2 papers
math.MG2026
Exparabolas of a Triangle
Martin Lukarevski, Hans-Peter Schröcker
Among a triangle's exparabolas (parabolas escribed to the triangle), three are distinguished by having locally maximal parameter. They are determined by a simple cubic equation and…
math.MG2026
Uniqueness of Maximal Inscribed Parabolas and Minimal Circumscribing Horocycles
Martin Lukarevski, Hans-Peter Schröcker
We prove existence of three unique ``max-exparabolas'' to a triangle. Each of these parabolas is internally tangent to one edge and the two other sides. Among all like parabolas, i…