Stanley Rabinowitz

activity

20192026

collaborators

10 papers

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.HO2025

More Shapes of Central Quadrilaterals

Stanley Rabinowitz, Ercole Suppa

Let E be a point in the plane of a convex quadrilateral ABCD. The lines from E to the vertices of the quadrilateral form four triangles. If we locate a triangle center in each of t…

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…

math.HO2023

A Triad of Circles Associated with a Triangle

Ercole Suppa, Stanley Rabinowitz

We study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the c…

math.HO2023

Properties of Ajima Circles

Stanley Rabinowitz, Ercole Suppa

We study properties of certain circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the arc of a…

math.HO2019

Relationships Between Six Incircles

Stanley Rabinowitz

If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six smaller triangles. We give theorems about the relationship between the radii of the cir…