Poncelet and the arquimedean twins
We give a sharp construction for twins in arbelos, based on polar reciprocity. In the process, new circles displaying arquimedean afinities came into scene.
math.MG↗
arXiv subjects
Liliana Gabriela Gheorghe
Publications and source records attributed to Liliana Gabriela Gheorghe.
Fine proprieties of Lemoine point and the inscribed conic
The center of an inscribed conic which have a given perspector is the complement of its isotomic conjugate. We provide a synthetic proof, based on fine proprieties of Lemoine point.
math.MG↗
When Euler (circle) meets Poncelet (Porism)
We describe all triangles that shares the same circumcircle and Euler circle. Although this two circles do not form a poristic pair of circles, we find a poristic circle "in-between" that enable to solve this problem using Poncelet porism.
math.MG↗
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 its boundary consists of two elliptic arcs and a point $P_0$. Interestingly, the conic passing through the four arc endpoints and by $P_0$ has a remarkable property: one of its foci is $M$. We provide a synthetic proof based on Poncelet's polar duality and inversive techniques. Additional intriguing properties of Reuleaux negative pedal are proved using straightforward techniques.
math.DS↗