scholarly journals Poncelet polygons in higher space

1920 ◽  
Vol 26 (6) ◽  
pp. 274-276
Author(s):  
Albert A. Bennett
Keyword(s):  
Poncelet Polygons

scholarly journals Caustics of Poncelet Polygons and Classical Extremal Polynomials

2019 ◽  
Vol 24 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Vladimir Dragović ◽  
Milena Radnović
Keyword(s):  
Extremal Polynomials ◽  
Poncelet Polygons

scholarly journals On partial isometries with circular numerical range

2021 ◽  
Vol 8 (1) ◽  
pp. 176-186
Author(s):  
Elias Wegert ◽  
Ilya Spitkovsky
Keyword(s):  
Blaschke Product ◽  
Partial Isometry ◽  
Shift Operator ◽  
Numerical Range ◽  
Elliptic Functions ◽  
Blaschke Products ◽  
Partial Isometries ◽  
Unitary Similarity ◽  
Boundary Interpolation ◽  
Poncelet Polygons

Abstract In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂ n cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n. The proof is based on the unitary similarity of A to a compressed shift operator SB generated by a finite Blaschke product B. We then use the description of the numerical range of SB as intersection of Poncelet polygons, a special representation of Blaschke products related to boundary interpolation, and an explicit formula for the barycenter of the vertices of Poncelet polygons involving elliptic functions.

scholarly journals Centers of Mass of Poncelet Polygons, 200 Years After

2016 ◽  
Vol 38 (2) ◽  
pp. 29-34 ◽  
Author(s):  
Richard Schwartz ◽  
Sergei Tabachnikov
Keyword(s):  
Poncelet Polygons ◽  
Centers Of Mass

Poncelet Polygons

2008 ◽  
pp. 1-7
Author(s):  
O. Bottema ◽  
Reinie Erne
Keyword(s):  
Poncelet Polygons

Modular curves and Poncelet polygons

1993 ◽  
Vol 295 (1) ◽  
pp. 25-49 ◽  
Author(s):  
W. Barth ◽  
J. Michel
Keyword(s):  
Modular Curves ◽  
Poncelet Polygons

PONCELET POLYGONS

Science ◽  
1916 ◽  
Vol 43 (1101) ◽  
pp. 149-158 ◽  
Author(s):  
H. S. White
Keyword(s):  
Poncelet Polygons
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