Yes, they do.
No. If the four points are coplanar, they determine only one plane!
Since the question is unfinished, I'll assume the most obvious completion: "planes." Yes, a triangular pyramid is composed of 4 non-co-planar points which form 4 intersecting planes.
space
Any 4 points can lie in a plane, 3 points determine a plane and just take the 4th to be say the origin.
In Newtonian three dimensional space, two points can create a line, three to "define" it. In Einsteins "time-space", a minimum of four points are required.
you cannot do this on the plane. try proving this yourself. but a regular tetrahedron in space for example is an example where there four points equidistant from each other.
The range of four probes gives you the material to test the probe. The best way to determine the optimum choice of the probe tip for specifications for a given material is the four points.
Follow ASTM-D698 A or ASTM-D1557 AorB for a modified proctor. Determine at leats four points at different moistire content and plot a curve.
No, they always are From Wikipedia.org, "The World's Encyclopedia" when I searched coplanar In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three distinct points are always coplanar; but four points in space are usually not coplanar. Since 3 points are always coplanar. A point and line are always coplanar
- If you're working on a single sheet of paper (2-D), then you can draw four lines that intersect in 1, 2, 3, 4, 5, or 6 points. - If in 3-D space, then you can also draw four lines that don't intersect at all.
They could need three dimensional space. Although points are 1-dimensional objects, it is easy to have four points that need 3-d space: for example the vertices of a tetrahedron (triangular pyramid). Similarly, skew line will need 3-d space.
As far as I know, four points is the norm in most states. States are, however, free to determine how many points they wish to assess for it, so it may vary between states.