Monday, July 20, 2009

functions - polynomials through points


A group of n arbitrary points on the x-y plane uniquely defines a polynomial function of degree n-1 (provided that no two points share the same x-value). While other sketches explore the curve's response to a change in parameters, this tactile picture offers what is probably a more aesthetic understanding of the nature of the curve. The math behind such a picture is a learning experience in itself, as it (perhaps unexpectedly) involves the calculation of inverse matrices. There are tools included to construct a cubic with four mouse-clicks and a parabola with three, and an additional version of each tool that includes the function equation.

Keywords: polynomial, cubic curve, parabola, line, function, regression, linear algebra, matrices, system of equations, inverse matrix

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