantspacking

    Anything that must not move gets three feet. A tripod cannot rock, so it never needs adjusting once it is set down, on any ground at all.

  5. Step 5 of 5

    A folded napkin is not a repair.

    1 Pack under theshort foot2 All four feettouch3 Slide it, andthe wobble isback
    You have not fixed the chair. You have fixed one spot on the floor.

    Packing under one foot builds a new surface that all four happen to meet. Move the chair a few centimetres and the floor underneath is different again, so the fix travels nowhere.

The short version

Three feet always reach the floor together because three points decide a flat surface — a fourth foot has to match a surface that was settled without it.

Try it yourself

Rock a wobbling chair, then turn it a quarter turn on the spot and try again. Often the wobble goes, because a different three feet are now doing the deciding.

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