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This article looks at several geometric, straightedge-and-compass constructions for trisecting a line segment, comparing them based on the numbers of lines or circles required for the construction.
Marden's Theorem concerns the relative positions of the roots of a cubic polynomial and those of its derivative. This article gives a proof of Marden's theorem, along with dynamic geometry animations and some of the history of the result.
This article explores the symmetry method in elementary differential equations, which uses the invariance of the equation under certain transformations to create a coordinate system in which the equation greatly simplifies.