Geometry Question

[Student558]

How many unique planes can be determined by four noncoplanar points? I keep looking this up but to no avail, there seems to be no answer that I can find. Is there anyone out there who could help answer this?
Thanks, Student558

 

[Dr.Peterson]

How many unique planes can be determined by four noncoplanar points? I keep looking this up but to no avail, there seems to be no answer that I can find. Is there anyone out there who could help answer this?
Thanks, Student558

Well, rather than looking it up, can you think about it yourself? What thoughts do you have?

How many points does it take to determine a plane? How many ways are there to select that many points from the 4 you have?

 

[Student558]

It takes 3 to determine a plane, right? So, 12 ways?

 

[Student558]

I was earlier thinking four planes...I am not sure...

 

[Dr.Peterson]

It takes 3 to determine a plane, right? So, 12 ways?

Are you saying there are 12 combinations of 3 out of 4 points?

I was earlier thinking four planes...I am not sure...

That could be a good thought; what led to it?

One way to think is that when you choose three points to form a plane, you are choosing one point to exclude ...

 

[HallsofIvy]

This not so much a "geometry" problem as it is a "combinations" problem. There are 4 given points and any three will determine a plane. How many sets of three objects can be chosen from a set of four?