Algebra in the Service of Geometry: Can Euler's Line Be Parallel to a Side of a Triangle?

  • Algebra in the Service of Geometry: Can Euler's Line Be Parallel to a Side of a Triangle?

    Damon Diemente
    This investigation of Euler's line has become a regular and valued unit in my honors-geometry syllabus. It originated with an intelligent question from a curious student. Its geometric foundation comprises sophisticated Euclidean triangle geometry. Its solution requires plentiful but not excessively complicated algebra. It culminates in the discovery of a conic locus that can be verified by construction on a computer screen.