Igor Minevich

activity

20122025

most citedVertex positions of the generalized orthocenter and a related elliptic curve

2 citations · 8 across the 10 of their papers we have counts for

collaborators

10 papers

math.AG2025

A quadrilateral half-turn theorem

Igor Minevich, Patrick Morton

If $A B C$ is a given triangle in the plane, $P$ is any point not on the extended sides of $A B C$ or its anticomplementary triangle, $Q$ is the complement of the isotomic conjugate of…

math.GM2017

Real elliptic curves and cevian geometry

Igor Minevich, Patrick Morton

We study the elliptic curve $E_{a} : (a x + 1) y^{2} + (a x + 1) (x - 1) y + x^{2} - x = 0$ , which we call the geometric normal form of an elliptic curve. We show that any elliptic curve whose $j$ -invariant…

math.MG2016★ 1 cited

Synthetic foundations of cevian geometry, IV: the TCC-perspector theorem

Igor Minevich, Patrick Morton

In this paper we give a completely synthetic proof of the TCC-perspector theorem, that the isogonal conjugate $γ (H)$ of the generalized orthocenter $H$ (defined in Part III of this…

math.HO2016

A cevian locus and the geometric construction of a special elliptic curve

Igor Minevich, Patrick Morton

In a previous paper we defined the circumconic of a triangle $A B C$ with respect to a point $P$ as the conic $C ~ = T_{P^{'}}^{- 1} (N_{P^{'}})$ , where $N_{P^{'}}$ is the $9$ -point conic fo…

math.MG2016★ 2 cited

Vertex positions of the generalized orthocenter and a related elliptic curve

Igor Minevich, Patrick Morton

We study triangles $A B C$ and points $P$ for which the generalized orthocenter $H$ corresponding to $P$ coincides with a vertex $A, B$ , or $C$ . The set of all such points $P$ is a un…

math.MG2015★ 1 cited

Synthetic foundations of cevian geometry, III: The generalized orthocenter

Igor Minevich, Patrick Morton

In this paper, the third in the series, we define the generalized orthocenter $H$ corresponding to a point $P$ , with respect to triangle $A B C$ , as the unique point for which the li…

math.MG2015★ 2 cited

Synthetic foundations of cevian geometry II: The center of the cevian conic

Igor Minevich, Patrick Morton

This paper continues the investigation of Part I, by studying the conic $C_{P}$ on the five points $A B C P Q$ , where $A B C$ is a given ordinary triangle and $Q$ is the isotomco…

math.GM2015★ 1 cited

Synthetic foundations of cevian geometry, I: Fixed points of affine maps in triangle geometry

Igor Minevich, Patrick Morton

We give synthetic proofs of many new results in triangle geometry, focusing especially on fixed points of certain affine maps which are defined in terms of the cevian triangle $DEF…

math.RA2012★ 1 cited

Symmetric Matrices over F_2 and the Lights Out Problem

Igor Minevich

We prove that the range of a symmetric matrix over F_2 contains the vector of its diagonal elements. We apply the theorem to a generalization of the "Lights Out" problem on graphs.

math.NT2012

Elliptic Curves with Supersingular Reduction over $Γ$ -extensions

Igor Minevich, Florian Sprung

This is a translation of a research announcement by Anas G. Nasybullin from 1976, in which he states formulas for the p-primary part of the Tate-Shafarevich group of an elliptic cu…

A quadrilateral half-turn theorem

Real elliptic curves and cevian geometry

Synthetic foundations of cevian geometry, IV: the TCC-perspector theorem

A cevian locus and the geometric construction of a special elliptic curve

Vertex positions of the generalized orthocenter and a related elliptic curve

Synthetic foundations of cevian geometry, III: The generalized orthocenter

Synthetic foundations of cevian geometry II: The center of the cevian conic

Synthetic foundations of cevian geometry, I: Fixed points of affine maps in triangle geometry

Symmetric Matrices over F_2 and the Lights Out Problem

Elliptic Curves with Supersingular Reduction over Γ-extensions

Elliptic Curves with Supersingular Reduction over $Γ$ -extensions