Four Theorems with Their Foci on Ellipses

DOI10.1080/00029890.2019.1537459zbMath1410.51029OpenAlexW2914812699WikidataQ128421034 ScholiaQ128421034MaRDI QIDQ3120220

Pamela Gorkin

Publication date: 1 March 2019

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2019.1537459

zbMATH Keywords

Poncelet's theoremelliptical range theoremBlaschke ellipse theoremSiebeck's theorem

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Real and complex geometry (51M99) Blaschke products (30J10)

Related Items (3)

Poncelet-Darboux, Kippenhahn, and Szegő: interactions between projective geometry, matrices and orthogonal polynomials ⋮ Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators ⋮ Matricial Proofs of Some Classical Results about Critical Point Location

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the numerical range of a bounded operator
• Numerical range and Poncelet property.
• Numerical ranges and Poncelet curves
• Numerical range circumscribed by two polygons
• UB-matrices and conditions for Poncelet polygon to be closed
• Numerical range of a normal compression. II
• Polygons and Numerical Ranges
• A Simple Direct Proof of Marden's Theorem
• A Conjectured Analogue of Rolle's Theorem for Polynomials with Real or Complex Coefficients
• Another Application of Siebeck's Theorem
• Triangles, Ellipses, and Cubic Polynomials
• A Simple Proof of Poncelet's Theorem (on the Occasion of Its Bicentennial)
• An Elementary Proof of Marden's Theorem
• How Conics Govern Mobius Transformations
• Solving the Ladder Problem on the Back of an Envelope
• Numerical range ofs(φ)
• Lucas' theorem refined^∗
• Three Problems in Search of a Measure
• Ellipses and Finite Blaschke Products
• A Geometric Proof of the Siebeck–Marden Theorem
• Numerical Range of a Normal Compression
• A simple proof of the elliptical range theorem
• Sendov conjecture for high degree polynomials
• On the numerical range of a matrix
• A Generalization of a Theorem of Bôcher
• The Toeplitz-Hausdorff Theorem Explained
• On Compressions of Matrices
• A note on the zeros of the sections of a partial fraction
• Numerical ranges, Poncelet curves, invariant measures
• On compressions of normal matrices

This page was built for publication: Four Theorems with Their Foci on Ellipses