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Q: How many points are needed to define a plane?

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To create a plane, infinitely many. But to uniquely define one, 3 are enough.

zero

Three collinear points don't define a plane."Define" means narrow it down to one and only one unique plane, so that it can't be confused with any other one.There are many different planes (actually infinite) that can contain three collinear points, so no unique plane is defined.

Any Euclidean plane has infinitely many points.

In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!

Related questions

Three.

4 points define a plane.

To create a plane, infinitely many. But to uniquely define one, 3 are enough.

Three

2

They define one plane. A line is defined by two points, and it takes three points to define a plane, so two points on the line, and one more point not on the line equals one plane.

It takes three points to make a plane. The points need to be non-co-linear. These three points define a distinct plane, but the plane can be made up of an infinite set of points.

zero

Two.

A minimum of three points are required to define a plne (if they are not collinear). And in projective geometry you can have a plane with only 3 points. Boring, but true. In normal circumstances, a plane will have infinitely many points. Not only that, there are infinitely many in the tiniest portion of the plane.

A minimum of three points are required to define a plne (if they are not collinear). And in projective geometry you can have a plane with only 3 points. Boring, but true. In normal circumstances, a plane will have infinitely many points. Not only that, there are infinitely many in the tiniest portion of the plane.

A plane can be determined by three points, as long as the three points do not lie along a single line.

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