Three Random Tangents to a Circle
Steven R. Finch
TL;DR
This paper investigates properties of random triangles circumscribing a circle, including side density and median calculations, highlighting open problems in perimeter density analysis.
Contribution
It provides the first known calculation of side density and median for random circumscribed triangles, advancing geometric probability understanding.
Findings
Side density for random circumscribed triangles calculated
Median side length found to be approximately 5.5482
Perimeter density remains an open problem
Abstract
Among several things, we find the side density for random triangles circumscribing the unit circle and calculate that its median is 5.5482.... An analogous exact computation for perimeter density remains open.
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Taxonomy
TopicsMorphological variations and asymmetry · Point processes and geometric inequalities · Mathematics and Applications