Jawad Sadek, Isogonal conjugates in an n-simplex,
Forum Geometricorum, 17 (2017) 425--432.
Abstract. As "one of the crown jewels of modern geometry", the symmedian point is not well known by mathematicians or mathematics educators. Locating a person in space without a GPS, or analysing data for a harbor mine-detecting algorithm are but some of the more recent applications to the symmedian point. In this article, we extend the notions of the symmedian point and isogonal conjugates to n-simplexes. Unlike another attempt, our generalisation preserves all the interesting properties of the symmedian point of a triangle. Also, its connection to the least squares point of a simplex is shown. In addition, the symmedian point is given in terms of a simple formula in barycentric coordinates.
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