The Stability of a Triangle
The three-legged stool/chair should have felt more stable than one with four legs
Why is a three-legged stool more sturdy?
It seems strange because you would think that more legs on a stool or chair would make it more sturdy or stable but in fact not!.
What geometry concept can be used to explain this?
The reason actually lies in the fact that it only takes three points to define a plane.
Any point that is added to that plane will make it harder and harder for the plane to be stable.
Here's a great activity to show this concept:
Your fingers will represent points and the paper will represent a plane.
- Take your thumb, index finger, and middle finger and try to put a piece of paper on top of them
- You should notice that any way you place your three fingers the paper will always uniquely lie on all three points.
- Now add a fourth finger by having a new person use their index finger as a new point.
- Notice how hard it is to exactly fit the paper on the plane.
Triangles are so sturdy/stable becuase they will always define a plane. no matter where the vertices of the triangle lie.
What are some real-life objects that use this knowledge to be more sturdy/stable?
- A tripod for a camera (Click here to see a photo of one)
- A tripod for a transit (this is an instrument surveyors use)
Move to the next section called "The rigidity of a triangle" to learn another neat fact about triangles.
Go to The Rigidity of a Triangle