Noncoplanar: is it possible to draw three points that are...

[ammond30]

Is it possible to draw three points that are noncoplanar?

My guess is no but I don't know how to explain.

Thanks

 

[stapel]

A related question: Is it possible to construct a three-legged stool, such that one of the legs cannot touch the floor?

(We're only considering the legs and the floor; we don't care if the stool is useless for sitting on. :wink

Now think of three points (the ends of the legs) and planes (the floor)....

Eliz.

 

[tkhunny]

Three points define a unique plane.

If you pick a plane BEFORE you pick the points, that is a different matter.

 

[ammond30]

So, using the example of the stool I am guessing that it is possible to draw three points that are noncoplanar, if you have more than one plan?!

I'm I right?

 

[stapel]

Are you picking the plane, and then seeing if the three points lie in it? Or are you picking any three points, and then seeing if any plane passes through them?

Think about the stool: If you set the stool down, but then say "No, I meant that wall, not this floor, for my plane", then the legs -- points -- don't lie in your chosen plane. But if you design the stool any higgelty-piggelty way you like, will there ever be a flat floor on which you can not rest the legs?

Eliz.

 

[ammond30]

Eliz,

This is my first experience with geometry, and now i am really confused, the question in the text book is; Is it possible to draw three points that are noncoplanar? Explain.

This is the only thing that has me stumped.

 

[tkhunny]

Three points DEFINE a unique plane.

If you pick a plane BEFORE you pick the points, that is a different matter.