In the above title 10 and 1000 are arbitrary numbers I will use them below to signify the concept of a smaller and larger number. I know that n points are described by at most an x^(n-1) polynomial. What I really mean to ask is: Is it possible to take a "smaller" amount of points say 10, go through a series of transformations, turn them into a "larger" number of points, say 1000, so that the larger number of points all lie on a line described by a polynomial with a degree less than the degree of the polynomial that describes the 10 points? Assume that the 10 points are described by a 10-1 = 9 degree polynomial. I would then want to take my new polynomial (along with some meta data) and derive the original 10 points. Is any of this possible? Any recommended resources to get me started or point me in the right direction? Note this is just for fun and not any sort of homework or test problem so it may just be impossible.