Triangle on Algebraic Curves (English)
Published in Christian-Albrechts-Universität zu Kiel Jugend Forscht, 2024
Given a conic section (ellipse, hyperbola, or parabola), consider three points on the curve where two points are fixed and the third varies along the conic. The triangle formed by these points changes continuously, and various notable triangle centers (e.g. circumcenter, orthocenter, incenter) trace distinct loci as the moving point traverses the conic. This study involves deriving the algebraic expressions for these loci and analyzing their geometric properties.
Recommended citation: Yimu Mao. (2023). "Dreieck auf dem algebraische Kurven."
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