Stanley Rabinowitz

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20192026

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math.GM2026

Average Chord Lengths in a Triangle

Stanley Rabinowitz

Let $P$ be a point inside a triangle $T$ . We consider the average length of the chords of $T$ through $P$ , where the direction of the chord is chosen uniformly. An elementary formu…

math.GM2026

The Probability That the Incenter of a Triangle Lies in a Random Diameter Disk

Stanley Rabinowitz

Let $P$ and $Q$ be independent points chosen uniformly from the interior of a nondegenerate triangle $A B C$ , and let $I$ be its incenter. We study the probability that the closed di…

math.GM2026

Perspective Central Triangles Formed from a Triangle and a Transversal

Stanley Rabinowitz, Ercole Suppa

Let $ℓ$ be a line not passing through any vertex of a triangle $A B C$ and not parallel to any side. Line $ℓ$ meets the sidelines $B C$ , $C A$ , $A B$ of $△ A B C$ at points…

math.GM2026

Natural Orderings of Triangle Centers

Stanley Rabinowitz

Triangle centers are usually studied individually or through special geometric relationships, but little attention has been given to global structure among them. In this paper we i…

math.GM2026

Some Geometric Properties of the Yff Points of a Triangle

Stanley Rabinowitz, Francisco Javier García Capitán

The Yff points of a triangle were introduced by Peter Yff in 1963. Since then, very few new facts have been discovered about these points. We present some geometrical properties of…

math.GM2025

More Relationships between a Central Quadrilateral and its Reference Quadrilateral

Stanley Rabinowitz, Ercole Suppa

The diagonals of a quadrilateral form four associated triangles, called half triangles. Each half triangle is bounded by two sides of the quadrilateral and one diagonal. If we loca…