# Parallelograms inscribed in a curve having a circle as π/2-isoptic

Annales UMCS, Mathematica (2008)

- Volume: 62, Issue: 1, page 105-111
- ISSN: 2083-7402

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topAndrzej Miernowski. "Parallelograms inscribed in a curve having a circle as π/2-isoptic." Annales UMCS, Mathematica 62.1 (2008): 105-111. <http://eudml.org/doc/268006>.

@article{AndrzejMiernowski2008,

abstract = {Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.},

author = {Andrzej Miernowski},

journal = {Annales UMCS, Mathematica},

keywords = {Convex curve; support function; curvature; convex curve},

language = {eng},

number = {1},

pages = {105-111},

title = {Parallelograms inscribed in a curve having a circle as π/2-isoptic},

url = {http://eudml.org/doc/268006},

volume = {62},

year = {2008},

}

TY - JOUR

AU - Andrzej Miernowski

TI - Parallelograms inscribed in a curve having a circle as π/2-isoptic

JO - Annales UMCS, Mathematica

PY - 2008

VL - 62

IS - 1

SP - 105

EP - 111

AB - Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.

LA - eng

KW - Convex curve; support function; curvature; convex curve

UR - http://eudml.org/doc/268006

ER -

## References

top- Berger, M., Geometrie, Vol. 2, Nathan, Paris, 1990.
- Cieślak, W., Miernowski, A. and Mozgawa, W., Isoptics of a strictly convex curve, Global Differential Geometry and Global Analysis, 1990 (Berlin), Lecture Notes in Math., 1481, Springer, Berlin, 1991, 28-35. Zbl0739.53001
- Cieślak, W., Miernowski, A. and Mozgawa, W., Isoptics of a strictly convex curve II, Rend. Sem. Mat. Univ. Padova 96 (1996), 37-49. Zbl0881.53003
- Connes, A., Zagier, D., A property of parallelograms inscribed in ellipses, Amer. Math. Monthly 114 (2007), 909-914. Zbl1140.51010
- Green, J. W., Sets subtending a constant angle on a circle, Duke Math. J. 17 (1950), 263-267. Zbl0039.18201
- Matsuura, S., On nonconvex curves of constant angle, Functional analysis and related topics, 1991 (Kyoto), Lecture Notes in Math., 1540, Springer, Berlin, 1993, 251-268.
- Richard, J-M., Safe domain and elementary geometry, Eur. J. Phys. 25 (2004), 835-844.[Crossref] Zbl1162.70320
- Wunderlich, W., Kurven mit isoptischem Kreis, Aequationes Math. 6 (1971), 71-78. Zbl0215.50103

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