🚀 go-pugleaf

In article <311F9C84.3B26@structure.chimie.usherb.ca>,
Paul Rowntree  <rowntree@structure.chimie.usherb.ca> wrote:
>Christopher H. Clark wrote:
>> 
>> Jonathan Cohen wrote:
>> >
>> > In article <3118310E.52F@psu.edu>, Christopher H. Clark <chc104@psu.edu> wrote:
>> > >Actually, you only need 2 points to define a plane: a point on the plane and
>> > >a normal vector.
>> >
>> > Sorry to quibble, but...
>> >
>> >    A VECTOR IS NOT A POINT!!!!
>> >
>> > Now back to our regular program.
>> 
>> Points are vectors.
>> ^^^^^^^^^^^^^^^^^^
>
>Sorry, but I must take offense here.  A point in Cartesian space has three 
>aspects [X,Y,Z].  A vector requires a direction, and depending on how sticky you 
>are, probably a length.  This implies 6 independent aspects.  Result;  A plane 
>requires 3 points.  Always.
>
>Cheers

Note that while I objected to the original poster's terminology, the
fact remains that a six-tuple of numbers is enough to define a plane,
while three individual points require a nine-tuple of numbers to
represents.  Thus, the 3 points contain some information in addition to
what plane they define.

So... if you want to describe a plane using points, it requires 3
points, but a point on a plane plus a normal vector also define a plane,
using less information.

Jon