Why would a 3 legged stool can stand and a 4 legged stool can woggle?

Long answer short: 3 points always make a plane (and a circle but that's of no concern here).

4 points are not as likely to form a flat plane. 3 are a guarantee.

For something that has no actual means of balance, such as a human, an object with three points of contact can stand. It is difficult to make a 3 leg stool wobble because at least three points need to be in contact with the ground for it to stand unless balanced.

Consider a 4 legged stool now. The legs typically form a square on the ground, or a rectangle. This results in straight lines. If the ground is curved, one of the 4 legs may not be in contact. You may even get into a situation where it totters back and forth with only two legs ALWAYS in contact, and one of the other 2 in contact at any given point. However, for it to remain still without being balanced, 3 of the 4 legs must touch.

So why make 4 leg stools? On a flat surface, you are less likely to tip a stool with 4 legs than a stool with 3. On an uneven stuface, you may be better off with 3.

3 Leg Stool

Cost per leg of 4-legged stools = $20/4 = $5 Cost per leg of 3-legged stools = $15/3 = $5 Therefore, the cost of all the stools is 108*$5 = $540

Because all it takes is for 1 leg to be shorter on the 4 legged stool and you instantly have a wobble.

On the 3 legger, all 3 legs are necessary for operation, always having weight/pressure on them, not allowing for a wobble.

One more reason why 3 is a great number.

III

A stool must have at least 3 points of contact on the ground at all times. On a 4-legged stool, the third point on contact can change from the third to the fourth leg, causing the stool to wobble.

Beause 3 is the least number of legs you need to make a stand balance, and it must use all 3 to balance.

When you have 4, it will rely on the least number of legs to balance which is 3. So if one is not the correct length it will wiggle between the least number depending up on the shift of weight on top of them.

David

cuz the 4legged can walk ......:S

or because with the odd number you have the right support 1 in the center 2 off to the side