Does any convex quadrilateral have circumscribed ellipses?

Open Mathematics (2017)

• Volume: 15, Issue: 1, page 1463-1476
• ISSN: 2391-5455

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Abstract

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The past decades have witnessed several well-known beautiful conclusions on four con-cyclic points. With highly promising research value, we profoundly studied circumscribed ellipses of convex quadrilaterals in this paper. Using tools of parallel projective transformation and analytic geometry, we derived several theorems including the proof of the existence of circumscribed ellipses of convex quadrilaterals, the properties of its minimal coverage area, and locus center, respectively. This simple approach lays a solid foundation for its application to three-dimensional situations, which is namely the circumscribed quadric surface of a solid figure and its wide-range utility in construction engineering. Meanwhile, we have a new insight into innate connection of conic sections as well as a taste of beauty and harmony of geometry.

How to cite

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Jia Hui Li, et al. "Does any convex quadrilateral have circumscribed ellipses?." Open Mathematics 15.1 (2017): 1463-1476. <http://eudml.org/doc/288515>.

@article{JiaHuiLi2017,
abstract = {The past decades have witnessed several well-known beautiful conclusions on four con-cyclic points. With highly promising research value, we profoundly studied circumscribed ellipses of convex quadrilaterals in this paper. Using tools of parallel projective transformation and analytic geometry, we derived several theorems including the proof of the existence of circumscribed ellipses of convex quadrilaterals, the properties of its minimal coverage area, and locus center, respectively. This simple approach lays a solid foundation for its application to three-dimensional situations, which is namely the circumscribed quadric surface of a solid figure and its wide-range utility in construction engineering. Meanwhile, we have a new insight into innate connection of conic sections as well as a taste of beauty and harmony of geometry.},
author = {Jia Hui Li, Zhuo Qun Wang, Yi Xi Shen, Zhong Yuan Dai},
journal = {Open Mathematics},
keywords = {Convex quadrilateral; Circumscribed ellipse; Parallel projective transformation; Analytical geometry; Conic section},
language = {eng},
number = {1},
pages = {1463-1476},
title = {Does any convex quadrilateral have circumscribed ellipses?},
url = {http://eudml.org/doc/288515},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Jia Hui Li
AU - Zhuo Qun Wang
AU - Yi Xi Shen
AU - Zhong Yuan Dai
TI - Does any convex quadrilateral have circumscribed ellipses?
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1463
EP - 1476
AB - The past decades have witnessed several well-known beautiful conclusions on four con-cyclic points. With highly promising research value, we profoundly studied circumscribed ellipses of convex quadrilaterals in this paper. Using tools of parallel projective transformation and analytic geometry, we derived several theorems including the proof of the existence of circumscribed ellipses of convex quadrilaterals, the properties of its minimal coverage area, and locus center, respectively. This simple approach lays a solid foundation for its application to three-dimensional situations, which is namely the circumscribed quadric surface of a solid figure and its wide-range utility in construction engineering. Meanwhile, we have a new insight into innate connection of conic sections as well as a taste of beauty and harmony of geometry.
LA - eng
KW - Convex quadrilateral; Circumscribed ellipse; Parallel projective transformation; Analytical geometry; Conic section
UR - http://eudml.org/doc/288515
ER -

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