John D. Cook • 4/16/2026

Newton diameters

This article discusses Newton's generalized definition of a diameter for algebraic curves, where a line crossing an nth-degree polynomial's zero set exactly n times is considered a diameter. It explains Newton's theorem that the centroids of intersections of parallel diameters lie on a line, illustrated with the elliptic curve y² = x³ − 2x + 1. The post includes references to Bézout's theorem and related mathematical concepts, aimed at readers interested in algebraic geometry and historical mathematical results.

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#mathematics #Geometry #Polynomials