The Is-It-A-Circle Question Given a finite set of points (say, around 15 points) in 3 dimensions, determine if those points all lie on a circle (to within a certain degree of accuracy). In general, you must come up with an algorithm for testing the points. The points may be completely and utterly noncircular in nature (in which case your algorithm should say “not a circle”), the points may be almost a circle but not quite, such as being bent out of shape by 20% or curved a little out of a plane (in which case your algorithm should still say “not a circle”) or it may be almost a perfect circle, in which case I very much hope your algorithm will say “yes a circle, thank you.” You should use linear algebra as part of the algorithm. In general, it is a good idea to split the problem into two parts: 1) try to put all the 3d points into a single 2D plane 2) given points in 2d, determine if those are all in a circle If you write an actual computer program, that would be awesome. At the very least, you will have to use some computer program (such as Matlab or Mathematica) to help out since otherwise it will be too much work to do by hand. I will give you a few sets of data points, and you must demonstrate that your algorithm correctly classifies each set.
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