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02/05/2022
Exploring the Dynamics of the Circumcenter Map
Using experimental techniques, we study properties of the "circumcenter ...
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01/23/2022
Poncelet Spatio-Temporal Surfaces and Tangles
We explore geometric and topological properties of 3d surfaces swept by ...
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01/18/2022
The Wrought Iron Beauty of Poncelet Loci
We've built a web-based tool for the real-time interaction with loci of ...
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12/30/2021
Triads of Conics Associated with a Triangle
We revisit constructions based on triads of conics with foci at pairs of...
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12/05/2021
New Properties and Invariants of Harmonic Polygons
Via simulation, we discover and prove curious new Euclidean properties a...
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12/03/2021
A Web of Confocal Parabolas in a Grid of Hexagons
If one erects regular hexagons upon the sides of a triangle T, several s...
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11/01/2021
Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family
We study loci and properties of a Parabola-inscribed family of Poncelet ...
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10/26/2021
Cramer-Castillon on a Triangle's Incircle and Excircles
The Cramer-Castillon problem (CCP) consists in finding one or more polyg...
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10/12/2021
Poncelet Parabola Pirouettes
We describe some three-dozen curious phenomena manifested by parabolas i...
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08/11/2021
Loci of Poncelet Triangles with Multiple Caustics
We analyze loci of triangles centers over variants of two-well known tri...
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06/08/2021
An App for the Discovery of Properties of Poncelet Triangles
We describe a newly-developed, free, browser-based application, for the ...
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06/01/2021
A Theory for Locus Ellipticity of Poncelet 3-Periodic Centers
We present a theory which predicts when the locus of a triangle center i...
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04/27/2021
Poncelet Plectra: Harmonious Curves in Cosine Space
It has been shown that the family of Poncelet N-gons in the confocal pai...
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03/20/2021
New Invariants of Poncelet-Jacobi Bicentric Polygons
The 1d family of Poncelet polygons interscribed between two circles is k...
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02/18/2021
Invariant Center Power and Elliptic Loci of Poncelet Triangles
We study center power with respect to circles derived from Poncelet 3-pe...
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01/25/2021
Poncelet Propellers: Invariant Total Blade Area
Given a triangle, a trio of circumellipses can be defined, each centered...
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12/21/2020
Family Ties: Relating Poncelet 3-Periodics by their Properties
We study the dynamic geometry, loci, and invariants of three Poncelet fa...
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11/12/2020
Invariants of Self-Intersected N-Periodics in the Elliptic Billiard
We study self-intersected N-periodics in the elliptic billiard, describi...
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10/19/2020
Intriguing Invariants of Centers of Ellipse-Inscribed Triangles
We describe invariants of centers of ellipse-inscribed triangle families...
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10/03/2020
An Infinite, Converging, Sequence of Brocard Porisms
The Brocard porism is a known 1d family of triangles inscribed in a circ...
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09/18/2020
Loci of the Brocard Points over Selected Triangle Families
We study the loci of the Brocard points over two selected families of tr...
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09/16/2020
Related by Similarity II: Poncelet 3-Periodics in the Homothetic Pair and the Brocard Porism
Previously we showed the family of 3-periodics in the elliptic billiard ...
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09/05/2020
Area-Invariant Pedal-Like Curves Derived from the Ellipse
We study six pedal-like curves associated with the ellipse which are are...
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08/20/2020
A Special Conic Associated with the Reuleaux Negative Pedal Curve
The Negative Pedal Curve of the Reuleaux Triangle w.r. to a point M on i...
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06/23/2020
Steiner's Hat: a Constant-Area Deltoid Associated with the Ellipse
The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary...
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06/23/2020
A Family of Constant-Area Deltoids Associated with the Ellipse
The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary...
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06/23/2020
A Family of Constant-Areas Deltoids Associated with the Ellipse
The Negative Pedal Curve (NPC) of the Ellipse with respect to a boundary...
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04/28/2020
Related by Similiarity: Poristic Triangles and 3-Periodics in the Elliptic Billiard
Discovered by William Chapple in 1746, the Poristic family is a set of v...
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04/26/2020
Seventy New Invariants of N-Periodics in the Elliptic Billiard
We introduce 70 experimentally-found invariants of Poncelet N-periodics ...
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04/14/2020
The Circumbilliard: Any Triangle can be a 3-Periodic
A Circumconic passes through a triangle's vertices. We define the Circum...
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04/06/2020
Circum- and Inconic Invariants of 3-Periodics in the Elliptic Billiard
A Circumconic passes through a triangle's vertices; an Inconic is tangen...
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04/06/2020
Circuminvariants of 3-Periodics in the Elliptic Billiard
A Circumconic passes through a triangle's vertices; an Inconic is tangen...
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01/30/2020
The Ballet of Triangle Centers on the Elliptic Billiard
The dynamic geometry of the family of 3-periodics in the Elliptic Billia...
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01/30/2020
Loci of 3-Periodics in an Elliptic Billiard: Intriguing Phenomena
We analyze the family of 3-periodic (triangular) trajectories in an Elli...
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01/22/2020
New Properties of Triangular Orbits in Elliptic Billiards
In this paper we present invariants of the 1d family of 3-periodics (tri...
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01/22/2020
Loci of 3-periodics in an Elliptic Billiard: why so many ellipses?
We analyze the family of 3-periodic (triangular) trajectories in an Elli...
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01/22/2020
Loci of Triangular Orbits in an Elliptic Billiard: Elliptic? Algebraic?
We analyze the family of 3-periodic (triangular) trajectories in an Elli...
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01/22/2020
Loci of Triangular Orbits in an Elliptic Billiard
We analyze the family of 3-periodic trajectories in an Elliptic Billiard...
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11/04/2019
