3 ms·

I'd love to see a three-legged table stand up with the fourth corner under load.

kazinator 3y ago
It has a leg there; it's just called a three legged table, because one of the legs is geometrically implied by the other three.
- SamBam 3y ago
  Surely you only need two, as you could use two diagonal legs. Let's see if the name "two-legged table" takes off.
  - lupire 3y ago
    You only need 1 center leg.
- dylan604 3y ago
  my grandfather was a custom cabinet builder, and for whatever reason 4 legged tables were his absolute nemesis. i have the last remaining 3 legged table of his. it's a round table, so i thought the 3 legs were a design choice. that notion was corrected when my dad started laughing at remembering his dad's sheer frustration when he realized 3 of 4 table legs were the same length...on multiple occasions.
  - kazinator 3y ago
    Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor.
    - addaon 3y ago
      > Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor. Unless you're able to rotate it: https://www.scientificamerican.com/article/strange-but-true-turning https://www.scientificamerican.com/article/strange-but-true-...
      - TeMPOraL 3y ago
        Wish I'd be able to rotate my floor instead.
adrianmonk 3y ago
There are ways: (1) Diagonal legs that give the table a wide stance. Draw a triangle that the tabletop fits entirely inside of. The legs touch the ground at the vertices of the triangle. (2) Make the table itself arbitrarily heavy. A downward force on the corner of the tabletop will create torque around an axis, and this torque wants to tip it over. But the table's center of mass is on the other side of this axis, and the table's weight creates torque too. If the table's mass is high enough, this torque is greater, and it won't tip. (3) Screw the table to the floor. Is this a table? I think it's still a table. You often see tables attached to the floor. (4) Make one leg really wide so that it stretches from one corner to the other. The other two legs can be traditional.
- kazinator 3y ago
  The table + load will tip over if the center of mass is vertically outside of the convex polygon formed by the tips of the legs (in this case a triangle); i.e. the base of the object. Center of mass over base -> stable Center of mass outside base -> capsize

It has a leg there; it's just called a three legged table, because one of the legs is geometrically implied by the other three.

SamBam 3y ago
Surely you only need two, as you could use two diagonal legs. Let's see if the name "two-legged table" takes off.
- lupire 3y ago
  You only need 1 center leg.
dylan604 3y ago
my grandfather was a custom cabinet builder, and for whatever reason 4 legged tables were his absolute nemesis. i have the last remaining 3 legged table of his. it's a round table, so i thought the 3 legs were a design choice. that notion was corrected when my dad started laughing at remembering his dad's sheer frustration when he realized 3 of 4 table legs were the same length...on multiple occasions.
- kazinator 3y ago
  Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor.
  - addaon 3y ago
    > Even if a four legged table's legs are all perfectly equal so their tips lie in the same plane, that perfectly will be thwarted by an uneven floor. Unless you're able to rotate it: https://www.scientificamerican.com/article/strange-but-true-turning https://www.scientificamerican.com/article/strange-but-true-...
    - TeMPOraL 3y ago
      Wish I'd be able to rotate my floor instead.

adrianmonk 3y ago

There are ways: (1) Diagonal legs that give the table a wide stance. Draw a triangle that the tabletop fits entirely inside of. The legs touch the ground at the vertices of the triangle. (2) Make the table itself arbitrarily heavy. A downward force on the corner of the tabletop will create torque around an axis, and this torque wants to tip it over. But the table's center of mass is on the other side of this axis, and the table's weight creates torque too. If the table's mass is high enough, this torque is greater, and it won't tip. (3) Screw the table to the floor. Is this a table? I think it's still a table. You often see tables attached to the floor. (4) Make one leg really wide so that it stretches from one corner to the other. The other two legs can be traditional.

kazinator 3y ago
The table + load will tip over if the center of mass is vertically outside of the convex polygon formed by the tips of the legs (in this case a triangle); i.e. the base of the object. Center of mass over base -> stable Center of mass outside base -> capsize