Do Four Points Define a Hyperplane or Extend Beyond?

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Four points can define a hyperplane in four-dimensional space, but they do not necessarily define a three-dimensional plane if they are not coplanar. Similarly, three points can define a three-dimensional plane, but they may not always be collinear, meaning they do not necessarily define a line. The discussion highlights the importance of point arrangement in determining dimensionality. Understanding these relationships is crucial in geometry and higher-dimensional mathematics. The conversation emphasizes the nuances of point configuration in defining geometric structures.
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If three points make a plane? what does four make 1 also until you reach 6 how does that system work?
 
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Four points would define a hyperplane (literally, a 4-dimensional plane), but do not necessarily define a normal 3-dimensional plane -- they may not be coplanar.

In the same way, three points define a normal 3-dimensional plane, but do not necessarily define a line -- they may not be collinear.

- Warren
 

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